Shalane wants to open a snow cone shop in Panama City, Florida, but does not know if she should keep her shop open all year round, or just for a portion of the year. She decides to collect data on the relationship between the temperature outside and snow cone sales in Panama City in order to decide if her shop should remain open in the winter months. A scatter plot with a line of best fit that was generated with technology is shown.

The angle of elevation is approximately 36.87 degrees and the horizontal distance is 264.6 feet

a.

The diagram is attached below;

b. We can use the tangent function to find the angle of elevation:

tan(θ) = opposite / adjacent

tan(θ) = 300 / 400

tan(θ) = 0.75

θ = tan^(-1)(0.75)

θ ≈ 36.87 degrees

So the angle of elevation from the boat to the parasail rider is approximately 36.87 degrees.

c. We can use the Pythagorean theorem to find the horizontal distance from the parasail rider to the boat:

d = √(400^2 - 300^2)

d ≈ 264.6 feet

So the horizontal distance from the parasail rider to the boat is approximately 265 feet.

Learn more on angle of elevation here;

https://brainly.com/question/25748640

#SPJ1

Answer:

sqrt(2)/2

Step-by-step explanation:

Given tan(x)=2-cot(x), find sin(x).

Rewrite in terms of sine and cosine:

sin(x)/cos(x)=2-cos(x)/sin(x)

Multiply both sides by cos(x)sin(x):

sin^2(x)=2sin(x)cos(x)-cos^2(x)

Rewrite cos^2(x) using the identity sin^2(x)+cos^2(x)=1:

sin^2(x)=2sin(x)cos(x)-(1-sin^2(x))

Distribute:

sin^2(x)=2sin(x)cos(x)-1+sin^2(x)

Subtracting sin^2(x) on both sides:

0=2sin(x)cos(x)-1

Add 1 on both sides:

1=2sin(x)cos(x)

Use identity sin(2x)=2sin(x)cos(x) to rewrite right:

1=sin(2x)

Since sin(pi/2)=1, then 2x=pi/2.

Dividing both sides by 2 gives x=pi/4.

So sin(pi/4)=sqrt(2)/2

Answer:

20% of 75 is 15

Answer:

The correct answer is 15.

Step-by-step explanation:

To find 20% of 75, we must multiply 75 by 20%.

75 x 0.20 = 15

Therefore, the correct answer is 15.

Hope this helps! :D

Answer:

the median is 8 because it is the middle number there is no mode mean is 7

Mean:7

Median:7

Mode: No mode

Mean:the sum of all observation divided by several observation

median:it is the middlemost observation of data arraged in increasing or decreasing order values

mode:it is the value that occurs most frequently in a set of data

hope it helps

The derivative of y = 4 log(2x) with respect to x is dy/dx = 0.

To find the derivative of y with respect to x, where y = 4 log(2x), we can apply the chain rule and the derivative of the natural logarithm function.

Recall that the derivative of the natural logarithm function ln(u) is given by:

d/dx ln(u) = (1/u) * du/dx

In this case, u = 2x. So, we have:

dy/dx = d/dx [4 log(2x)]

Applying the chain rule, we get:

dy/dx = (d/dx) [4] * (d/dx) [log(2x)]

The derivative of a constant (4) is zero, so the first term becomes 0:

dy/dx = 0 * (d/dx) [log(2x)]

Now, let's focus on the second term and apply the derivative of the natural logarithm function:

dy/dx = 0 * (1/(2x)) * (d/dx) [2x]

The derivative of 2x with respect to x is simply 2:

dy/dx = 0 * (1/(2x)) * 2

Simplifying further, we get the answer:

dy/dx = 0

To know more about derivative refer here:

https://brainly.com/question/29144258#

#SPJ11

The value of x in the given similar triangles ADB and BCE is 4.5.

To solve for x in the given similar triangles ADB and BCE, we can set up the proportion of corresponding sides:

In triangle ADB, we have:

AB/BD = x/DE

Substitute the given values:

3/4 = x/6

Now, cross-multiply and solve for x:

3 * 6 = 4x

18 = 4x

x = 18/4

x = 4.5

So, the value of x is 4.5.

To know more about similar triangles, refer here:

https://brainly.com/question/29731302

#SPJ6

Answer:

The number of questions in Mark's homework is:

Step-by-step explanation:

To identify the number of questions of the homework, first, you must identify the percentage that is the 12 question Mark calculates by himself: if in 80% he uses calculator, in 20% he doesn't, I mean, he uses his own calculates, by this reason:

With this data, we can use a simple rule of three and find the number of question that correspond to 80%.

If:

Then:

At last, we add the 80% and the 20% of the questions:

As you can see, the number of questions in Mark's homework is 60 questions.

Answer:

1

Step-by-step explanation: Pretty simple, all you have to do is multiply 1/2 by 2 and you get your answer which is 1

Answer:

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

Area is the product of two dimensions, so the ratio of areas of similar figures is equal to the square of the scale factor k.

