The ridgeline will be 18.67 feet above the house.
What will be the height of the ridgeline above the house?Generally, a height refers to the measurement of someone or something from head to foot or from base to top.
To find the height of the ridgeline, we will use the formula: Height = (Pitch / 12) * Span
Given data:
Pitch = 7
Span = 32 feet
Inputting the values, we have:
Height = (7 / 12) * 32
Height = 0.5833 * 32
Height = 18.6656
Height = 18.67 feet.
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Add.
−5/6+(−2 5/8)
Enter your answer as a simplified fraction by filling in the boxes.
pllzzzzz helppppp
a solid sphere is cut into 12 equal wedges. the volume of each wedge is V=1/9πr^3. solve the formula for r.
The formula, solved for r is r = ∛(9V/π)
Subject of formulaFrom the question, we are to solve for r is the given formula
The given formula is
V = 1/9πr³
Multiply both sides of the equation by 9 to get
9V = πr³
Now, divide both sides by π
∴ r³ = 9V/π
r = ∛(9V/π)
Hence, the formula, solved for r is r = ∛(9V/π)
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Find x and simplify completely
Answer:
x = [tex]6\sqrt{3}[/tex] i
Step-by-step explanation:
We can write the following equation according to Euclidian Theorem to find the value of x:
[tex]x^{2}[/tex] = 12*9 multiply 9 and 12
[tex]x^{2}[/tex] = 108 find the root of both sides
x = [tex]6\sqrt{3}[/tex] is the value of x
PreCalc work, Need help with writing piece wise functions with graphs level 2. Giving branliest.
The piece-wise linear functions can be written as follows:
[tex]f(x) = -0.5x + 3, x < 5[/tex].[tex]f(x) = -5, x = 5[/tex][tex]f(x) = -x + 9, x > 5[/tex].What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For x less than 5, the y-intercept is of b = 3 and the function also gos through (2,2), hence the slope is:
m = (2 - 3)/(2 - 0) = -0.5.
Hence the rule is:
[tex]f(x) = -0.5x + 3, x < 5[/tex].
When x = 5, the function is constant at -5, hence:
[tex]f(x) = -5, x = 5[/tex]
For x less than 5, the function goes through points (6,3) and (7,2), hence the slope is:
m = (2 - 3)/(7 - 6) = -1.
Then:
y = -x + b
When x = 6, y = 3, hence the y-intercept is given as follows:
3 = -6 + b
b = 9.
Hence the rule is:
[tex]f(x) = -x + 9, x > 5[/tex].
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Questions on a statistics exam are considered good questions provided the questions discriminate between students who have
studied for the exam and those who have not studied. Suppose that on a particular statistics exam the students were separated
into two gnpups, Group 1 that studied and Group 2 that had not studied. Data was collected and a 95% confidence interval for
the difference in the proportion of those passing the exam from Group 1 that studied and the proportion of those passing the
exam from Group 2 that had not studied. The confidence interval turned out to be (0.005, 0.125). Select the best answer.
Let P, = the proportion of Group 1 students that passed the exam
Let Py = the proportion of Group 2 students that passed the exam
The data fails to show with 95% confidence that these questions discriminated between those who studied and those who did
not study.
© We are 95% confident that those who studied had a higher passing rate than those who did not study.
We are 95% confident that those who studied had a lower passing rate than those who did not study.
None of the above
Using the interpretation of the confidence interval, the correct option is:
We are 95% confident that those who studied had a higher passing rate than those who did not study.
What is the interpretation of a x% confidence interval?It means that we are x% confident that the population parameter(mean/proportion/standard deviation) is between a and b.
The confidence interval of the difference is:
(0.005, 0.125).
Since the entire interval is positive, the correct option is:
We are 95% confident that those who studied had a higher passing rate than those who did not study.
