while hiking you see a 100ft observation tower on top of a 1100ft hill. The angle of elevation to the top of the tower is 6. How far away is the tower?.
Answers
Answer:692.82 ft
Step-by-step explanation:
Given
Height of tower is \(h=100\ ft\)
Tower is mounted at the top of \(H=1100\ ft\) hill
angle of elevation \(\theta =60^{\circ}\)
Using figure we can write
\(\tan \theta =\dfrac{h+H}{\text{Distance}}\)
\(\tan 60^{\circ}=\dfrac{100+1100}{\text{Distance}}\)
\(Distance =\frac{1200}{\tan 60^{\circ}}\)
\(Distance=\frac{1200}{\sqrt{3}}\)
\(Distance=692.82\ ft\)
Related Questions
We are testing our hypothesis at the 01 significance level. Write the conclusion to the test, in context relating to the original data (interpret the result).
Answers
The conclusion depends on the specific hypothesis being tested and the obtained p-value compared to the significance level.
What is the relationship between sample size and margin of error in a survey?The break down the key elements involved in hypothesis testing and the interpretation of the result:
Hypothesis Testing: Hypothesis testing is a statistical method used to make inferences and draw conclusions about a population based on sample data.It involves formulating a null hypothesis (H0) and an alternative hypothesis (Ha).Significance Level: The significance level, denoted as α (alpha), is the predetermined threshold used to determine the level of evidence required to reject the null hypothesis. It represents the probability of rejecting the null hypothesis when it is true. In this case, the significance level is stated as 0.01 or 1%.Conclusion: The conclusion of the test is based on comparing the p-value (probability value) obtained from the test with the significance level. The p-value represents the probability of observing the test statistic (or a more extreme value) under the assumption that the null hypothesis is true.If the p-value is less than the significance level (p < α), it suggests strong evidence against the null hypothesis. In this case, the conclusion would be to reject the null hypothesis in favor of the alternative hypothesis. This indicates that there is significant support for the claim made in the alternative hypothesis.If the p-value is greater than or equal to the significance level (p ≥ α), it suggests that there is insufficient evidence to reject the null hypothesis. The conclusion would be to fail to reject the null hypothesis, meaning that there is not enough statistical evidence to support the alternative hypothesis.To write the conclusion in context relating to the original data, the specific hypothesis being tested and the corresponding data must be provided.
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Compare the two integers below:
11____-1
<
>
=
Answers
Answer:
B. >
Step-by-step explanation:
Yes, you got it correct! Anything with a "-" is always less than a "+". Look at it this way:
I have 11 dollars (+11) and you owe me one dollar (-1). Now which is better?
Hope this helps
~R3VO
Please help! 40 points! Convert the following function from vertex form to standard form. Show your work.
f(x) = 3(x — 8)^2 — 160
Answers
The required standard form of the function is f(x) = 3x² - 48x + 32.
The vertex form of a quadratic function is:
f(x) = a(x - h)² + k
Where (h, k) is the vertex of the parabola and a is a coefficient that determines the shape of the parabola.
In the given function, we can see that the vertex is at (8, -160) and a is 3. So we have:
f(x) = 3(x - 8)² - 160 (vertex form)
Expanding the square, we get:
f(x) = 3(x - 8)(x - 8) - 160
f(x) = 3(x² - 16x + 64) - 160
Distributing the 3, we get:
f(x) = 3x² - 48x + 192 - 160
Simplifying, we get:
f(x) = 3x² - 48x + 32
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If bookshelf A is 6 feet long and bookshelf B is 8 feet long, what is the length of bookshelf C?
A.14
B.12
C.16
D.10
Help me please
Answers
Answer:
3.5 feet = 3 feet 6 inches
3 * 12 = 36
36 + 6 = 42 inches long
42 / 5/8 → 42 * 8/5 = 42*8/5
336 / 5 = 67.2
We can't put up part of a book, so we can fit 67 books.
Step-by-step explanation:
Which sequence has a common difference of 3?
