in the figure below, when the sun angle of elevation is 50°, the tree casts a shadow 80 feet long which can be used to find the height of the tree?
Answers
We can use the tangent of 50º. The height is approximately 95.34 ft
1) We can trace a right triangle over that mark and calculate that height, using a trigonometric ratio.
2) As we have the adjacent leg to that 50º angle and the opposite leg, we can use the tangent of 50º to find that height out.
[tex]\begin{gathered} \tan (50)=\frac{x}{80} \\ x=80\cdot\tan (50) \\ x\approx\text{ 95.34} \end{gathered}[/tex]3) Hence the answer is
We can use the tangent of 50º. The height is approximately 95.34 ft
Related Questions
Determine whether the graph represents a function.
Answers
A, the relation is not a function
in order for something to be a function, x (the input) can't repeat itself more than once
A rectangle has a length of 9 inches and a widt of 5 inches whose sides are changing. The length is increasing by 3 in/sec and the width is shrinking at 9 in/sec. What is the rate of change of the perimeter?
Answers
Given:
A rectangle has a length of 9 inches and a width of 5 inches whose sides are changing. The length is increasing by 3 in/sec and the width is shrinking at 9 in/sec.
To find:
The rate of change of the perimeter.
Solution:
It is known that the perimeter of the rectangle is twice the sum of length and width.
[tex]P=2(l+w)[/tex]DIfferentiate the perimeter with respect to t:
[tex]\frac{dP}{dt}=2(\frac{dl}{dt}+\frac{dw}{dt})[/tex]From the given information:
[tex]\begin{gathered} \frac{dP}{dt}=2(3-9) \\ =2(-6) \\ =-12 \end{gathered}[/tex]Thus, the perimeter of the rectangle is decreasing at the rate of 12 inches per second.
if a certain number is added to the numerator and denominator of 9/13 the result is 9/11. find the number
Answers
We have the following:
When they tell us a certain number, we will assume a value x.
This number is added to the numerator and denominator of the fractional number 9/13 and gives us the result 9/11.
it is as follows
[tex]\frac{x+9}{x+13}=\frac{9}{11}[/tex]solving for x:
[tex]\begin{gathered} \frac{x+9}{x+13}=\frac{9}{11} \\ 11\cdot(x+9)=9\cdot(x+13) \\ 11x+99=9x+117 \\ 11x-9x=117-99 \\ 2x=18 \\ x=\frac{18}{2}=9 \end{gathered}[/tex]Therefore, the certain number is 9
Solve the quadratic equation by using the quadratic formula. If the solutions are not real, enter NA. 3x2−5x+1=0 Enter the exact answers.
Answers
The given quadratic equation is,
[tex]3x^2-5x+1=0[/tex]let us use the formula,
[tex]\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]where,
[tex]\begin{gathered} a=3 \\ b=-5 \\ c=1 \end{gathered}[/tex]subistute the values in the formula,
[tex]\begin{gathered} =\frac{-(-5)\pm\sqrt[]{(-5)^2-4\times3\times1}}{2\times3} \\ =\frac{5\pm\sqrt[]{25-12}}{6} \\ =\frac{5\pm\sqrt[]{13}}{6} \\ x=\frac{5+\sqrt[]{13}}{6},x=\frac{5-\sqrt[]{13}}{6} \end{gathered}[/tex]The roots of the quadratic equation are ,
[tex]x=\frac{5+\sqrt[]{13}}{6},x=\frac{5-\sqrt[]{13}}{6}[/tex]In a test of the effectiveness of garlic for lowering cholesterol, 48 subjects were treated with garlic in a processed tablet form. Cholesterol levels were measured before and after the treatment. The changes (before−after) in their levels of LDL cholesterol (in mg/dL) have a mean of 5.3 and a standard deviation of 19.6. Construct a 95% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment. What does the confidence interval suggest about the effectiveness of garlic in reducing LDL cholesterol?
Answers
1) The 95% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment is 5.3 ± 5.6.
2) Regarding the effectiveness of garlic in reducing LDL cholesterol, the confidence interval suggests A. The confidence interval limits contain 0, suggesting that the garlic treatment did not affect the LDL cholesterol levels.
