From the top of the cliff 8m high,two boats are seen in the direction due west.find the distance between the boats if the angles of depression from the top of the cliff are 45° and 30°.Find also the actual distance of the farther boat from the top of the cliff.
Answers
Answer:
Distance between 2 boats= 5.86m (3 s.f.)
Actual distance from farther boat from top of cliff= 16m
Step-by-step explanation:
Please see the attached pictures for full solution.
Related Questions
Damian reads 21 pages in 1 hour. How many pages can he read in 3 hours? StartFraction 21 pages Over 1 hour EndFraction = StartFraction question mark pages Over 3 hours EndFraction To go from 1 hour to 3 hours, you _______ . Damian can read _________ pages in 3 hours.
Answers
Answer: (Multiply by 3)
63 pages in 3 hours
Step-by-step explanation:
Answer:
To go from 1 hour to 3 hours, you
✔ multiply by 3
.
Damian can read
✔ 63
pages in 3 hours.
Step-by-step explanation:
A commuter train travels 65 kilometers in 27 minutes. What is it’s speed in kilometers per hour?
Answers
Answer:
Per hour: 2.40740740741
Step-by-step explanation:
you have to divided 65 and 27 so
65/27
which is 2.40740740741
Six measurements were made of the magnesium ion concentration (in parts per million, or ppm) in a city's municipal water supply, with the following results. It is reasonable to assume that the population is approximately normal. Based on a 95% confidence interval for the mean magnesium ion concentration, is it reasonable to believe that the mean magnesium ion concentration may be greater than 199.5? (Hint: you should first calculate the 95% confidence interval for the mean magnesium ion concentration.)
a) The likelihood cannot be determined
b) Yes
c) No
Answers
Answer:
Option B is correct.
It is reasonable to believe that the mean magnesium ion concentration may be greater than 199.5 as the confidence interval obtained contains values that are greater than 199.5
Step-by-step explanation:
Complete Question
Six measurements were made of the magnesium ion concentration (in parts per million, or ppm) in a city's municipal water supply, with the following results. It is reasonable to assume that the population is approximately normal.
170 201 199 202 173 153
Based on a 95% confidence interval for the mean magnesium ion concentration, is it reasonable to believe that the mean magnesium ion concentration may be greater than 199.5? (Hint: you should first calculate the 95% confidence interval for the mean magnesium ion concentration.)
A) The likelihood cannot be determined.
B) Yes
C) No
Solution
For this question, obtaining the confidence interval will give a clear solution to the problem.
Since the Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence, if the range obtained contains values greater than the standard we are comparing against (199.5), then the confidence interval proves that the mean magnesium ion may be greater than 199.5.
But to obtain the confidence interval, we need the mean and standard deviation for the sample.
170, 201, 199, 202, 173, 153
Mean = (sum of variables)/(total number of variables)
Sum of variables = 170+201+199+202+173+153 = 1098
Total number of variables = 6
Mean = (1098/6) = 183
Standard deviation = σ = √[Σ(x - xbar)²/N]
x = each variable
xbar = mean = 183
N = number of variables = 6
Σ(x - xbar)² = (170-183)² + (201-183)² + (199-183)² + (202-183)² + (173-183)² + (153-183)²
= 169 + 324 + 256 + 361 + 100 + 900
= 2110
σ = √(2110/6) = 18.75
Mathematically,
Confidence Interval = (Sample mean) ± (Margin of error)
Sample Mean = 183
Margin of Error is the width of the confidence interval about the mean.
It is given mathematically as,
Margin of Error = (Critical value) × (standard Error of the mean)
Critical value will be obtained using the t-distribution. This is because there is no information provided for the population mean and standard deviation.
To find the critical value from the t-tables, we first find the degree of freedom and the significance level.
Degree of freedom = df = n - 1 = 6 - 1 = 5.
