An ant stands atop a grassy hill looking at a castle. A horizontal bridge 20 feet long crosses the gap, forming a right angle with the castle wall. The hill slopes down to a moat (water) that is 10 feet wide. The moat has 0 alligators because this is a math problem, not Louisiana. The castle is 38 feet tall, measuring from moat to roof.

a) Draw a sketch showing all the information you have right now.

b) The angle of elevation from the ant to the castle roof is 54.5°. Find the height of the castle above the bridge to the nearest foot (whole number).

c) What is the distance of the vertical drop from the bridge into the moat?

d) Find the angle between the hillside and the underside of the bridge. You may assume that the hill's slope is perfectly straight.

Step-by-step explanation:

Given formula

an = n² + 4

Now the first four terms of the sequence are

a1 = 1² + 4 = 5

a2 = 2² + 4 = 4 + 4 = 8

a3 = 3² + 4 = 9 + 4 = 13

a4 = 4² + 4 = 16 + 4 = 20

The terms are

5 , 8 , 13 and 20.

The expected value of the spinner landing on pink will be 18.

The anticipated value is an extension of the weighting factor in statistical inference. Informally, the anticipated value is the simple average of a significant number of outcomes of a randomly selected variable that was separately chosen.

The expected value is given below.

E(x) = np

Where n is the number of samples and p is the probability.

If Kelly spins the spinner 120 times. The table is given below.

Color      Frequency

Pink               6

Purple          12

Yellow          9

Blue             13

Total           40

Then the probability of the pink color will be

p = 6 / 40

p = 0.15

Then the expected value of the spinner landing on pink will be

E(x) = 120 x 0.15

E(x) = 18

The expected value of the spinner landing on pink will be 18.

More about the expected value link is given below.

https://brainly.com/question/13945225

#SPJ2

Step-by-step explanation and Answer :)

So we can split this shape into a few easier shapes to solve the area!

There are multiple combinations:

rectangle, triangle, and another rectangle

rectangle, trapezium

The second option is faster so lets use that :)

[tex]187m^{2}[/tex]

You should draw a dotted line across the top of the rectangle so now there is a rectangle on the bottom and a trapezium on the top!

[tex]A_{square} = b * h\\A_{square} = 16 * 6\\A_{square} = 96m^{2} \\\\\\A_{trap} = \frac{(a + b)h}{2}\\[/tex]

[tex]A_{trap} = \frac{(10 + 16)7}{2}\\\\A_{trap} = \frac{(182)}{2}\\\\A_{trap} = 91 m^{2}[/tex]

96 + 91 = [tex]187m^{2}[/tex]

Hope this helps!

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Answer:

4.5

Step-by-step explanation:

Its asking if y was six what would x be. Then you get n.

Answer: 335

Step-by-step explanation:

20% = 0.2

450 x .2 = 90

450 - 90 = 360

360 - 25 = 335

Answer:

3.6

Step-by-step explanation:

The average of 9 scores is x.

average = (sum of scores)/(number of scores)

x = (sum of scores)/9

sum of scores = 9x

The sum of the 9 scores is 9x.

The tenth score is 36 more than x, so it is x + 36.

The sum of the 10 scores is 9x + x + 36 = 10x + 36.

The average of the 10 scores is (10x + 36)/10 = x + 3.6

The difference of averages is

x + 3.6 - x = 3.6

Answer:

Lin ran at 2.9 meters per second. She can run 174 meters in a minute (2.9 times 60)

Step-by-step explanation:

If she can run 2.9 meters in a second then when you times that by four you get how far she can run in a minute

Step-by-step explanation:

[tex] \frac{15}{100} \times 250 = 37.50 + 93.30 = 130.80[/tex]

Answer:

72km/h

Step-by-step explanation:

the formula of changing metres per second to km/h is 18/5 and kilometre per hour into metres per second is 5/8 in hope it helps.

Answer:

B. -6 and 3

Step-by-step explanation:

2x^2+6x-36=0

(x+6)(x-3)=0

Solve x+6=0 x-3=0

Answer:

No thanks

Step-by-step explanation:

Answer:

sure what up?

Step-by-step explanation:

Answer:

false

Step-by-step explanation

Answer:

w = 68.84

Step-by-step explanation:

cross-multiply:

95w = 6540

w = 6540/95

Answer:7

Step-by-step explanation:

Start out by finding the area of the square.

a = 4²

a = 16

Since all we have to look at is 1/4 of this square, multiply the area by 1/4.

(16)1/4

4

The area of the triangle is 4.

Now we need the area of the circle.

a = πr²

Sub: a = π(2)²

a = π(4)

Since the portion of the circle that covers the triangle is 1/4 of the circle, subtract 1/4 of the area of the circle from the area of the circle.

a = 4 - 1/4(π(4))

a = 4 - 1/4π x 1

a = 4 - 1/4π

Now this is where it's supposed to go, considering the fact that π isn't given a value.

Normally, I'd use 3.14 for π, as the entire population would, and then it would be easy, but obviously that isn't an option.

Now this answer isn't up there, so my best option is to tell you it's most likely c, and I hope I'm right.

Uhh good luck I guess this math test is weird

-Xax

Answer:

D or an F depends on the grading system

Step-by-step explanation:

Answer:

6 2/3.. i think

Step-by-step explanation:

hopefully u understand my messy handwriting

Answer:

1024(0.50)^x

Step-by-step explanation:

Initial value = 1024

Players eliminated per round =half = 50% of players in the round

Using the relation :

A(x) = P(1 - r)^x (decreasing hence, negative)

A(x) = 1024(1 - 50%) ^x

A(x) = 1024(1 - 0.50)^x

A(x) = 1024(0.50)^x

A mortgage loan is termed as a loan that is used to purchase or maintain a home, land or other pieces of real estate.

The borrower agrees to repay the amount of loan to the lender over a period of time, usually in a series of regular installments divided into principal and interest. The property is used as security for the loan.

Calculation of the amount of mortgage is as follows:

[tex]\text{Interest}= \text{Mortgage amount} \times\frac{0.05}{12}\times3[/tex] = 1875

[tex]\text{Principal Pay }= 1000 \times3[/tex] = 3000

Total amount paid = Interest + principal pay = 1875 + 3000 = 4875

Initial balance = 150000

The remaining balance for the mortgage amount = initial balance - the total amount paid.

Amount of mortgage = $ 145125.

Therefore the closest to the mortgage balance after 3 months of payments is

(1) $145,165.

To know more about the calculation of the mortgage amount, refer to the link below:

https://brainly.com/question/24913140

Answer:

39

Step-by-step explanation:

1:4:4

13:52:52

52-13 = 39

Answer:

c

a

Step-by-step explanation:

Answer:

5. is C which is 9.

6. is B which is 37.

Step-by-step explanation:

The first on is C. 9 because to find the interquartile range you need to subtract the upper quartile range by the lower quartile range. The upper is 16 and the lower is 7 so you do 16-7 which is 9.

The last question is B. 37 because the lower quartile range is first line in the box plot which is 37.

Answer:

Nope

Step-by-step explanation:

If they did, school wouldn't be a thing and I would be living in the Marvel universe lol

Answer:

-16

Step-by-step explanation:

Answer:

angle wet and angle vet are equal because et bisects wev.

angle wet=angle vet

48°=3x+9

48-9=3x

39=3x

39/3=x

13=x

Answer:

21sq

Step-by-step explanation:

multiply the l times the w which would be 3x7 and get 21.

Answer:

21 cm

Step-by-step explanation:

Answer:

add them together

Step-by-step explanation: