Cape Hatteras Lighthouse was built in 1870 and rises 208 feet above sea level. From the top of the lighthouse, the lighthouse keeper observes two ships along the same line of sight. The angle of depression to ship 1 is 20  and the angle of depression to ship 2 is 12.5  . For safety purposes, the keeper thinks the two ships should be at least 300 feet apart. If they are less than 300 feet apart, she will sound a warning. How far apart are the vessels? Will she sound the warning?

Answer: Approximately 33 feet

Step-by-step explanation: Please refer to the attched diagram.

The 20ft ladder is placed on the wall at an agle of 85° with the ground.

If the person on the ladder were to lean back and fall to the ground (rotating the ladder away from the wall), then the distance he would have covered before he hits the ground is depicted by the arc as shown in the diagram. The ladder upon touching the ground would remain the same, which is 20 feet. So what the question requires is the length of the arc made during the fall, and the length of the ladder both on the wall an on the floor would be the radius (20 ft) while the angle subtended by the arc is 95° ( angles on a straight line equals 180, that is 85 + 95 = 180)

Therefore the length of an arc is given as;

Length of arc = (∅/360) x 2πr

Where ∅ = 95 and r = 95

Length of arc = (95/360) x 2 x 3.14 x 20

Length of arc = (19/72) x 125.6

Length of arc = 2386.4/72

Length of arc = 33.1444

Length of arc ≈ 33 feet (To the nearest foot)

The person on the ladder would have travelled approximately 33 feet before he/she hits the ground.

The person falls a distance of approximately 19.924 feet.

In this question, we must determine the vertical distance travelled by the person ([tex]y[/tex]), in feet. Let consider that the ladder is set between a horizontal ground and a vertical wall.

Then, the vertical distance is determined by the following trigonometric expression:

[tex]y = l\cdot \sin\theta[/tex] (1)

Where:

If we know that [tex]l = 20\,ft[/tex] and [tex]\theta = 85^{\circ}[/tex], then the vertical distance travalled by the person:

[tex]y = (20\,ft)\cdot \sin 85^{\circ}[/tex]

[tex]y \approx 19.924\,ft[/tex]

The person falls a distance of approximately 19.924 feet.

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Answer:

(a)25% of 100 < 75% of 100

(b)25% of -100 > 75% of -100

Step-by-step explanation:

If Lillian says that 25% of a number will always be less than 75% of any other number.

We are required to complete two inequality one of which supports and the other refutes the statement.

Support

Let our number be 100

25% of 100 < 75% of 100

25<100

This is true.

Refute

Let our number be -100

25% of -100 > 75% of -100

-25>-100

Therefore, for negative numbers, the inequality will not be true as:

-25>-100.

Answer:

x = 0, 2π/3, 4π/3

Step-by-step explanation:

2 cos(2x) − 2 cos x = 0

Use double angle formula.

2 (2 cos²x − 1) − 2 cos x = 0

Simplify.

4 cos²x − 2 − 2 cos x = 0

2 cos²x − 1 − cos x = 0

2 cos²x − cos x − 1 = 0

Factor.

(cos x − 1) (2 cos x + 1) = 0

Solve.

cos x = 1 or -½

x = 0, 2π/3, 4π/3

To solve this problem, we have to use trigonometric function in which we can use some trigonometric equations on this. The solutions to this equation is

[tex]\pi , \frac{\pi}{3}, \frac{5\pi}{3}[/tex]

We would apply a simple mathematical rule here;

[tex]a(b+c)=ab+ac[/tex]

Let's substitute our functions and solve

[tex]2cos(2x)+2cosx=0\\2(2cos^2x-1)+2cosx=0\\4cos^2x-2+2cosx=0\\2cos^2x+cosx-1=0\\2cos^2x=2cosx-cosx-1=0\\2cos^2x+cosx-1=0\\[/tex]

We can solve the quadratic equation and get a solution to this problem.