What is the confidence interval estimate?The confidence interval estimate shows us the mean estimate plus or minus the margin of error (or variation in the estimate).
On the other hand, the margin of error is the difference between the actual and projected results in a random sample.
The number of subjects treated with garlic, n = 48
The mean changes in LDL cholesterol level = 5.3
The standard deviation = 19.6
The 95% confidence interval gives a Z-score of 1.96
The margin of error = Z-score x standard deviation/√n
= 1.96 x 19.6/√48
= 1.96 x 19.6/6.9
= 1.96 x 2.84
= 5.6
Lower Limit = Mean - Margin of Error
= 5.3 - 5.6
= -0.3
Upper Limit = Mean + Margin of Error
= 5.3 + 5.6
= 10.9
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Question Completion with Answer Options:2. What does the confidence interval suggest about the effectiveness of garlic in reducing LDL cholesterol?
A.The confidence interval limits contain 0, suggesting that the garlic treatment did not affect the LDL cholesterol levels.
B.The confidence interval limits do not contain0, suggesting that the garlic treatment did affect the LDL cholesterol levels.
C.The confidence interval limits do not contain0, suggesting that the garlic treatment did not affect the LDL cholesterol levels.
D.The confidence interval limits contain 0, suggesting that the garlic treatment did affect the LDL cholesterol levels.
what is the slope of any line is perpendicular to the equation y=1/2x-7
Answers
The slope = -2
Explanations:The given equation is:
[tex]y\text{ = }\frac{1}{2}x\text{ - 7}[/tex]This is of the form y = mx + c
where the slope, m = 1/2
The equation perpendicular to the equation y = mx + c is:
[tex]y-y_1=\frac{-1}{m}(x-x_1)[/tex][tex]\begin{gathered} \text{The slope = }\frac{-1}{m} \\ \text{The slope = }\frac{-1}{\frac{1}{2}}=\text{ -2} \end{gathered}[/tex]The slope = -2
The one-to-one function f is defined below.
Answers
The inverse function of the relation is f-1(x) = 5x/(7x -6), while the domain and the range are x < 6/7 or x > 6/7 and f(x) < 5/7 or f(x) > 5/7, respectively
How to determine the inverse function?The definition of the function is given as
f(x) = 6x/7x - 5
Rewrite the function as
y = 6x/7x - 5
Next, we swap or switch the variables x and y
So, we have the following equation
x = 6y/7y - 5
Cross multiply in the above equation
This gives
x(7y - 5) = 6y
Open the brackets
7xy - 5x = 6y
Collect the like terms
7xy -6y = 5x
Factor out y
y(7x -6) = 5x
So, we have
y = 5x/(7x -6)
Express as inverse function
f-1(x) = 5x/(7x -6)
Using a graphing calculator, we have
Domain: x < 6/7 or x > 6/7
Range: f(x) < 5/7 or f(x) > 5/7
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a motorboat travels 456 km in 8 hours going upstream and 783 km in 9 hours going downstream. what is the rate of the boat in still water and what is the rate of current?
Answers
Complete the following proof
Given: = 3(5x + 1) = 13x + 5
Prove: x = 1
Answers
Solving the Question
[tex]3(5x + 1) = 13x + 5[/tex]
Plug in x=1:
[tex]3(5(1) + 1) = 13(1) + 5\\3(5 + 1) = 13 + 5\\3(6) = 18\\18=18[/tex]
This statement is true.
Find the perimeter of rectangle given below and drop the appropriate expression. DRAG & DROP THE ANSWER 2s - 6 38 - 12 Perimeter = 264
Answers
1) In order to determine the perimeter of the figure, you take into account tht the perimeter is the sum of the values of all sides of a figure.
In this case, the sides of the triangle are s-4, s-8, and 6 respectivelly.