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does this represent quntitites that are proportional
Answer:
B
Step-by-step explanation:
Not all of the pairs represent the same ratio
Here are the gold medal times for the women’s 100-meter freestyle (swimming) in every other Summer Olympics:
The least-squares regression line equation is y = -0.28x + 610.31
The scatter plot of the dataTo plot the scatter plot of the data, we represent the x-axis with year and we represent the y-axis with time
Next, we plot the scatter plot using the dataset
See attachment for the scatter plot
Describe the relationship between the variables in the graph.From the attached scatter plot, we can see that the relationship between the variables in the graph is approximately linear.
This is so because the points appear to be on a straight line
Find the correlation coefficient.To do this, we make use of a graphing calculator, with the following summary:
X Values
∑ = 21608Mean = 1964.364∑(X - Mx)2 = SSx = 10062.545Y Values
∑ = 686.41Mean = 62.401∑(Y - My)2 = SSy = 842.83X and Y Combined
N = 11∑(X - Mx)(Y - My) = -2806.684R Calculation
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))
r = -2806.684 / √((10062.545)(842.83)) = -0.9638
Hence, the correlation coefficient is -0.9638
Find the least-squares regression line.To do this, we make use of a graphing calculator, with the following summary:
Sum of X = 21608Sum of Y = 686.41Mean X = 1964.3636Mean Y = 62.4009Sum of squares (SSX) = 10062.5455Sum of products (SP) = -2806.6836The least-squares regression line equation is
y = bx + a
Where
b = SP/SSX = -2806.68/10062.55 = -0.27892
a = MY - bMX = 62.4 - (-0.28*1964.36) = 610.30872
So, we have
y = -0.27892x + 610.30872
Approximate
y = -0.28x + 610.31
Hence, the least-squares regression line equation is y = -0.28x + 610.31
The estimated gold medal time for 1924 and for 1976.We have:
y = -0.28x + 610.31
Substitute 1924 and 1976 for x
y = -0.28 * 1924 + 610.31 = 71.59
y = -0.28 * 1976 + 610.31 = 57.03
Are these estimates reliable?
Yes, the estimates are reliable
Are they reasonable?
Yes, the estimates are reasonable
Why are your answers in Question 5 different than the times given in the table?The results are different because the answers in 5 are estimated from the formula while the table are the actual values
Find the estimated gold medal time for 2022 and for 2200.We have:
y = -0.28x + 610.31
Substitute 2022 and 2200 for x
y = -0.28 * 2022 + 610.31 = 44.15
y = -0.28 * 2200 + 610.31 = -5.69
Are these estimates reliable?
No, the estimates are not reliable
Are they reasonable?
The estimate in 2022 is reasonable, while the estimate in 2200 is not reasonable
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What kind of multi step do I have to do to prove a is parallel to b and m parallel to n.
The proof that line n is perpendicular to both a and b is proved below using definition of right angle and perpendicular transversal theorem.
How to prove Perpendicular and Parallel Lines?
We are given that;
Line a is parallel to line b
Line m is parallel to line n.
A) We want to prove that line a is perpendicular to n.
From the image, we see that there is a right angle sign on the opposite side of ∠1 facing m.
Now, we know that by definition of a right angle that ∠1 will also be a right angle.
Since angle 1 is a right angle, then we can say the line transversal a is perpendicular to line m.
B) We want to prove that line b is perpendicular to n.
The definition of the perpendicular transversal theorem, states that if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other.
Thus, b will be perpendicular to n.
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What is the perimeter of a yard with length = 4 x + 6 2 x + 1 feet and width = x − 3 2 x + 1 feet? 4 x − 3 4 x + 12 feet 4 x − 3 2 x + 6 feet 8 x − 6 4 x + 12 feet 8 x − 6 2 x + 6 feet
The perimeter of the given yard is P = 10x + 6
Perimeter of a rectangleThe formula for calculating the perimeter of a rectangle is expressed as:
P = 2(l + w)
where
l is the length
w is the width
Given the following parameters
length = 4x+6
width = x-3
Substitute
P = 2(4x+6+x-3)
P = 2(5x + 3)
P = 10x + 6
Hence the perimeter of the given yard is P = 10x + 6
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Determine the interval(s) on which the given function is decreasing?