Hence the scale factor is:

Therefore the ratio of corresponding parts is:

To answer this question, we will use the concepts of mean number and standard deviation in the context of a binomial distribution. In this case, the number of trials (n) is 65, and the probability of success (learning to push the lever) is 0.70.

(a) Find the mean number of rats that will learn to push the lever:

Mean (µ) = n * p
Mean (µ) = 65 * 0.70
Mean (µ) = 45.5

So, on average, 45.5 rats will learn to push the lever.

(b) Find the standard deviation of the number of rats that will learn to push the lever:

Standard Deviation (σ) = √(n * p * q)
Where q is the probability of failure (1 - p)

In this case, q = 1 - 0.70 = 0.30

Standard Deviation (σ) = √(65 * 0.70 * 0.30)
Standard Deviation (σ) = √(13.65)
Standard Deviation (σ) ≈ 3.69

The standard deviation of the number of rats that will learn to push the lever is approximately 3.69 (rounded to two decimal places).

To learn more about standard deviation : brainly.com/question/13905583

#SPJ11

The expression will be 5 + 11x.

What is an expression?

An expression in mathematics is a combination of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.)

It is possible to compare expressions to phrases. In English, a phrase by itself may contain an action, but it does not constitute a whole sentence.

Explanation: 3 + 7

Let the number to be "x"

Step 1 : the number is multiplied by - 8

           So, -8 x

Step 2 : subtracted from the sum of 5 and 3 times the number

       So,  (5 +3x) - (-8x)

           = 5+3x + 8x

           = 5 + 11x

Hence, The final expression will be 5 + 11x.

To earn more about Expressions, visit the link:

https://brainly.com/question/723406

#SPJ1

The Unit vector is  (-5/√33, -2/√33, -2/√33), A+2B is 8a x - 3a y - 3a z, IA-5CI is -3a x - 4a y - 8a z,  (A×B)/(A⋅B) is (a z - a y, -a z, a x - a y)/(2a x a y - a y a z - 3a y a z), A−2B+C is 5a x + 6 and C−4(A+B) is -5a x - 3a y + 23a z.

To find the unit vector along the line joining point (2,4,4) to point (-3,2,2), we need to find the direction vector of the line and then normalize it to obtain a unit vector.

The direction vector of the line is given by subtracting the coordinates of the initial point from the coordinates of the final point:

Direction vector = (-3, 2, 2) - (2, 4, 4) = (-3-2, 2-4, 2-4) = (-5, -2, -2)

To obtain the unit vector, we divide the direction vector by its magnitude:

Magnitude of direction vector = √((-5)^2 + (-2)^2 + (-2)^2) = √(25 + 4 + 4) = √33

Unit vector = (-5/√33, -2/√33, -2/√33)

To determine A + 2B, we can simply add the corresponding components of A and 2B:

A + 2B = (2a x + 5a y - 3a z) + 2(3a x - 4a y) = 2a x + 5a y - 3a z + 6a x - 8a y = 8a x - 3a y - 3a z

To calculate |A - 5C|, we subtract the corresponding components of A and 5C, take the magnitude of the resulting vector, and simplify:

A - 5C = (2a x + a y - 3a z) - 5(a x + a y + a z) = 2a x + a y - 3a z - 5a x - 5a y - 5a z = -3a x - 4a y - 8a z

|A - 5C| = √((-3)^2 + (-4)^2 + (-8)^2) = √(9 + 16 + 64) = √89

To find (A × B)/(A ⋅ B), we first calculate the cross product and dot product of A and B:

A × B = (2a x + a y - 3a z) × (a y - a z) = (a z - a y, -a z, a x - a y)

A ⋅ B = (2a x + a y - 3a z) ⋅ (a y - a z) = (2a x)(a y) + (a y)(-a z) + (-3a z)(a y) = 2a x a y - a y a z - 3a y a z

(A × B)/(A ⋅ B) = (a z - a y, -a z, a x - a y)/(2a x a y - a y a z - 3a y a z)

To calculate A - 2B + C, we subtract the corresponding components of A, 2B, and C:

A - 2B + C = (2a x + a y - 3a z) - 2(a y - a z) + (3a x + 5a y + 7a z) = 2a x + a y - 3a z - 2a y + 2a z + 3a x + 5a y + 7a z = 5a x + 6

To find C - 4(A + B), we calculate 4(A + B) first and then subtract the corresponding components of C:

4(A + B) = 4[(2a x + a y - 3a z) + (a y - a z)] = 4(2a x + 2a y - 4a z) = 8a x + 8a y - 16a z

C - 4(A + B) = (3a x + 5a y + 7a z) - (8a x + 8a y - 16a z) = 3a x + 5a y + 7a z - 8a x - 8a y + 16a z = -5a x - 3a y + 23a z

In both cases, we obtain expressions that represent vectors in terms of the unit vectors a x , a y , and a z .