[tex](cosx+1)(2cosx-1)=0[/tex]

Using factorization method,

[tex]cosx+1 = 0\\cosx = -1\\x = cos^-^1(-1)\\x = \pi[/tex]

The second solution is

[tex]2cosx-1=0\\2cosx=1\\cosx=\frac{1}{2} \\x = cos^-^1(\frac{1}{2} \\x = \frac{\pi}{3}, \frac{5\pi}{3}[/tex]

From the above calculations, the solutions to this equation is

[tex]\pi , \frac{\pi}{3}, \frac{5\pi}{3}[/tex]

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Answer:

B

Step-by-step explanation:

Step-by-step explanation:

Given

6x² + 5x + 1

= 6x² + ( 2 + 3)x + 1

= 6x² + 2x + 3x + 1

= 2x ( 3x + 1 ) + 1 ( 3x + 1)

= ( 3x + 1) ( 2x +1)

Hope it will help :)

Answer: 4ft too the 2 power

Step-by-step explanation:

Answer:

2

Step-by-step explanat

Answer:The answer is 50

Step-by-step explanation:

The first step is to add up the numbers in order to get the outcome

5 red + 20 blue +25 green =5+20+25 =50

Step 2

Probability =no of events /no of outcome

We were asked to find the probability of red

Where red represent event

And the summation of red ,green and blue represents outcome .

So probability of red =5/50 = 1/10

Step 3

Recall in the question ,we were told that the card was selected 500 times ,so we multiply the probability of getting red by 500

1/10 *500 =50

Therefore the probability of drawing a red card from the special deck 500 times is 50 .

Answer:

The amount of payment that needs to be applied to the debt balance to bring the debt to limit ratio to 15% is $2,250

Step-by-step explanation:

Here we have the card limit as $3,000

The card debit to limit ratio should be kept below 15%

Therefore, card limit of $3,000 = 100%

The protect FICA score card debt to limit ratio required required is 15% that is;

Maximum appropriate card debt is 15% of Max allowable card debt

Maximum appropriate card debt  = 15% of $3,000 = $450.00

Current debt on card = $3,000

Payment to be applied to the balance to pay it down to 15% is given by

[tex]\$3,000 - \frac{15}{100} \times \$3000 = \$3,000 - \$450 = \$2550[/tex]

Therefore a $2,550 payment will be applied to the balance to pay it down to 15%.

Final answer:

To reduce your credit card debt to 15% of a $3,000 limit, you would need to make a payment of $2,550. This is calculated by determining 15% of the limit and subtracting it from the current balance to find the necessary payment amount.

Explanation:

Calculating Payment to Lower Credit Card Debt to Ratio

If your credit card has a limit of $3,000 and you wish to keep your credit card debt to limit ratio below 15%, first determine what 15% of your credit limit is. Calculate 15% of $3,000, which is $450. Since your current balance is the full limit of $3,000, subtract the target balance of $450 from $3,000. The result is the payment needed to reduce your debt to within the desired ratio.

$3,000 * 0.15 = $450 (15% of your credit limit)

$3,000 - $450 = $2,550

Therefore, a payment of $2,550 will bring your balance down to 15% of the credit limit. Managing your credit utilization is important not just for meeting the credit score components but also for maintaining good financial health.

Answer:

5 hours 19 minutes 18 seconds

Step-by-step explanation:

Answer:

5:19:18

Step-by-step explanation:

Answer:

correct option is  C. $399,060

Step-by-step explanation:

given data

balloon mortgage = 7/23

initial payments = $915

time = 30 year

new payments = $895

solution

we know here that 7/23 is that loan has fixed rate =  first 7  years.

so that initial payments for 7 years is here

initial payment = 7 × 12 × 915

initial payment = $76860

and

payments for 30 years when refinance her balloon

payments for 30 year = 30 × 12 × 895

payments for 30 year = $322200

so total financed cost paid for her house is

total financed cost =  $76860 + $322200  

total financed cost = $399,060

so correct option is  C. $399,060

Final answer:

To determine the total financed cost of Margaret's house, one must sum the payments made during the initial balloon mortgage and the subsequent 30-year mortgage, totaling $399,060 (Option C).