Significance level for 95% confidence interval
(100% - 95%)/2 = 2.5% = 0.025
t (0.025, 5) = 2.57 (from the t-tables)
Standard error of the mean = σₓ = (σ/√n)
σ = standard deviation of the sample = 18.75
n = sample size = 6
σₓ = (18.75/√6) = 7.656
95% Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]
CI = 183 ± (2.57 × 7.656)
CI = 183 ± 19.675
95% CI = (163.325, 202.675)
95% Confidence interval = (163.3, 202.7)
It is reasonable to believe that the mean magnesium ion concentration may be greater than 199.5 as the confidence interval obtained contains values that are greater than 199.5
Hope this Helps!!!
Of the mathematics degrees awarded in recent years, 76% were bachelor’s degrees, 21% were master’s degrees and the remaining 3% were doctorates. Moreover, women earned 52% of bachelors, 40% of masters and 22% of doctorates. What is the probability that a randomly chosen mathematics degree was a master's degree given that it was awarded to a woman? Give your answer to 4 decimal places.
Answers
Answer:
0.1729 = 17.29% probability that a randomly chosen mathematics degree was a master's degree given that it was awarded to a woman
Step-by-step explanation:
Bayes Theorem:
Two events, A and B.
[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]
In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.
In this question:
Event A: Given to a woman.
Event B: Masters degree.
21% were master’s degrees
This means that [tex]P(B) = 0.21[/tex]
Women earned 40% of masters
This means that [tex]P(A|B) = 0.4[/tex]
Probability of the degree being given to a women:
52% of 76%, 40% of 21% and 22% of 3%. So
[tex]P(A) = 0.52*0.76 + 0.4*0.21 + 0.22*0.03 = 0.4858[/tex]
What is the probability that a randomly chosen mathematics degree was a master's degree given that it was awarded to a woman?
[tex]P(B|A) = \frac{0.21*0.4}{0.4858} = 0.1729[/tex]
0.1729 = 17.29% probability that a randomly chosen mathematics degree was a master's degree given that it was awarded to a woman
You are a medical assistant in a pediatrician’s office and one of your responsibilities is evaluating the growth of newborns and infants. Your first patient, a baby girl named Ivy Smith, was 21.5 inches long at 3 months old. At 8 months, you measure her at 24 inches long. For your medical records, all measurements must be given both in inches and in centimeters: 1 inch = 2.54 cm
I need to come up with an equation for this.
Answers
Consider a value to be significantly low if its z score less than or equal to minus2 or consider a value to be significantly high if its z score is greater than or equal to 2. A data set lists weights (grams) of a type of coin. Those weights have a mean of 5.45961 g and a standard deviation of 0.05215 g. Identify the weights that are significantly low or significantly high. What weights are significantly low? Select the correct answer below and fill in the answer box(es) to complete your choice.
Answers
Answer:
lowest score is 5.35531
highest score is x=5.45961
Step by step Explanation:
· A Z-score reffered to as a numerical measurement that identifies a value's relationship to the mean of a group of values. Z-score is usually measured in terms of standard deviations from the mean.
We were to Consider a value to be significantly low if its z score less than or equal to minus2 or consider a value to be significantly high if its z score is greater than or equal to 2
the z-score is given by:
z-score=(x-μ)/σ
where:
x=score
μ=mean=5.45961
σ=std deviation=0.05215
To calculate the lowest cost when the the z-score is -2, we have
[tex]-2=(x-5.45961)/0.05215[/tex]
To get the value of x then we collect like terms
-0.1043 = =(x-5.45961)
x=-0.1043 + 5.45961
[tex]X=5.35531[/tex]
therefore, the lowest score is 5.35531
Let us calculate the highest score when the z-score is 2 ,
then highest score will be:
[tex]2=(x-5.45961)/0.05215[/tex]
To get the value of x then we collect like terms
0.1043 = =(x-5.45961)
x=0.1043 + 5.45961
[tex]X=5.45961[/tex]
therefore the highest score is x=5.45961
Ten teaching assistants are available for grading papers in a particular course. The first exam consists of four questions, and the professor wishes to select a different assistant to grade each question (only one assistant per question). In how many ways can assistants be chosen to grade the exam
Answers
Answer:
There are 210 ways
Step-by-step explanation:
The number of ways or combinations in which we can select x elements from a group of n elements where the order doesn't matter can be calculated as:
[tex]nCx=\frac{n!}{x!(n-x)!}[/tex]
So, we have 10 teaching assistants and we need to choose 4 (one assistant per question) to grade each question. It means that n is equal to 10 and x is equal to 4.