The perimer is the sum of the values of the sides, then, you have:
P = (s-4)+(s-8)+(6) "P is the perimeters"
= s-4+s-8+6 "sum simmilar terms, terms with variables and idependet term"
= 2s-6
Hence, the perimeter of the triangle is 2s - 6
2) The perimeter of a rectangle is P = 2w + 2l, in order to solve for w you proceed as follow:
P = 2w + 2l "subtract 2l both sides"
P - 2l = 2w "divide by 2 both sides"
(P - 2l)/2 = w
Hence, w = (P - 2l)/2
Right Triangle ABC is pictured below.Which equation gives the correct value for BC?Option 1: sin(32) = BC/8.2Option 2: cos(32) = BC/10.6Option 3: tan(58) = 8.2/BCOption 4: sin(58) = BC/10.6
Answers
Given the image, we are asked which equation gives the correct value for BC?
Explanation
From the image;
[tex]\begin{gathered} A+B+C=180 \\ 32+B+90=180 \\ B=180-90-32 \\ B=58^0 \end{gathered}[/tex]Therefore,
[tex]tan58^0=\frac{opposite}{Adjacent}=\frac{8.2}{BC}[/tex]Answer: Option three
Translate the sentence into an equationThe difference of Mai’s height and 13 is 53Use a variable M to represent Mai’s height
Answers
The difference in math means the result of subtracting one number from another.
m = Mai’s height
Therefore, the equation is:
[tex]m-13\text{ = 53}[/tex]What is the range of f(x) = 3x + 9?
{y | y < 9}
{y | y > 9}
{y | y > 3}
{y | y < 3}
Answers
The range of f(x) = 3x + 9
{y | y > 9}, Option B
This is further explained below.
What is the range?Generally, Based on the possibilities that have been presented to us, we may speculate that x is inside the exponent of 3.
Therefore, the formula for the function f(x) is really f(x) = 3x +9
Now that we have a function, we need to determine its range of values.
It is clear that the first component is an exponential term denoted by 3x, and that the second term is the number 9.
It is common knowledge that the product 3x will always be higher than 0.
As a result, the result of adding 3x to 9 will always be more than 9.
As a result, the range would be y more than 9.
In conclusion, option B "y | y > 9" is the range
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Answer: B
Step-by-step explanation: Trust
Use percents to find price of each set of items.(1) You purchase one pair of jeans, 2 hoodies and 3 t-shirts. what is the Total cost with no Sale? You purchase the same items but now you receive a 40% off coupon, How much is your total including the discount?
Answers
We can multiply the number of items by the price of each item to find the total cost:
[tex]\begin{gathered} C=C_{jeans}+C_{hoodies}+C_{shirts}=1\cdot25+2\cdot30+3\cdot8 \\ C=25+60+24 \\ C=109 \end{gathered}[/tex]The total cost is $109.
If we have a 40% discount, we have to substract it from the total cost.
The discount is equal to 40% of the total cost, so we can calculate the discount as:
[tex]D=\frac{40}{100}\cdot C=0.4\cdot109=43.60[/tex]Then, we will pay a total cost with discount of:
[tex]C^{\prime}=C-D=109-43.60=65.40[/tex]The total including the discount is $65.40.
NOTE: we could also have calculated it as 109*(1-0.4)=109*0.6=65.40.
What is your answer? estion 3 Why is this your answer? 60 40 20 Which is the correct answer? 4 5 6 Time (seconds) Why is this the correct answer? statement is TRUE about the motion of this object as shown in the graph? The object was accelerating from t = 1 tot = 3 The object was slowing down from t = 4.5 to t= 6. © The object returned to its original location by t = 6 seconds. The object was traveling at a constant speed from t = 3 to t = 45 seconds
Answers
As we can see in the graph the object returned to its original position in t=6.
It's not accelarating because acceleration is the second derivate of the position, and the position is determined by a linear equation.
The answer is C.
What is the value of 7C4?A). 35B). 840C). 2,520D). 5,040
Answers
Answer:
A) 35
Explanation:
The combination nCx can be calculated as:
[tex]\text{nCx}=\frac{n!}{x!(n-x)!}[/tex]Where n! = n(n-1)(n-2)...(2)(1)
So, to find 7C4, we need to replace n by 7 and x by 4 to get:
[tex]7C4=\frac{7!}{4!(7-4)!}=\frac{7!}{4!(3)!}[/tex]Therefore, 7C4 is equal to:
[tex]7C4=\frac{7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1}{(4\cdot3\cdot2\cdot1)(3\cdot2\cdot1)}=\frac{5040}{24(6)}=\frac{5040}{144}=35[/tex]So, the answer is:
A) 35
Find the solutions of the following equations in the interval [0, 2π).