Explanation:

The total financed cost that Margaret paid for her house can be calculated by adding the payments made during her initial 7-year balloon mortgage period to the payments for the 30-year mortgage she refinanced into.

For the balloon mortgage: 7 years = 84 months. Therefore, the total paid during this period is 84 months × $915/month = $76,860.

For the refinanced mortgage: 30 years = 360 months. Hence, the total paid after refinancing is 360 months × $895/month = $322,200.

Adding these two amounts gives us the total financed cost which is $76,860 + $322,200 = $399,060. The answer to the student’s question is C. $399,060.

Answer:

3$

Step-by-step explanation:

Because every 3 numbers are divisble by 3 and the other 2 are not. Then the chance of you winning is 66%, therefore he should pay you half of what he would make. If this makes sense.

Answer:

A rate

Step-by-step explanation:

Its a ratio that compares unlike units.

Answer:

30 cm^2.

Step-by-step explanation:

This is a right angled triangle because it fits the Pythagoras theorem ( 13^2 = 12^2 + 5^2).

The area = 1/2 * 12 * 5

=  30 cm^2.

Answer:

800 minutes

Step-by-step explanation:

Make 2 expressions, one for Plan A, and one for Plan B

Plan A:

$9, and 0.17 per minute

9+0.17x

Plan B:

$25, and 0.15 per minute

25+0.15x

We want to find when they are the same, so we can set them equal to each other

9+0.17x=25+0.15x

Solve by isolating the variable, x

Subtract 9 from both sides

0.17x=16+0.15x

Subtract 0.15x from both sides

0.02x=16

Divide both sides by 0.02

x=800  

At 800 minutes they will cost the same

Answer:

$294

Step-by-step explanation:

1 is equivalent to 100% which would mean .05 is equivalent to 5%.

Therefore, multiply the base cost by 1.05 to find the total cost.

$280 x 1.05 = $294

Answer:

8 busses

Step-by-step explanation:

just divide 412 by 57 and you get 7.228070175438596 witch you round up to 8

Answer:

You need 8 buses

Step-by-step explanation:

Divide 412 by 57 and you will get the answer

I hope this will  help u

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Answer:

Their dads weight is not important don't body shame him peeps. 96-29=67, therefore that is how much she weighs, leaving out the unnecessary info.

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

area is base times height so 3 times 2 is 6

Hello there!

The area of the purple rectangle is 6 m^2, because 3x2 is 6, and the area of the green one is 24 m^2. Add them together to get the total area:

24 + 6 = 30 m^2

:)

Answer:

The area of the bedroom actually is 453.75 sq ft.

Step-by-step explanation:

Given that,

A blueprint shows the master bedroom to be 5 inches long and 3 inches wide.

The scale on blueprint is 2 inches : 11 feet.

It means 2 inches = 11 feet.

Then,

1 inches [tex]=\frac{11}{2}[/tex] feet = 5.5 feet.

So,

The length of the bedroom is 5 inches = (5×5.5) feet=27.5 feet

The wide of the bedroom is 3 inches = (3×5.5) feet= 16.5 feet

The area of the bedroom actually is = length × wide

                                                            =(27.5×16.5) square ft

                                                            =453.75 square ft

Final answer:

To find the area of the actual bedroom, you need to use the scale provided on the blueprint. By setting up ratios and solving for the actual length and width, you can find that the area of the actual bedroom is 453.75 square feet.

Explanation:

To find the area of the actual bedroom, we need to use the scale provided on the blueprint. The scale states that 2 inches on the blueprint represents 11 feet in reality. So, we can set up a ratio to find the actual length and width of the master bedroom:

Length ratio: 2 inches ⁠∩⁠ 11 feet = 5 inches ⁠∩⁠ x feet
Width ratio: 2 inches ⁠∩⁠ 11 feet = 3 inches ⁠∩⁠ y feet

By cross-multiplying and solving for x and y, we can find that x = 27.5 feet and y = 16.5 feet. Therefore, the actual length of the bedroom is 27.5 feet and the actual width is 16.5 feet. To find the area, we simply multiply the length and width: Area = 27.5 feet × 16.5 feet = 453.75 square feet.