Answer:
(-∞, -1) U (0, ∞)
Step-by-step explanation:
To figure out which parts of the function are decreasing, we need to read the graph left to right.
Given this information, we can figure out that the first part of the graph is decreasing, starts to go up a little bit, and then starts to decrease again.
How do we write this in mathematical terms, however? We simply take the x-values for which parts it decreases.
The graph started on negative infinity, and kept decreasing until -1 on the x-axis. We can write this as (-∞, -1). The graph starts to increase, which is not relevant to the question. As it starts to decrease again, it starts on 0, and slowly decreases to the right, meaning that it is going towards positive infinity. We can write this as (0,∞).
Now that we have both parts of the decreasing function, we can combine them using the union symbol (∪).
Therefore, our final answer is (-∞, -1) U (0, ∞).
Which graph shows the solution to the inequality lx+3l≥2 ?
Howard and Jane are surveying their neighbors about the community garden. Their questions, written on the survey, are below:
Howard: Did you visit the garden this month?
Jane: How many times do you visit the garden in a month?
Who wrote a statistical question and why?
Jane, because there will be variability in the responses collected
Jane, because there can be only one answer to the question
Howard, because every neighbor will give the same answer
Howard, because there can be many answers to the question
According to the information, it can be inferred that Jane's question is the one that classifies as statistical because there will be variability in the answers (option A).
How to identify the statistical question?A statistical question is a type of question that is used to obtain information about a specific population and its trends or preferences.
In this case the statistical question is Jane's question because there will be variability in the answers, for example you will find that some people go to the garden once and others ten times a month.
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A ball is thrown in the air from the top of a building. Its height, in meters above ground, as a function of time, in seconds, is given by
h(t) = −4.9t(squared) + 20t + 12.
How long does it take to reach maximum height? (Round your answer to three decimal places.)
The ball takes approximately a time of 2.041 seconds to reach its maximum height.
What time does the ball take to reach maximum height?
The height of the ball as a function of time is modelled by a quadratic equation, the required information can be found by transforming the expression into vertex form:
h = - 4.9 · t² + 20 · t + 12
h = - 4.9 · (t² - 4.082 · t - 2.449)
h + (- 4.9) · (6.615) = - 4.9 · (t² - 4.082 · t + 4.166)
h - 32.414 = - 4.9 · (t - 2.041)²
The ball takes approximately a time of 2.041 seconds to reach its maximum height.
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Christine has scored 73, 85, 70, and 63 on her previous four tests. What score does she need on her next test so that her average (mean) is 73?
Answer:
74
Step-by-step explanation:
(73 + 85 + 70 + 63 + x)/5 = 73.
You find the average by adding all of the test scores and dividing that number by the number of tests. We had four test, so will will take that total, plus some mystery number (let's call it x), we divide that total by 5 because now there are 5 tests and not 4. We already know what we want the average to be, we want the average to be 73. We now have:
(291 + x)/5 = 73 Multiply both sides by 5
291 + x =365 Subtract 291 from both sides to get
x = 74
Answer: 74
Step-by-step explanation:
The mean is the average of all the values, which we find by finding the sum of each value and dividing by the total number of data points.
With 5 data points, we can use this equation to find, x, or the data point needed to obtain a mean of 73:
[tex]\frac{73+85+70+63+x}{5}=73\\ 291+x=365\\x=74[/tex]
A cylinder and a cone have the same radius and height. The volume of the
cylinder is 639 ft3. What is the volume of the cone?
You need 30 quarts of water based paint to paint the interior of a house. If the price ofa gallon of paint is $22, how much will cost the paint for the interior of the house?
please help me!! i don’t understand this like at all this is algebra btw
The length and width of the fence should be made 76.25 feet and 23.75 feet respectively. Also, the expression for the length is L = 3W + 5 and the perimeter is P = 2(4W + 5).