Answers
In order to solve this equation, we can first do the following steps to simplify it:
Domingo had 250 baseball cards, andJennifer had 82 baseball cards. At thefirst meeting of the Card Club and atevery meeting thereafter, Domingo sold12 cards to Jennifer. After which meetingdid the two have the same numberof cards?
Answers
Data:
Domingo: D
Jennifer: J
Initial number of cards:
D=250
J=82
After each meeting(m):
D=250-12m
J=82+12m
After the first meeting: m=1
[tex]D=250-12(1)=238[/tex][tex]J=82+12(1)=94[/tex]You increase in 1 the m after each meeting and get the next table:
Then, they have the same number of cards after 7th meetinga. A company has a policy of retiring company cars; this policy looks at number of miles driven, purpose of trips, style of car and other features. The distribution of the number of months in service for the fleet of cars is bell-shaped and has a mean of 45 months and a standard deviation of 3 months. Using the empirical rule (as presented in the book), what is the approximate percentage of cars that remain in service between 48 and 51 months?b. The physical plant at the main campus of a large state university recieves daily requests to replace fluorescent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 64 and a standard deviation of 7. Using the empirical rule (as presented in the book), what is the approximate percentage of lightbulb replacement requests numbering between 57 and 64?
Answers
In this case
[tex]\begin{gathered} 48=45+3 \\ 51=45+2(3) \end{gathered}[/tex]Therefore, the percentage that lies between 45 and 48 is given by
[tex]\frac{68}{2}=34\text{ \%}[/tex]And, the percentage that lies between 45 and 51 is given by
[tex]\frac{68}{2}=34\text{ \%}[/tex]Tyrone's car can travel about 30 miles for each gallon
of gas.
Using d for distance traveled in miles and g for
gallons of gas, write two different equations relating d
and g.
Answers
The equation can be written as d=30g
What is an equation?
An equation can be compared to a scale on which objects are weighed. When the two pans are filled with the same amount of anything (like grain), the scale will balance and the weights will be considered equal. To maintain the scale in balance, if any grain is taken out of one of the balance's pans, an equal amount must be taken out of the other pan. More broadly, if the identical operation is carried out on both sides of an equation, the equation remains in balance. Equations are used to describe geometric shapes in Cartesian geometry. The goal has changed since the equations under consideration, such as implicit equations or parametric equations, contain an unlimited number of solutions.
Tyrone's car can travel about 30 miles for each gallon
So, the equation can be written as d=30g, where d is distance travelled and g is gallons of gas used.
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Kindly help with these questions.
Answers
because the constant relationship between the x and y coordinates makes the point go through the origin and makes a straight line.
The answer of the second question is k
X is the x coordinate
Y is the y coordinate
so, K is the constant of proportionality.
John owes $25.20 to his mom. He borrowed $27.60 from his dad. Howmuch does he owe in all? Write your answer as a rational number *
Answers
John owes to his Mom and Dad.
From Mom = 25.20
From Dad = 27.60
The total amount he owes is the sum of both. We just add both the amounts.
Total: 25.20 + 27.60 = $52.80
Geo help please The price of an item has been reduced by 5% the original price was $60 what is the price of the item now
Answers
To answer this question, we can proceed as follows:
1. The original price of the item was $60.
2. If the price of this item has been reduced by 5%, we need to find the 5% of the original price as follows:
[tex]5\%=\frac{5}{100}\Rightarrow5\%(\$60)\Rightarrow\frac{5}{100}\cdot\$60=\frac{\$300}{100}=\$3[/tex]3. Therefore, the price of the item now is:
[tex]P_{\text{item}}=\$60-\$3=\$57[/tex]In summary, the price of the item now is $57.
[From the question, we have that the words "reduced by" imply a subtraction.]
