The top of a lighthouse is 100 m above sea level. The angle of elevation from the
deck of the sailboat to the top of the lighthouse is 28°. Calculate the distance
between the sailboat and the lighthouse.

3s represents three times Sydney's age. Sydney's age is symbolized with an S.

[tex]a^{2} {c}^{2} - {a}^{2} {d}^{2} - {b}^{2} {c}^{2} + {b}^{2} {d}^{2} + 4abc[/tex]

The correct question is:

A circle has a radius of 45 units and is centered at (-2.4, -4.8).

What is the equation of this circle?

Answer:

Equation of the circle is;

(x + 2.4)² + (y + 4.8)² = 2304

Step-by-step explanation:

The standard equation of a circle is;

(x - a)² + (y - b)²  =  r²

where;

(a,b) is the center of the circle and r is the radius of the circle

Now, from the question, the circle is centered at (-2.4, -4.8) and the radius is 45

Thus, plugging those values into the standard form of equation of a circle, we have;

(x - (-2.4))²  +  (y - (-4.8))²  = 48²

This gives;

(x + 2.4)² + (y + 4.8)² = 2304

Answer:

The answer is A

Step-by-step explanation:

Answer:

[tex]Expected \ mean = \dfrac{sum \ of \ values }{n}[/tex]

[tex]Expected \ mean = \dfrac{315 }{7}[/tex]

Expected mean = 45

The Chi - Square Value = 15.556

Conclusion:

We conclude that there is equal number of average interest in the course across all regions.  

Thus, the CFO is correct, the the frequencies in the regions are not significantly different by using a Chi-Square Goodness of Fit Test with a 1% significance level.

Step-by-step explanation:

From the question; Let state our null hypothesis and alternative hypothesis

Null Hypothesis

[tex]\mathbf{H_0:}[/tex]There is equal number of average interest in the course across all regions.  

Alternative Hypothesis

[tex]\mathbf{H_a:}[/tex] At least one of the region differs in average number of interest in the course.

The table can be better structured as :

Region          Enrollment

1                       45

2                       60

3                       30

4                       40

5                       50

6                       55

7                       35

From above; we know the number of sample = 7

Then our expected mean can be calculated as :

[tex]Expected \ mean = \dfrac{sum \ of \ values }{n}[/tex]

[tex]Expected \ mean = \dfrac{315 }{7}[/tex]

Expected mean = 45

SO, let's construct our Chi-Square  Statistics Test Table as follows:

Observed       Expected       Expected       (O-E)²         [tex]\dfrac{(O-E)^2}{E}[/tex]

(O)                         (E)            proportion    

45                          45           0.142857          0                   0

60                          45           0.142857       225                 5

30                          45           0.142857        225                5

40                          45           0.142857          25               0.556

50                          45           0.142857          25               0.556

55                          45           0.142857         100               2.222

35                          45           0.142857          100              2.222

                                                                                          15.556

The Chi - Square Value = 15.556

Degree of freedom = n- 1

Degree of freedom = 7 - 1

Degree of freedom = 6

Level of significance ∝ = 1% = 0.01

The Critical value of Chi Square test statistic at df = 6 and 0.01 significance level is 16.812

The Decision rule is to reject the Null hypothesis if The Chi Square test statistic X² > 16.812

Thus , since  the Chi Square test statistic is lesser than the critical value,

i.e  15.556 < 16.812 ,we accept null hypothesis [tex]\mathbf{H_0}[/tex]

Conclusion:

We conclude that there is equal number of average interest in the course across all regions.  

Thus, the CFO is correct, the the frequencies in the regions are not significantly different by using a Chi-Square Goodness of Fit Test with a 1% significance level.

Answer:

3 both ways x = 3

EXPLANATION:

plug in inputs and do a little simplifying we get

x = 6 ± √(36-36) all of that over 2

So we simplify and we get 6±sqrt(0) / 2

Then we get 6/2 = 3

x-0 = x+0

thats why there is only one answer

Answer:

The value of X is 3

Step-by-step explanation:

x²-6x+9=0

x²- 3x - 3x + 9= 0

X(x-3) -3(x-3)=0

(x-3) (x-3)=0

(x-3)²=0

(x-3)=0

x-3 = 0

X= 3

Answer: r= 12.58m

Step-by-step explanation:

100% SURE

Answer:

3/11 divided by 3/11 is 1

9/10 divided by 3/5 is 1 1/2 (1.5)

Step-by-step explanation:

Answer:

1

1.5

Step-by-step explanation:

3/11 ÷ 3/11 = 1

9/10 ÷ 3/5 = 3/2 ≈ 1.5

Answer:

Option (4). (-1.1, 0.9)

Step-by-step explanation:

In a graph of any function, values of f(x) are represented by the values on the y-axis for the different input values on x-axis.

For the given graph, values of f(x) are less than zero.

That means interval in which the values of the function are negative for the different values of x.

Negative values of the given function are in the intervals (-∞, -3), (-1.1, 9).

Therefore, from the given options, Option (4) will be the answer.