Learn more about Unit vector here:

brainly.com/question/28028700

#SPJ11

Answer:

A and G I guess

Step-by-step explanation:

Hope I helped

Answer:

4y-28 = 0

4y = 28

y=28/4

y = 7

Answer:

Diagonal =26.11 units

Step-by-step explanation:

Answer:

189

Step-by-step explanation:

First d 2*27 which is 54. 27x3 is 81. so we're left with 81+54*2. 54x2 = 108. 81+108 is 189 :) I hope this helps.

The 5th value of the 60% percentile is 47 when for each test score in the data set is 12, 28, 35, 47, 49, 50.

Given that,

For each test score in the data set, the percentile rank is determined. 12, 28, 35, 42, 47, 49,  

We have to find what number represents the 60% of the population.

We know that,

So,

Percentile rank =[(Number of values below x)+0.5]/ total number of values × 100

For 12,

Percentile rank = [0 +0.5]/7×100

= 7th

For 28,

Percentile rank = [1 +0.5]/7×100

= 21st

For 35,

Percentile rank = [2 +0.5]/7×100

= 36th

For 42,

Percentile rank = [3 +0.5]/7×100

= 50th

For 47,

Percentile rank = [4 +0.5]/7×100

= 64th

For 49,

Percentile rank = [5 +0.5]/7×100

= 79th

For 50,

Percentile rank = [6 +0.5]/7×100

= 93rd

Now,

n = 7

60th percentile = 60% of n

So,

60% of n = 60/100×7

= 0.6×7

= 4.2

Therefore, The 5th value of the 60% percentile is 47 when for each test score in the data set is 12, 28, 35, 47, 49, 50.

To learn more about percentile visit: https://brainly.com/question/1594020

#SPJ4

Answer:

with what i dont see nothing

Step-by-step explanation:

XD

you were right this was super easy.

Answer:

A

Step-by-step explanation:

4 needs to be × by x and 3 needs to be +

Answer:

25.9

Step-by-step explanation:

25.9

pi-pi+pi/pi is 0+(1*25.9) which is 25.9

Hope this helps :D

Answer:

x = 141

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

30 boys

1/2 play football

30/2 = 15

15 boys left

2/3 play rugby

15 x 2/3 = 10

The probability that a randomly selected bee outside the hive is a drone is 0.25 or 25%.

To find the probability that a randomly selected bee outside the hive is a drone, we need to consider the total number of bees outside the hive and the number of drones outside the hive.

Given information:

Total number of bees in the colony: 1,000

Number of drones in the colony: 500

Number of drones outside the hive: 100

Number of non-drone bees in the colony: 1,000 - 500 = 500

Number of non-drone bees outside the hive: 300

To calculate the probability, we divide the number of favorable outcomes (drones outside the hive) by the total number of possible outcomes (bees outside the hive).

Probability of selecting a drone outside the hive = Number of drones outside the hive / Number of bees outside the hive

Probability = 100 / (100 + 300) = 100 / 400 = 0.25

Therefore, the probability that a randomly selected bee outside the hive is a drone is 0.25 or 25%.

Learn more about Probability  here:

https://brainly.com/question/23417919

#SPJ8

Answer:

The first number is 184

Step-by-step explanation:

Hope this helps u!! :D

Answer: 2 red balloons and 4 white balloons in each bunch

Step-by-step explanation:

divide 16/8 = 2 balloons in each bunch

divide 32/8 = 4 balloons in each bunch

Answer:

.667

Step-by-step explanation:

4/6 = 2/3 = .667

The probability that it is a 5 or an even number is 5/6 or 0.834 if

you roll a six-sided die.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

Number of total outcomes = 6

P(5) = 1/6

P(even) = 4/6

The probability that it is a 5 or an even number:

P = 1/6 + 4/6 = 5/6

P = 0.834

Thus, the probability that it is a 5 or an even number is 5/6 or 0.834 if

you roll a six-sided die.

Learn more about the probability here:

brainly.com/question/11234923

#SPJ5

The measure of angle A, B, C are 60°,60°,60°

A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices. A triangle is also a polygon.

The sum of angle in a polygon is 180°. i.e

A+B + C = 180°

therefore we can say that;

2x+2x + 3x-30 = 180

7x -30 = 180

7x = 180+30

7x = 210

divide both sides by 7

x = 210/7 = 30

therefore ;

angle A = 2× 30 = 60°

angle B = 2×30 = 60°

angle C = 3×30-30 = 90-30 = 60°

learn more about sum of angle in a triangle from

https://brainly.com/question/25215131

#SPJ1

Answer:

b) √29

Step-by-step explanation:

Given: The origin is (0, 0), the point P is (2, -5).

We need to use the distance formula.

Distance formula =

Here x2 = 2, x 1 = 0, y1 =0, y2 = -5

Distance =

= √(4 + 25)

= √29

The answer is b) √29

Hope you will understand the concepts

Thank you!!

-24 i hope this is right

Answer:

−24

Steps for answer:

1. Simplify  6÷3  to  2.

−3×(6+2)

2. Simplify  6+2 to  8.

−3×8

3. Simplify

−24