3, 12, 21, 30
8, 12, 16, 20
5, 10, 15, 20
3, 6, 9, 12
Answers
A plane can fly 640 miles in the same time as it takes a car to go 240 miles. If the car travels 100 mph slower than the plane, find the speed (in mph) of the plane.
Answers
Answer:
Let s be the speed of the plane. Then s - 100 is the speed of the car.
640/s = 240/(s - 100)
640(s - 100) = 240s
8(s - 100) = 3s
8s - 800 = 3s
5s = 800, so s = 160 mph
The speed of the plane is 160 mph, and the speed of the car is 60 mph.
A consistent, dependent system of equations is a system with __________. A. only one line B. intersecting lines that have different slopes and different y-intercepts C. intersecting lines that have the same slope but different y-intercepts D. intersecting lines that have the same slope and the same y-intercept
Answers
Answer:
D. intersecting lines that have the same slope and the same y-intercept
Step-by-step explanation:
Equations that are dependent describe the same line: lines with the same slope and y-intercept. Dependent equations are always consistent.
Marisa buys 4 books at $13 per book. What integer represents the total change in the amount of money Marisa has?
Answers
Answer:
52
Step-by-step explanation: Just Multiply 4x13
Answer:
-$52
Step-by-step explanation:
-$13 * 4 = -$52
(i think it's negative because it ask for the change.)
3 dogs plus 5 cats cost $365. 5 dogs plus 3 cats cost $491. What is the cost of one cat?
Answers
Answer:
Solution given;
let dogs be d and cats be c.
according to the question
3 d +5 c =$365........[1]
5d+3c=$491.............[2]
By doing elimination method
multiplying equation 1 by 5 and equation 2 by 3 and subtracting
we get
15d+25c=$365*5
15d+9c=$491*3
- - -
____________
;16c=$352
c=\( \frac{352}{16} \)=$22
the cost of one cat is $22.
1.0- ! 0.8- 8 8 Chance.of.Admit 0.6- 8 : 8 0.4- 290 310 320 330 340 GRE. Score 300 Confidence Level for Slope and Intercept: Regression Analysis of Chance.of.Admit (Y) explained by GRE.Score (X) Coefficient Table: Estimate Std. Error t value Prl>[t]) Cl Lower Bound (Intercept) -2.44 0.12 -20.68 0.00 -2.67 GRE.Score 0.01 0.00 26.84 0.00 0.01 R-squared: 0.6441835 sigma: 0.08517377 CI Upper Bound -2.20 0.01 8. Is the linearity condition met? Yes, the residual plot is normal. Yes, there is no megaphone pattern found in the scatterplot Yes, the scatterplot shows a linear pattern in the data Yes, there is no megaphone pattern in the residual plot. 9. Select "Proceed to Regression Analysis". Refer to the table. If we perform at test for the slope of the regression line, what is the test statistic and p-value for this procedure? t = -20.68, p-value = -2.67 t = 26.84, p-value = 0.00 t = 26.84, p-value = 0.01 t = -20.68, p-value = 0.00 10. Calculate a 95% confidence interval for the slope on the line. Assuming that a = 0.05, can we use this interval as evidence that there is a linear relationship between GRE score and chance of admission? No. We don't know the alternative hypothesis, so we cannot make a conclusion on the relationship between GRE score and chance of admission. Yes. Because our alternative hypothesis is one-sided and O is not found in the confidence interval, we reject the null hypothesis and conclude that there is a linear relationship between GRE score and chance of admission. No. Confidence intervals cannot be used to make conclusions for hypothesis tests. Yes. Because our alternative hypothesis is two-sided and O is not found in the confidence interval, we reject the null hypothesis and conclude that there is a linear relationship between GRE score and chance of admission.
Answers
The test statistic and p-value for the slope of the regression line are t = 26 and p-value = 0.00.
Based on the given information, the analysis is focused on determining whether there is a linear relationship between GRE score and the chance of admission. The pattern observed in the scatterplot shows a linear pattern in the data, indicating a potential linear relationship between the two variables.