Where may estimation of decimals be useful in every-day life? Give an example
Answers
You can use decimal numbers (those numbers that have a comma after an interger part and before the decimal part)
You can use decimal numbers in real life in measures as:
Examples:
weight (you can weight 132,27 lb)
volumen of soda (you can drink a glass of soda of 8,45 oz = 0,25 L)
The temperature ( the temperature can be 89,9 F)
All the examples above have decimal number that can be useful in every-day life.
18. What is the probability of drawing a BLACK card with an odd number OR a card with a LETTER?A.21261B..ع1726p D. 13
Answers
Let:
A = Draw a black card
B = Draw and odd number
C = Draw a card with a letter
so:
[tex]\begin{gathered} P(A\cap B)=\frac{8}{52}=\frac{2}{13} \\ P(C)=\frac{16}{52}=\frac{4}{13} \end{gathered}[/tex]Therefore:
[tex]P((A\cap B)\cup C)=\frac{2}{13}+\frac{4}{13}=\frac{2+4}{13}=\frac{6}{13}[/tex]5 In nahiangle Bcm. Ireos B = / 13 which function also cauals
Answers
Given data:
The given measurement of angle C is 90 degrees.
The given value of cos(B) =5/13.
The sum of all angles of triangle is,
[tex]\begin{gathered} \angle A+\angle B+\angle C=180^{\circ} \\ \angle A+\angle B+90^{\circ}=180^{\circ} \\ \angle A+\angle B=90^{\circ} \\ \angle B=90^{\circ}-\angle A \end{gathered}[/tex]Substitute the above value in the given expression.
[tex]\begin{gathered} \cos (90^{\circ}-A)=\frac{5}{13} \\ \sin A=\frac{5}{13} \end{gathered}[/tex]Thus, the correct answer is sin(A), so the third option is correct.
212385758487✖️827648299199375
Answers
Answer:
1.7578071e+26
Step-by-step explanation:
How much will it cost to buy a low fence to put all the way around the bed? The fencing material costs $0.59 per foot and can only be bought in whole numbers of feet.
Answers
To find the cost we first need to know how many feet of fence we need. To do this we add all the lengths of the sides:
[tex]6+6+8.5=20.5[/tex]Now, since we can only buy whole numbers of feet we need to buy 21 feets of fence, then the total cost is:
[tex]21\cdot0.59=12.39[/tex]Therefore the cost will be $12.39
Find the area of the figure.A. 57 square yardsB. 66 square yardsC. 180 square yards D. 234 square yards
Answers
We would section the figure into two shapes as shown below
We can see a trapezium and a rectangle. We would find the area of each figure and add them.
For the trapezium,
Area = 1/2 * (a + b)h
a nd b are the opposite sides of the trapezium while h represents the height.
Thus,
a = 20, b = 24 and h = 9es of the trapezium while h represents the height.
Thu sid
In a third day of randomly selected subjects, the mean age of the 36 respondents is 40 years and the standard deviation of ages is 10 years. Use the sample results to construct a 95% confidence interval estimate of the mean age of the population from which the sample was selected. Repeat the previous problem assuming that the population standard deviation is known to be six years.
Answers
a. Given that:
- The mean age of the 36 respondents is 40 years.
- The standard deviation of ages is 10 years.
You need to construct a 95% confidence interval estimate of the mean age of the population from which the sample was selected.
Then, you need to use this formula:
[tex]x\pm z\cdot\frac{\sigma}{\sqrt{n}}[/tex]Where "x" is the sample mean, "z" is the confidence level value, "n" is the sample size, and σ is the standard deviation.
In this case:
[tex]\begin{gathered} x=40 \\ \sigma=10 \\ n=36 \end{gathered}[/tex]Therefore, by substituting values into the formula:
[tex]40\pm\frac{10}{\sqrt{36}}[/tex]You get these two values:
[tex]40+\frac{10}{\sqrt{36}}\approx41.67\text{ }[/tex][tex]40-\frac{10}{\sqrt{36}}\approx38.33[/tex]b. If you assume that:
[tex]\sigma=6[/tex]You get the following values by substituting them into the formula:
[tex]40+\frac{6}{\sqrt{36}}=41[/tex][tex]40-\frac{6}{\sqrt{36}}=39[/tex]Hence, the answers are:
a.
[tex](38.33,41.67)[/tex]b.
[tex](39,41)[/tex]