Therefore, the number of ways that the assistants can be chosen to grade the exam are calculated as:
[tex]10C4=\frac{10!}{4!(10-4)!}=210[/tex]
Which of the following is(are) the solution(s) to | x-1|-8?
A. X= 7.-9
B. X = 9
C. X = -79
D. X = 7
Answers
Answer:
Step-by-step explanation:
|x-1|=8
if (x-1) >= 0 meaning x >= 1
then |x-1| = x-1
and then the solution of the equation is
x-1=8
<=> x = 9
if (x-1) <= 0 meaning x <= 1
then |x-1| = -(x-1) = -x+1
so the solution of the equation is
-x+1=8
<=> -x = 7
<=> x = -7
so the solutions are -7 and 9
answer C
do no hesitate if you need further explanation
thank you
What is 11/12 divided 1/3
Answers
Answer:
2.75 or 2 3/4
Step-by-step explanation:
so here you use the recipricle of 1/3. so you would do 11/12 X 3/1 =33/12= 2 3/4
Answer: 11/4
Step-by-step explanation:
to divide a fraction by another, you multiply by the reciprocal(the opposite of a certain fraction). the reciprocal of 1/3 is 3/1. so:
[tex]\frac{11}{12} / \frac{1}{3} = \frac{11}{12} * \frac{3}{1} = \frac{33}{12} = \frac{11}{4}[/tex] (divide both sides by 3 to simplify for the last one)
What’s the correct answer for this question?
Answers
Answer:
C:
Step-by-step explanation:
Both angles add up to 180°
<BCG + <BFG = 180°
2x+146+4x+238=180
6x+384 = 180°
6x = 180-384
6x = -204
Dividing both sides by 6
x = -34
Which choice is equivalent to the expression below?
root-81
A. 9i
B. i root9
C. root9i
D. -9
E. -root9
Answers
Answer: B
Step-by-step explanation:
3. In 28 days, a person saved $42. What was this person's
average daily savings?
Answers
Answer:
The average would be 42 / 28 = $1.50 / day.
Answer:
$1.50 per day
Step-by-step explanation:
Take the dollar amount and divide by the number of days
42 dollars / 28 days
1.50 dollars per day
$1.50 per day
Mathematics
ose the correct answer:
. What number should be added to (-5/16) to get ( 7/24)?
Answers
Answer:
0.6042 or 29/48
Step-by-step explanation:
-5/16 = -0.3125
7/24 = 0.2917
0.2917 - -0.3125 = 0.6042
0.6042 ≅ 29/48
Answer:
29/48
Step-by-step explanation:
-5/16 + x= 7/24
x= 7/24-(-5/16)
x=7/24+5/16
x= 2*7/2*24+ 3*5/3*16
x=29/48
During the late 1980s and the early 1990s the Pepsi Challenge was in full swing. During the challenge, participants were asked to taste cola from both Coke and Pepsi. Once they had tasted both drinks, the participants were asked to report which was better tasting. The results indicated that participants found Pepsi products to be better tasting. What is the dependent variable in this study? coruse hero psyc 255
Answers
Answer:
Taste
Step-by-step explanation:
In the challenge, participants were asked to taste cola from both Coke and Pepsi. They were to give a report on which of the two drinks tasted better.
The taste reported by the participants is dependent on the type of cola taken (either Coke or Pepsi).
Therefore, the taste is the dependent variable while the types of cola are the independent variables.
Complete the point-slope equation of the line through (− 2 ,6 ) ( 1 , 1 )
Answers
Answer:
y=-5/3x+8/3
Step-by-step explanation:
You want to find the equation for a line that passes through the two points:
(-2,6) and (1,1).
First of all, remember what the equation of a line is:
y = mx+b
Where:
m is the slope, and
b is the y-intercept
First, let's find what m is, the slope of the line...
The slope of a line is a measure of how fast the line "goes up" or "goes down". A large slope means the line goes up or down really fast (a very steep line). Small slopes means the line isn't very steep. A slope of zero means the line has no steepness at all; it is perfectly horizontal.