To test this hypothesis, a regression analysis was performed, which yielded a coefficient table with estimates for the intercept and slope of the regression line. The p-value for the slope test was found to be 0.00, which suggests strong evidence for a significant linear relationship between GRE score and the chance of admission.
Furthermore, a 95% confidence interval for the slope was calculated, which did not include the null value of zero. This means that we can reject the null hypothesis and conclude that there is a linear relationship between the GRE score and the chance of admission.
In summary, based on the analysis and statistical tests performed, there is evidence to support a linear relationship between the GRE score and the chance of admission.
The test statistic and p-value for the slope of the regression line are t = 26. ,an p-value = 0.00.
A 95% confidence interval for the slope on the line is (0.01, 0.01). Since 0 is not found in the confidence interval and our alternative hypothesis is two-sided, we reject the null hypothesis and conclude that there is a linear relationship between GRE score and the chance of admission.
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TRUE OR FALSE?
All square roots can be simplified to a decimal answer and still be equivalent.
Answers
THE ANSWER IS TRUE :P
Step-by-step explanation:
All the square roots can be simplified to a decimal answer and still be equivalent.
What is Square Root?Square root of a number is the value such that the value when multiplied to itself two times gives the original number.
It is denoted by the symbol √.
For example, square root of 16 is 4 since 4 × 4 = 16
We know that every number has a square root.
All the numbers does not have a perfect square root.
The perfect square roots does exists for numbers 1, 4, 9, 16, 25, .......
All the other numbers in between has the square roots which are decimal numbers.
Hence, all square roots can be simplified to a decimal answer and still be equivalent.
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a tomato has a mass of 100 grams the mass of the ant is 4.0x10x^{3} gram the of the tomato is how much greater than the mass of the ant
Answers
Note that if a tomato has a mass of 100 grams and the mass of the ant is 4.0x10⁻³gram, then the mass of the tomato is 25,000 times greater than the mass of the ant.
What is the justification for the above result?The expression for finding the extent to which the Mass of the tomato is greater than that of the ant is given as follows:
100/4.0x10⁻³
= [100 x 10³] / 4.0x10⁻³ x 10³
= 100,000/4
= 25,000
Therefore, the tomato is 25,000 times the mass of the ant.
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Answer:yes 2.5* 10-2
Step-by-step explanation:
PQRS is a kite. Find the m∠Q.
Answers
Which of the four tables below represents a function? *
Answers
A function shouldn’t have repeated Xs which is all 3 other tables do.
Jeremy, Alicia and Edgar are playing a game where the object is to get
closest to zero points. If Jeremy has -250 points, Alicia hos -150 points and Edgar
has 300 points, who is the winner
Answers
Answer:
Alicia!
Step-by-step explanation:
-150 is closer to the number 0 than -250 or 300. :D
X+(-21)=21-(-59)
HELP
Answers
Answer:
x = 101
Step-by-step explanation:
\(x+(-21)=21-(-59)\\x-21=21+59\\x-21=80\\x=101\)
How long does it take for $150 to grow to $450 at 7% annual percentage rate compounded continuously?
Answers
It takes 15.69 years for $150 to grow to $450 at 7% annual percentage rate compounded continuously
what is compound interest?
Interest that is added to a loan or deposit sum is known as compound interest. In our daily lives, it is the notion that is employed the most frequently. Compound interest is calculated for a sum using the principal and interest accrued over time. Compound interest and simple interest differ primarily in this way.
Initial amount = P = $150
Final amount = A= $450
rate , r= 7% = 0.07
t = ?