Answer is (-1.1,0.9)

Step-by-step explanation:

Answer:

The probability that a study participant has a height that is less than 65 inches is 0.1103.

Step-by-step explanation:

We are given that the heights in the​ 20-29 age group were normally​ distributed, with a mean of 69.9 inches and a standard deviation of 4.0 inches.

A study participant is randomly selected.

Let X = heights in the​ 20-29 age group.

So, X ~ Normal([tex](\mu=69.9,\sigma^{2} =4.0^{2}[/tex])

The z-score probability distribution for the normal distribution is given by;

                             Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = mean height = 69.9 inches

           [tex]\sigma[/tex] = standard deviation = 4.0 inches

Now, the probability that a study participant has a height that is less than 65 inches is given by = P(X < 65 inches)

      P(X < 65 inches) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{65-69.9}{4}[/tex] ) = P(Z < -1.225) = P(Z [tex]\leq[/tex] 1.225)

                                                                 =  1 - 0.8897 = 0.1103

The above probability is calculated by looking at the value of x = 1.225 in the z table which lies between x = 1.22 and x = 1.23 which has an area of 0.88877 and 0.89065 respectively.

Question:

The relationship between t and r is expressed by the equation 2t+3r+6 = 0. If r increases by 4, which of the following statements about t must be true?

Answer:

The value of t is reduced by 6 when the value of r is increased by 4

Step-by-step explanation:

Given

[tex]2t + 3r + 6 = 0[/tex]

Required

What happens when r is increased by 4

[tex]2t + 3r + 6 = 0[/tex] -------- Equation 1

Subtract 2t from both sides

[tex]2t + 3r + 6 - 2t = 0 - 2t[/tex]

[tex]3r + 6 = - 2t[/tex] --- Equation 2

When r is increased by 4, equation 1 becomes

[tex]2T + 3(r+4) + 6 = 0[/tex]

Note that the increment of r also affects the value of t; hence, the new value of t is represented by T

Open bracket

[tex]2T + 3r+12 + 6 = 0[/tex]

Rearrange

[tex]2T + 3r+6 +12 = 0[/tex]

Substitutr -2t for 3r + 6 [From equation 2]

[tex]2T -2t +12 = 0[/tex]

Make T the subject of formula

[tex]2T = 2t - 12[/tex]

Divide both sides by 2

[tex]\frac{2T}{2} = \frac{2t - 12}{2}[/tex]

[tex]T = t - 6[/tex]

This means that the value of t is reduced by 6 when the value of r is increased by 4

Answer:

so the axis of symmetry is x=4

Answer: X = 4

Explanation: Hope it helps you♡

[tex]answer \\ \\ \frac{ \sqrt{5} }{2 \sqrt{a} } \\ please \: see \: the \: attached \: picture \: for \: full \: solution \\ hope \: it \: helps[/tex]

Answer:

see below

Step-by-step explanation:

i is the imaginary number and it represents the square root of -1

Answer:

d. That order is taken into account (consider rearrangements of the same items to be different sequences).

Step-by-step explanation:

Given the combination rule:

[tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]

A major difference between permutation and combination is the order of the items in the selection. If the order does not matter then we have a combination. If on the other hand, the order of the items matter, then it is a permutation.

Therefore, that which is not a rule for combination is Option D since, in combination, we do not consider rearrangements of the same items to be different sequences.

Answer:

Circle

Step-by-step explanation:

r = 2 cos θ

Multiply both sides by r.

r² = 2r cos θ

Convert to rectangular.

x² + y² = 2x

x² − 2x + y² = 0

Complete the square.

x² − 2x + 1 + y² = 1

(x − 1)² + y² = 1

This is a circle with center (1, 0) and radius 1.

The given function r = 2 cos θ is a circle with a center (1, 0) and radius of 1.

A circle is a shape consisting of all points in a plane that are given the same distance from a given point called the center.

Given function is r = 2 cos θ

Now, Multiply both sides by r.

r² = 2r cos θ

Convert to rectangular form;

x² + y² = 2x

x² − 2x + y² = 0

Using Complete the square.

x² − 2x + 1 + y² = 1

(x − 1)² + y² = 1

Hence, This is a circle with a center (1, 0) and radius of 1.

Learn more about circle here;

brainly.com/question/12512221

#SPJ2

Answer:

3/5

Step-by-step explanation:

because there are more red than blue and the fraction is 3/5 and the probability to pick a red worm is a lot higher than the blue. well there are 4 red worms and 1 blue so it would be 3 red worms out of 5 in total. this is more than 1 blue over 5. 3/5 is more than 1/5

hope this helped

Answer: 3/5

Step-by-step explanation:

Since 4 red gummies you have four out of 5 chance of getting red gummies. Without replacement there are now 4 gummies left and 3 red gummies. There for 3 out of 4 chance of getting another red gummy. Since at same time multiply. 4/5*3/4 = 12/20

Which can be simplified to 3/5

[tex]the \: answer \: is \: 10 \\ please \: see \: the \: attached \: picture \: for \\ full \: solution \\ hope \: it \: helps[/tex]

Answer:

10 is the answer for this question.