Answer:

E (X) = 1.8

Var (X) = 0.36

σ = 0.6

Step-by-step explanation:

Solution:-

- Denote the random variable X : is the number of red marbles that Suzan has in her hand after she selects three marbles.

- Total sample space (bag) have the following quantity of colored marbles:

                Bag : { 3 Red , 2 Green }

- Suzan selects three marbles from the bag. The Event (X) defines the number of red marbles out of 3.

- The total number of outcomes / selections for randomly selecting 3 balls from the bag:

               All outcomes = 5 C 3 = 10

- The probability distribution of the random variable X, we will use combinations to determine the required probabilities:

  X = 1 red marble:

        P ( X = 1 ) : Suzan chooses 1 Red marble from the available 3 red marble and 2 green marbles.

        P ( X = 1 ) = [ 3C1*2C2 ] / all outcomes = (3*1) / 10 = 0.3

X = 2 red marble:

        P ( X = 2 ) : Suzan chooses 2 Red marble from the available 3 red marble and 1 green marbles.

        P ( X = 2 ) = [ 3C2*2C1 ] / all outcomes = (3*2) / 10 = 0.6

X = 3 red marble:

        P ( X = 3 ) : Suzan chooses 3 Red marble from the available 3 red marble.

        P ( X = 3 ) = [ 3C3] / all outcomes = (1) / 10 = 0.1

- The probability distribution is as follows:

          X :         1                 2                3

       P (X):       0.3            0.6              0.1

- The expected value E(X) for the given random variable X is:

                E ( X ) = ∑Xi*P(Xi)

                           = 1*0.3 + 2*0.6 + 3*0.1

                           =1.8

- The variance Var(X) for the given random variable X is:

                Var ( X ) = ∑Xi^2*P(Xi) - [ E(X) ] ^2

                               = 1^2*0.3 + 2^2*0.6 + 3^2*0.1 - 1.8^2

                               = 0.36

- The standard deviation for the given random variable X is:

                σ = √Var(X)

                σ = √0.36

                σ = 0.6

The expected value, the variance, and the standard deviation of the given random variable X are 1.8, 0.36, and 0.6 respectively and this can be determined by using the given data.

Given :

X is the number of red marbles that Suzan has in her hand after she selects three marbles from a bag containing three red marbles and two green ones.

The total number of outcomes are:

[tex]\rm \; ^5C_3=10[/tex]

The probability of random variable X are as follows:

X = 1 red marble

P(X = 1) = [tex]\rm \; ^3C_1 \times ^2C_2[/tex] = 0.3

X = 2 red marbles

P(X = 2) = [tex]\rm \; ^3C_2 \times ^2C_1[/tex] = 0.6

X = 3 red marbles

P(X = 3) = [tex]\rm \; ^3C_3[/tex] = 0.1

So, the expected value is given by:

[tex]\rm E(X) = \sum X_i \times P(X_i)[/tex]

        [tex]= 1\times 0.3+2\times 0.6 + 3 \times 0.1[/tex]

        = 1.8

Now, the variance is given by:

[tex]\rm Var(X) = \sum X^2_i \times P(X_i)-(E(X))^2[/tex]

           [tex]=1^2\times 0.3+2^2\times 0.6+3^2 \times 0.1-1.8^2[/tex]

           = 0.36

Now, the standard deviation is given by:

[tex]\rm \sigma=\sqrt{Var(X)}[/tex]

[tex]\rm \sigma = \sqrt{0.36}[/tex]

[tex]\sigma = 0.6[/tex]

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Answer:

3/5

Step-by-step explanation:

The scale factor is found by taking the ratio of coresponding sides

side of triangle HKM

--------------------------------

side of triangle DFG

HK

---------

DF

18

----

30

3

----

5

Answer:

51°

Step-by-step explanation:

Angle K corresponds to Angle F

Angle F = 180 - 70 - 59

Angle F = 51°

Answer:

4

Step-by-step explanation:

Symmetry is when you can flip the figure over a line and it will perfectly match the other side.