Formula:
A=Pe^(rt)
450=150(2.7183)^(0.07*t)
(2.7183)^(0.07*t) = 450/150 = 3
Taking Ln on both sides, we get
(0.07*t) Ln(2.7183) = Ln(3)
=> t= Ln(3) /[ 0.07Ln(2.7183) ] = 15.69 years
It takes 15.69 years for $150 to grow to $450 at 7% annual percentage rate compounded continuously
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Translate this phrase into an algebraic expression, Nine more than the quotient of a number and 7 is 6
Answers
Answer:
x/7 + 9 = 6
Step-by-step explanation:
Hope this helps! Please give brainliest!
how do i find the values of x and y that make the quadrilateral a parallelogram
Answers
-4x. +12
25=x
3(25)-8=4y+7
75-8=4y+7
67=4y +7
-7
60=4y
y=15
lol i know this is correct bc this was a problem on my homework a couple days ago and i got it right
The values of x and y that make the quadrilateral a parallelogram are, X = 25 & Y = 15
What is quadrilateral?Quadrilateral are the type of polygon who has 4 sides, on the basis of length and angle between sides we can further classify quadrilateral into following categories;
for example, Rectangle, Square, Parallelogram, Rhombus, Trapezium
Given that,
A parallelogram whose all the angles are,
(4x + 13)°, (4y + 7)°, (3x - 8)°, (5x - 12)°
It is known that,
Opposite Interior angles of parallelogram are equal
so,
⇒ (4x + 13) = (5x - 12)
⇒ x = 25
⇒ (4y + 7) = (3x - 8)
⇒ 4y + 7 = 75 - 8
⇒ 4y = 60
⇒ y = 15
Hence, the values of x and y are respectively 25, 15
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sales tax on a purchase at Sam's club is 8.42%. if your buy $ 245.32 worth of merchandise what will the cost be with sales tax
Answers
First, we need to calculate 8.42% of $245.32
\(245.32\times\frac{8.42}{100}=20.65\)Then we need to add the 20.65 to 245.32
\(245.32+20.65=265.98\)ANSWER
The cost with the sales tax is $265.98
Mike reads 60 pages in 1 and ½ hours. How many pages would he read in 120 minutes.
A. 80 pages
B. 100 pages
C. 120 pages
D. 40 pages
Answers
Answer:
80 pages
Step-by-step explanation:
recall that there are 60 min in an 1 hour
hence in 1 1/2 hrs, there will be:
60 x 1-1/2
= 60 x (3/2)
= 90 min
It is given that mike reads 60 pages in 1 1/2 hrs (i.e 90 min), hence
90 min--------> 60 pages
1 min -------> 60/90 pages
120 min -------> (60/90) x 120 = 80 pages
Answer: (A) 80 pages
Step-by-step explanation:
60 pages to 1 and ½ hours
x pages to 120 minutes
Change 1 and ½ hourst to minutes
1 and ½ hours= 90 minutes
60 pages = 90 minutes
x pages = 120 minutes
x*90=60*120
x=60*120/90
x=80 pages
Lacquan is two less than four times Jane's age. Anautica is six more than three times Jane's age. If
Laquan and Anautica are the same age, how old is Jane?
Answers
Answer:
Jane is 8.
Step-by-step explanation:
Let L = Lacquan's age.
Let J = Jane's age.
Let A = Anautica's age.
L = 4J - 2
A = 3J + 6
Since L = A, then we equate the two equations above:
4J - 2 = 3J + 6
J = 8
Answer: Jane is 8.
please help asap, will give brainliest and 5.0 star rating
Answers
The set of numbers is {0, 0, 0, 1, 1, 1, 2, 3, 4, 4, 6}, and its mean is M = 2.
What is the mean of the numbers?If we have a set of N numbers {x₁, x₂, ..., xₙ}, the mean is given by:
M = (x₁ + x₂ + ...+ xₙ)/N
To find our set of numbers, just count how many ticks each number has on top of it, our set will be:
{0, 0, 0, 1, 1, 1, 2, 3, 4, 4, 6}
So we have 11 numbers in total.
The mean will be:
M = (0 + 0 + 0 + 1+ 1 + 1 + 2 +3 + 4 + 4 + 6)/11
M = 22/11 = 2
The mean is 2.
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A rectangular garden has dimensions of 100ft by 10ft next season the garden is decreased by 2/3 of its size what is the scale of the new drowning
Answers
The qyaeriin has no attached diagram. A related diagram was found and used to provide the steps required to solve the problem.