For lines like these, the slope is always defined as "the change in y over the change in x" or, in equation form:
So what we need now are the two points you gave that the line passes through. Let's call the first point you gave, (-2,6), point #1, so the x and y numbers given will be called x1 and y1. Or, x1=-2 and y1=6.
Also, let's call the second point you gave, (1,1), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=1 and y2=1.
Now, just plug the numbers into the formula for m above, like this:
m=
1 - 6
1 - -2
or...
m=
-5
3
or...
m=-5/3
So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+b like this:
y=-5/3x+b
Now, what about b, the y-intercept?
To find b, think about what your (x,y) points mean:
(-2,6). When x of the line is -2, y of the line must be 6.
(1,1). When x of the line is 1, y of the line must be 1.
Because you said the line passes through each one of these two points, right?
Now, look at our line's equation so far: y=-5/3x+b. b is what we want, the -5/3 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the two points (-2,6) and (1,1).
So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for b for the particular line that passes through the two points you gave!.
You can use either (x,y) point you want..the answer will be the same:
(-2,6). y=mx+b or 6=-5/3 × -2+b, or solving for b: b=6-(-5/3)(-2). b=8/3.
(1,1). y=mx+b or 1=-5/3 × 1+b, or solving for b: b=1-(-5/3)(1). b=8/3.
The circular area covered by a cell phone tower can be represented by the expression 225π miles2. What is the approximate length of the diameter of this circular area
Answers
Answer:
The length of the diameter of this circular area is of 30 miles.
Step-by-step explanation:
The area of a circular region can be represented by the following equation:
[tex]A = \pi r^{2}[/tex]
In which r is the radius. The diameter is twice the radius.
In this question:
[tex]A = 225\pi[/tex]
So
[tex]A = \pi r^{2}[/tex]
[tex]225\pi = \pi r^{2}[/tex]
[tex]r^{2} = 225[/tex]
[tex]r = \pm \sqrt{225}[/tex]
The radius is a positive measure, so
[tex]r = 15[/tex]
Area in squared miles, so the radius in miles.
What is the approximate length of the diameter of this circular area
D = 2r = 2*15 = 30 miles
The length of the diameter of this circular area is of 30 miles.
in a survey of more than 3000 people 93% of the respondents claimed to prefer Isaac's immaculate ice cream over any other brand of ice cream. which of the folloling groups were surveyed.
Answers
Answer:
The answer is 2,790.
Step-by-step explanation:
Here's a handy tool.
93% of 1 = 0.93 93% of 131 = 121.83 93% of 261 = 242.73 93% of 391 = 363.63
93% of 2 = 1.86 93% of 132 = 122.76 93% of 262 = 243.66 93% of 392 = 364.56
93% of 3 = 2.79 93% of 133 = 123.69 93% of 263 = 244.59 93% of 393 = 365.49
93% of 4 = 3.72 93% of 134 = 124.62 93% of 264 = 245.52 93% of 394 = 366.42
93% of 5 = 4.65 93% of 135 = 125.55 93% of 265 = 246.45 93% of 395 = 367.35
93% of 6 = 5.58 93% of 136 = 126.48 93% of 266 = 247.38 93% of 396 = 368.28
93% of 7 = 6.51 93% of 137 = 127.41 93% of 267 = 248.31 93% of 397 = 369.21
93% of 8 = 7.44 93% of 138 = 128.34 93% of 268 = 249.24 93% of 398 = 370.14
93% of 9 = 8.37 93% of 139 = 129.27 93% of 269 = 250.17 93% of 399 = 371.07
93% of 10 = 9.30 93% of 140 = 130.20 93% of 270 = 251.10 93% of 400 = 372.00
Please answer I need help!
Answers
Answer:
c & d
Step-by-step explanation:
the description matches the information in the table
Answer: A, B, C
Step-by-step explanation:
domain = x
range = y
Quadrilateral BCDE is a kite. What is BF?