Answer:

C. 1/25

Step-by-step explanation:

5^-2=5^(2*-1)

5^2=25

25^-1=1/25

Answer:

It is C 1/25 because it won't be -25 because a negative times a negative is a positive

Step-by-step explanation:

Answer:

B. (f - g)(x) = [tex]3^x-2x+14[/tex]

Step-by-step explanation:

→Set it up, like so:

[tex](3^x+10)-(2x-4)[/tex]

→Distribute the -1 to (2x - 4):

[tex]3^x+10-2x+4[/tex]

→Add like terms (10 and 4):

[tex]3^x-2x+14[/tex]

Answer:

Step-by-step explanation:

line equation:  y=mx + C

substitute given values

-7 = -3*0 + C

C=y= -7      ANS

Answer:

P = 0.1764

The events are dependent

Step-by-step explanation:

We have a total of 9 + 6 + 3 = 18 stuffed animals.

The probability of the first animal pulled being a bear is:

P(bear) = N(bear) / N(total)

P(bear) = 9 / 18 = 0.5

Then, for the second animal, we now have only 17 stuffed animals in total.

So the probability of the second animal pulled being a lion, given the first animal was a bear, is:

P(lion | bear) = N(lion) / N(total)

P(lion | bear) = 6 / 17 = 0.3529

So the final probability is the product of these probabilities:

P = P(bear) * P(lion | bear) = 0.5 * 0.3529 = 0.1764

To find if the events are dependent or independent, let's find the probability of the first pick being a lion:

P(lion) = N(lion) / N(total)

P(lion) = 6 / 18 = 0.3333

The probability of picking a lion is different from the probability of picking a lion given we already picked a bear, so the events are dependent.

Answer:

The standard deviation for the number of bags that are underfilled is 2.236.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval. The variance is the same as the mean, which mean that the standard deviation is the square root of the mean.

In this question:

Expected number of underfilled bags in a sample of n bags is:

[tex]\mu = 0.005*n[/tex]

1000 bags, so

[tex]\mu = 0.005*1000 = 5[/tex]

Standard deviation [tex]S = \sqrt{5} = 2.236[/tex]

The standard deviation for the number of bags that are underfilled is 2.236.

Answer:

y = 5x + 20

Step-by-step explanation:

The initial percent is 20.

Every minute, the percent goes up 5%, so the slope is 5.

So the equation of the line is y = 5x + 20.

Answer:

a) We can not estimate the probability.

b) Zero probability.

c) There is a probability between 95% and 99% that they have between 475 and 525 customers on a given day.

Step-by-step explanation:

a) We can not said nothing because we only know the average of customers per day. We need to know the probability distribution of the amount of customers per day to answer this question.

b) Now that we know that the variance is 100, although we do not know the exact distribution of the values, we can use the empirical rules to estimate the probability of having at least 700 customers on a given day.

If the variance is 100, the standard deviation is √100=10.

Applying the empirical rule (68-95-99.7 rule), we know that there is probability 0.15% of having at least 500+3*10=530 customers per day (more than 3 deviations from the mean).

Then, we can conclude that the probability of having at least 700 customers per day is zero.

c) To estimate this probability, we have to calculate how many deviations from the mean this values represent:

[tex]\Delta_1=475-500=-25=2.5\sigma\\\\\Delta_2=525-500=25=2.5\sigma[/tex]

We have an interval that have a width of ±2.5 deviations from the mean.

For 2 deviations from the mean, it is expected to have 95% of the data.

For 3 deviations from the mean, it is expected to have 99.7% of the data.

Then, for the interval 475 to 525, we can estimate a probability between 95% and 99%.

Answer:

a) The population population in this situation is all the local business

b) The sample is the 80 of local business selected.

c) The rate of nonresponse is 42.5%.

Step-by-step explanation:

Sampling

This is a common statistics practice, when we want to study something from a population, we find a sample of this population.

For example:

I want to estimate the proportion of New York state residents who are Buffalo Bills fans. So i ask, lets say, 1000 randomly selected New York state residents wheter they are Buffalo Bills fans, and expand this to the entire population of New York State residents.

The population for this survey is all New York State residents, while the sample are the 1000 New York State residents.

From telephone book listings, the committee chooses 80 businesses at random.

Survey: 80 businesses.

Population: All businesses in the college town.

Then

a) What is the population for this sample survey?

The population population in this situation is all the local business

b) What is the sample?

The sample is the 80 of local business selected.

c) What is the rate (percent) of nonresponse?

80 - 46 = 34 non-responses, out of 80

34/80 = 0.425

0.425*100 = 42.5%

The rate of nonresponse is 42.5%.

Answer:

I think its 1/9

Answer:

B

Step-by-step explanation:

Answer:

12 + -6i

a=12

b=-6

Step-by-step explanation:

( -4 + 3i ) ( -3 - 2i )

-4 * -3 = 12

3i * -2i= -6i

12 + -6i

Answer:

The range is simply all the y values of the ordered pairs in the relation so the answer (in increasing order) is -9, -4, 4, 10.