Answer:
1 inch = 8.333 feets
Step-by-step explanation:
Initial dimension of rectangle :
100 feets by 10 feets
Fractional decrease in garden = 2/3
New Dimension of garden :
2/3(100 feets) by 2/3(10 feets)
66.667 feets by 6.6667 feets
Hence
From the picture attached :
8 inch = 66.667
1 inch = 8.333
The new scale of the drawing = 1 inch = 8.333 feets
answer this: 25/x = 7/3
Answers
The solution to the proportional equation in this problem is given as follows:
x = 75/7.
How to solve the proportional equation?The proportional equation in the context of this problem is defined as follows:
25/x = 7/3.
The equation is proportional, meaning that we can obtain the value of x applying cross multiplication as follows:
7x = 25 x 3
7x = 75
x = 75/7.
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Find the average value of the function f(x) = (x + 2) on the interval [0, 3].
![Find the average value of the function f(x) = (x + 2) on the interval [0, 3].](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/P5zl0SIYRlJ5Lz5JinzKHjLeHoS5AWmn.png)
Answers
The average value of the function f(x) = (x + 2) on the interval [0, 3] is 7/2.
Calculate the definite integral of the function over the interval [a, b], then divide it by the interval's length (b - a), in order to determine the average value of a function f(x) over the interval.
Given that the interval is [0, 3] and the function f(x) = (x + 2), we have:
= (1/3) × [1/2 x² + 2x] evaluated from x=0 to x=3
= (1/3) × [(1/2 × 3² + 2×3) - (1/20² + 20)]
= (1/3) × [(9/2 + 6) - 0]
= (1/3) × (21/2)
= 7/2
Therefore, the average value of the function f(x) = (x + 2) on the interval [0, 3] is 7/2.
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Answer for brainliest. (easy question)
Answers
Answer: y=x-1
Step-by-step explanation:
Hey!
Your answer is y = x - 1!
Hopefully this helps! :3
PLS HELP! WILL MARK BRAINLIEST!
(also please add explanation if possible)
Mr. Smith makes a pasta sauce
He mixes tomato concentrate: olive oil at a ratio of 3: 1
How many liters of tomato concentrate does he need to mix if he adds 3 liters of olive
oil?
Answers
Answer:
9 litres.
Step-by-step explanation:
3 * 3 = 9
3:1
x:3
So x is 9
Calculate the future value of a three year uneven cash flow given below, using 11% discount rate:
Year 0 Year 1 Year 2 Year 3
0 $600 $500 $400
Answers
Therefore, the future value of a three-year uneven cash flow given below, using an 11% discount rate is $1,238.82.
To calculate the future value of a three-year uneven cash flow given below, using an 11% discount rate, we need to use the formula;
Future value of uneven cash flow = cash flow at year 1/(1+discount rate)¹ + cash flow at year 2/(1+discount rate)² + cash flow at year 3/(1+discount rate)³ + cash flow at year 4/(1+discount rate)⁴
Given the cash flows;
Year 0: $0
Year 1: $600
Year 2: $500
Year 3: $400
Then the Future value of uneven cash flow
= $600/(1+0.11)¹ + $500/(1+0.11)² + $400/(1+0.11)³
= $600/1.11 + $500/1.23 + $400/1.36
=$540.54 + $405.28 + $293.00
=$1,238.82
Therefore, the future value of a three-year uneven cash flow given below, using an 11% discount rate is $1,238.82.
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The table shows data from local cable companies, representing the number of channels offered (x) and monthly dollar
cost of service wy).
х
y
x2
ху
115
65
13,225
7,475
122
72
14,884
8,784
128
85
16,384
10,880
132
87
17,424
11,484
135
95
18,225
12,825
2x=632 Σv=404
2x2=80,142 Sxy=51,448
Which regression equation correctly models the data?
O y = 1.49x - 107.5
O y = 1.49x - 106.4
Answers
Answer:
c
Step-by-step explanation:
i made a 90 on edge