B
20
С
12
E
F
D
Answers
Answer:
32
Step-by-step explanation:
if u do pythagoras, sq root of 20^2-12^2=16
16x2=32
Use the following cell phone airport data speeds​ (Mbps) from a particular network. Find the percentile corresponding to the data speed 11.2 Mbps. 0.1 0.2 0.2 0.3 0.4 0.4 0.4 0.5 0.5 0.6 0.6 0.8 0.9 0.9 0.9 1.1 1.3 1.7 1.8 1.9 2.3 2.4 2.5 2.6 2.7 3.1 3.5 3.5 3.7 3.8 4.8 5.2 7.4 7.9 8.2 8.6 9.3 11.2 11.3 11.4 12.1 12.6 13.1 13.3 13.6 13.8 14.6 15.6 15.7 25.6
Answers
Answer: the percentile is 74%
Step-by-step explanation:
The given data distribution is arranged in increasing order as:
0.1 0.2 0.2 0.3 0.4 0.4 0.4 0.5 0.5 0.6 0.6 0.8 0.9 0.9 0.9 1.1 1.3 1.7 1.8 1.9 2.3 2.4 2.5 2.6 2.7 3.1 3.5 3.5 3.7 3.8 4.8 5.2 7.4 7.9 8.2 8.6 9.3 11.2 11.3 11.4 12.1 12.6 13.1 13.3 13.6 13.8 14.6 15.6 15.7 25.6
The total number of values given in the data is 50
Percentile = number of values in the distribution lesser than the given value × 100/ total number of values in the distribution
Considering the data speed of 11.2 Mbps, the number of data speed lower than 11.2 is 37
Percentile = (37 × 100)/50 = 74%
Describe the rate of change of f(x)=lnx. Your answer should explain how the slope changes when x is small and when x is large.
Answers
Answer:
By plotting the graph of f(x)=lnx, you can conclude that when x is small, dy/dx has a larger value. For instance, the gradient of the curve when x=0.5 is 2. However, as you move along the x axis, you will see that the graph levels off, indicating a decrease in the slope, or dy/dx. For example, if x=10, dy/dx = 0.1 and when x=20, dy/dx= 0.05 and so on. Eventually, when x is large enough the value of dy/dx will be negligible.
Thus, as x increases, the slope decreases.
Answer:
Explanation shown below
Step-by-step explanation:
f(x)=lnx;
The rate of change is defined as dy/dx;
dy/dx[Inx] = 1/x
and dy/dx is defined as the slope
The nature of the slope is as x increases ; the slope decreases and conversely meaning as x decreases, the slope increases.
At the neighborhood block party, John noticed that every 5 minutes, the
shadow of a nearby pine tree got six inches longer. The shadow was 12
feet long at 4:15pm. How long was the shadow at 5:00pm?
Answers
Answer:
7
Step-by-step explanation:
I think because at if you divide 45 by 6 because its 45 minutes from 4:15 to 5:00 and it grows 6 inches longer every five min
p(x) is a polynomial with integer coefficients and p(-3) = 0. Which statements must be true? Choose all that apply. x - 3 is a factor of the polynomial. -3 is the constant term of the polynomial. p( x) can have at most 3 linear factors. x + 3 is a factor of the polynomial.
Answers
Answer:
yes all that apply to this q9
ACB = DCE
A = 3x-10, C = 45°, D = 2x+10
Please help confused
Answers
Answer:
x = 20
Step-by-step explanation:
The congruence statement tells you that angle A is congruent to angle D. (Both are listed first in the triangle names.) This means ...
∠A = ∠D
3x -10 = 2x +10
x = 20 . . . . . . . . . . add 10-2x to both sides
A 50 ft kite string is flying on the beach above an umbrella. You are holding the end
of the string and are 12 feet from the umbrella. How high in the air is the kite flying?
Round to the nearest degree.
Answers
Answer:
The height of the kite is 48.54 feet
The angle of elevation is 76.11°
Step-by-step explanation:
To find the height of the kite, we can use the Pythagoras' theorem in the triangle created by the length of the string (hypotenuse), the height of the kite and the distance to the umbrella (catheti).
Then, we have:
50^2 = 12^2 + height^2
height^2 = 2500 - 144
height^2 = 2356
height = 48.54 ft
So the kite is 48.54 feet high in the air.