How to determine the fence's dimension?Mathematically, the perimeter of a rectangle can be calculated by using this formula;
P = 2(L + W)
Where:
P is the perimeter of a rectangle.L is the length of a rectangle.W is the width of a rectangle.Since the length of this fence is 5 more than 3 times the width, we have:
L = 3W + 5
Substituting the given parameters into the formula, we have;
200 = 2(3W + 5 + W)
200 = 2(4W + 5)
200 = 8W + 10
8W = 190
W = 190/8
W = 23.75 feet.
For the length, we have:
L = 3W + 5
L = 3(23.75) + 5
L = 76.25 feet.
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Geometry question! Help!
Answer: [tex]2\sqrt{2}[/tex]
Step-by-step explanation:
The inradius is given by the area of the triangle divided by the semiperimeter.
The semiperimeter is [tex]\frac{12+12+8}{2}=16[/tex].
Thus, by Heron's formula, the area is [tex]\sqrt{16(16-12)(16-12)(16-8)}=32\sqrt{2}[/tex].
Therefore, the radius is [tex]\frac{32\sqrt{2}}{16}=2\sqrt{2}}[/tex]
Rewrite without parentheses.
−6w x5 (2w³ +7w¹x² – 5x²)
-
Simplify your answer as much as possible.
0
Step-by-step explanation:
Help me am lost somewhere
Identify a pair of factors of −35 that has a sum of −2.
Answer:
-7 and 5
Step-by-step explanation:
If you multiply -7 and 5, you get -35
Add them, and you get -2.
Normandin Inc. has an unfunded pension liability of $575 million that must be paid in 20 years. To assess the value of the firm’s stock, financial analysts want to discount this liability back to the present. If the relevant discount rate is 6.8%, what is the present value of this liability?
The present value of this unfunded pension liability of $575 million in 20 years at a discount rate of 6.8% is $154,256,257.63.
What is the present value?The present value of an asset or liability refers to its future value discounted from a future period to the present period.
The present value can be computed using the PV table or formula.
We can also use an online finance calculator to determine the present value of the unfunded pension liability, as follows:
Data and Calculations:N (# of periods) = 20 years
I/Y (Interest per year) = 6.8%
PMT (Periodic Payment) = $0
FV (Future Value) = $575,000,000
Results:
PV = $154,256,257.63
Total Interest $420,743,742.37
Thus, the present value of this unfunded pension liability of $575 million in 20 years at a discount rate of 6.8% is $154,256,257.63.
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Which of the following points is in the solution set of y < x2 - 2x - 8?
The solution set of the given inequality has a domain of (-∞, ∞) and the vertex(h,k) = (1, -9)
What is the solution set for inequality?The solution set for inequality is the set of all solutions for which the inequality is defined. It can also be represented in an interval notation.
Given that:
y < x² - 2x - 8By rewriting the equation in the parabola standard form 4p(y-k) = (x - h)², we have:
[tex]\mathbf{4\times \dfrac{1}{4}(y-(-9)) = (x-1)^2}[/tex]
Therefore, the parabola properties are:
The solution set of the domain is (-∞, ∞)Vertex(h,k) = (1, -9) Focal length |p| = 1/4Learn more about the solution set of inequality here:
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c= 0.99, x= 14.6, s=0.75, n = 13
Answer:
sorry accidentally posted
Step-by-step explanation:
will update when question comes out
A theater group made appearances in two cities. The hotel charge before tax in the second city was $1500 higher than in the first. The tax in the first city was 8%, and the tax in the second city was 5%. The total hotel tax paid for the two cities was $692.50. How much was the hotel charge in each city before tax?