We see that if we draw a vertical line down the middle and a horizontal line across the middle, we get mirror images. So that's 2.

Then notice that we can draw two diagonals across the image, one from the upper left corner to the lower right corner and the other from the upper right corner to the lower left corner. That's another 2.

We try to find more, but try as we might, there are no others to be found.

Thus, there are 4 lines of symmetry.

Hope this helps!

Answer:

The correct option is;

(3) The sample of track athletes show that there is a correlation between foot size and running speed

Step-by-step explanation:

The statements are analysed as follows;

(1) Smaller foot sizes cause track athletes to run slower.

The above statement is a conclusion and it infers more information than is contained in the question statement because there are other factors such as taller athletes run faster than average sized athletes

(2) The sample of track athletes shows a causal relationship between

foot size and running speed.

The above statement is similar to the one above as it is a milder conclusion and it infers more information than is contained in the question statement

(3) The sample of track athletes shows a correlation between foot size

and running speed.

The  above statement is correct as is directly supported by the data as it is a statement made based directly the data

(4) There is no correlation between foot size and running speed in

track athletes.

The above statement is not supported by the available data.

Answer:

B

Step-by-step explanation:

got  it right on momentum

Answer:

225

Step-by-step explanation:

30%×750 = 30×750/100 = 3×75 = 225

Answer:

525

Step-by-step explanation:

10%= 75 (750 divided by 10)

30%= 225 (75 x 3)

750-225= 525

Answer:

The domain is the set of inputs, the range is the set of outputs

The true statements are options (A) f(x) has a domain of all real numbers, and (C) g(x) has a domain of all real numbers.

The domain of the function includes all possible x values of a function, and the range includes all possible y values of the function.

A. True: The function f(x) = (4)ˣ has a domain of all real numbers, as exponentiation is defined for any real number exponent.

B. False: The function g(x) = (4)⁻ˣ has a range of y ≥ 0, since exponentiation with negative exponent results in a positive number for any real number x.

C. True: The function g(x) = (4)⁻ˣ has a domain of all real numbers, as exponentiation is defined for any real number exponent.

D. False: The function h(x) = -(4)ˣ has a range of y ≤ 0, since exponentiation with positive exponent results in a positive number for any real number x, and multiplying it by -1 results in a negative number.

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The question seems to be incomplete, the complete question would be as:

Consider the three functions: f(x) = (4)ˣ, g(x) = (4)⁻ˣ, and  h(x) = –(4)ˣ

Which statements are true about the domain and range of f(x), g(x), and h(x)? Check all that apply.

A. f(x) has a domain of all real numbers.

B. g(x) has a range of y < 0.

C. g(x) has a domain of all real numbers.

D. h(x) has a domain of x > 0.

Answer:

B

Step-by-step explanation:

2/36=1/18=0,056 it's too easy

The probability that the sum adds to 2 or 12 is P = 0.056.

We have two number cubes, each one has 6 outcomes, so the total number of outcomes is:

C = 6*6 = 36 outcomes.

Now, we need to find the number of outcomes that add up to 2 or 12, these are:

Dice 1  dice 2    sum

  1           1            2

  6          6           12

So 2 out of 36 outcomes add up to 2 or 12, so the probability is:

P = 2/36 = 0.056

So the correct option is B.

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Answer:

Step-by-step explanation:

Answer:

A: 28

Explanation:

Vertical angles are congruent.

Answer:

The answer would be 28% because the angles are vertical, which also makes them congruent. Congruent angles have the same angle measure.

Answer:

n=74

Step-by-step explanation:

The equation would be:

n-14=60

Decreased means subtraction, so 14 is being subtracted from n, and it is equal to 60.

Solve for n, by isolating n.

To do this, add 14 to both sides

n-14+14=60+14

n=74