The angle of elevation can be calculated using the cosine relation:
cos(angle) = 12 / 50
cos(angle) = 0.24
angle = 76.11°
Removing which point from the coordinate plane would make the graph a function of x? On a coordinate plane, points are at (negative 2, negative 3), (negative 2, 1), (negative 4, 3), (0, 4), (1, 1), and (2, 3). (–4, 3) (–2, 1) (0, 4) (1, 1)
Answers
Answer:
(-2, 1)
Step-by-step explanation:
For a relation consisting of (x, y) pairs to be a function, all of the x-values must be unique. In the given relation, points (-2, -3) and (-2, 1) have the same x-value. Removing either point will make the relation a function.
Of these, the only one listed among answer choices is (-2, 1).
Answer:
-2 , 1
Step-by-step explanation:
good luck love
Type your answers into the boxes.
There are 36 students in a class. The pie chart shows the colour of their hair.
Students' Hair Colours
40°
Red
Blonde
Dark
240°
How many students have blonde hair?
How many students have dark hair?
How many students have red hair?
Answers
Answer:
(a)24
(b)8
(c)4
Step-by-step explanation:
Number of STudents in the Class = 36
Angle representing Students with Red Hair =40 degrees
Angle representing Students with Blonde Hair =240 degrees
Therefore:
(a)Number of Students with Blonde Hair
[tex]=\dfrac{240^\circ}{360^\circ} \times 36\\\\ =24$ students[/tex]
(b)Number of Students with Dark Hair
Angle representing students with dark hair = 360-(240+40)=80 degrees
Therefore:
Number of Students with Dark Hair
[tex]=\dfrac{80^\circ}{360^\circ} \times 36\\\\ =8$ students[/tex]
(c)Number of Students with Blonde Hair
[tex]=\dfrac{40^\circ}{360^\circ} \times 36\\\\ =4$ students[/tex]
There are 8 students that have blond hair
There are 24 students that have dark hair
There are 4 students that have red hair
Please find attached the pie chart used in answering this question
A pie chart is a graph that displays information in a circle. The circle is divided into slices which represent a numerical proportion. The sum of angles in a pie chart is 360 degrees
To determine the number of students with a type of hair, use this formula :
(degree of the slice that represents the hair type / 360) x total number of students in the class
Degree of the slice that represents blond hair = 360 - (240 + 40) = 80
Students that have blonde hair = [tex]\frac{80}{360}[/tex] x 36 = 8
Students that have dark hair = [tex]\frac{240}{360}[/tex] x 36 = 24
Students that have red hair = [tex]\frac{40}{360}[/tex] x 36 = 4
To learn more about pie charts, please check : https://brainly.com/question/11433309?referrer=searchResults
Eli uses 1/4 pound of apples to make 4 servings of fruit salad. He uses the same amount of apples for each serving. What amount of apples does he use for each serving of fruit salad?
Answers
Answer:
1/16 pound
Step-by-step explanation:
1/4 ÷ 4 = 1/4 x 1/4 = 1/16
Tori needs to make some house repairs in three years that will cost $9,000. She has some money in an account earning 9% annual interest. How much money needs to be in the account today so she will have enough to pay for the repairs
Answers
Answer:
She needs to have approximately $6950 on that account.
Step-by-step explanation:
Since the account has an interest rate of 9% annually, then it's compounded and the earnings can be found by the following expression:
[tex]M = C*(1 + r)^t[/tex]
Where M is the final amount, C is the initial amount, r is the interest rate and t is the time elapsed in years.
She needs the money in 3 years, therefore t = 3. Applying this to the problem we have:
[tex]9000 = C*(1 + 0.09)^3\\9000 = C*(1.09)^3\\C*1.295 = 9000\\C = \frac{9000}{1.295}\\C = 6949.81[/tex]
She needs to have approximately $6950 on that account.
which statement about numbers is true
Answers
Answer:
what are the answers fir this question
Answer:
Answer options are:
a. All integers are natural numbers.
b. All rational numbers are integers.
c. All natural numbers are whole numbers.
d. All rational numbers are natural numbers.
Step-by-step explanation:
Answer is C