Step-by-step explanation:
x = hotel charge before tax in 1st city
y = hotel charge before tax in 2nd city
y = x + 1500
x×0.08 + y×0.05 = 692.5
why ?
a% of b = b×a/100
why ?
b = 100%
1% = 100%/100 = b/100
a% = a×1% = a×b/100 = b×a/100
so, e.g. 8% of something is that something multiplied by 8/100 or 0.08
now, we are using the first equation in the second equation :
x×0.08 + (x + 1500)×0.05 = 692.5
x×0.08 + x×0.05 + 1500×0.05 = 692.5
x×0.13 + 75 = 692.5
x×0.13 = 617.5
x = 617.5 / 0.13 = $4,750
y = x + 1500 = 4750 + 1500 = $6,250
the hotel charge before tax in the first city : $4,750
the hotel charge before tax in the second city : $6,250
If in a one tail hypothesis test where H0 is not only rejected in the upper tail, the oval he = 0.0739 and Zstat = + 1.45, what is the statistical decision if the null hypothesis is tested at the .10 level of significance?
What is the statistical decision?
Reject or do not reject?
Considering the p-value, the decision is described as follows:
Since the p-value is less than [tex]\alpha[/tex], we reject [tex]H_0[/tex].
What is the relation between the p-value and the conclusion of the test hypothesis?Depends on if the p-value is less or more than the significance level:
If it is more, the null hypothesis is not rejected.If it is less, it is rejected.In this problem, we have that:
The p-value is of 0.0739.The significance level is of 0.1.Hence:
Since the p-value is less than [tex]\alpha[/tex], we reject [tex]H_0[/tex].
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Given the similar hexagon-based prisms pictured below, if prism 2 has a surface area of 256 cm, what is the surface area prism 1? Hint : the ratio of surface areas is the scale factor squared.
Using the hint that the ratio of surface areas is the scale factor squared, the surface area of prism 1 is 36 square cm
How to determine the surface area prism 1 using the hint that the ratio of surface areas is the scale factor squared?From the figure, we have the following parameters
Prism 1 = 3 cm
Prism 2 = 8 cm
Calculate the scale ratio of dilation from prism 2 to prism 1 using the following equation
Scale ratio = Prism 1/Prism 2
Substitute the known values in the above equation
Scale ratio = 3m/8m
This gives
Scale ratio = 0.375
The surface area of prism 1 is then calculated using the following equation
Area of prism 2 = Scale ratio^2 * Area of prism 1
Substitute the known values in the above equation
Area of prism 2 = 0.375^2 * 256 square cm
Evaluate the product
Area of prism 2 = 36 square cm
Hence, the surface area of prism 1 is 36 square cm
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You are training to compete in a 10-kilometer race, and you know the circular running trail at
your park is one mile long. How many times will you need to run this trail in order to run 10
kilometers? (round to the nearest whole number) 1 Kilometer=0.62
.
Answer:
6.2 rounds
Step-by-step explanation:
since 1 kilometer is 0.62 miles
10 kilometers is 6.2 miles
so about 6 and 1/5 rounds
write an inequality to represent the graph:
Answer:
Step-by-step explanation:
(c) Use a calculator to verify that Σ(x) = 64, Σ(x2) = 1118, Σ(y) = 628, Σ(y2) = 87,982, and Σ(x y) = 9,627.
Compute r. (Enter a number. Round your answer to three decimal places.)
The correlation based on the computation is 0.97.
How to compute the value?It should be noted that the question is that we should simply calculate the correlation which is r.
The correlation will be:
= Σ(x y) / (Σ(x²) × Σ(y²)
= 9627/✓(1118 × 87982)
= 9627 ✓98363876
= 9627/9917.86
= 0.97
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Use the graph of the polynomial function to find the factored form of the
related polynomial. Assume it has no constant factor.
The factored form of the related polynomial is (x - 1)(x - 9)
How to determine the factored form of the related polynomial?In this question, the given parameter is the attached graph
From the graph, we can see that the curve crosses the x-axis at two different points
These points are the zeros of the polynomial function.
From the graph, the points are
x = 1 and x = 9
Set these points to 0
x - 1 = 0 and x - 9 = 0
Multiply the above equations
(x - 1)(x - 9) = 0
Remove the equation
(x - 1)(x - 9)
Hence, the factored form of the related polynomial is (x - 1)(x - 9)
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