Suppose you are completely locked out outside of your house. You remember that you left your bedroom window, which is 12 feet above the ground, unlocked from the inside (meaning you can climb up the window if you have a ladder, which you do!). You go to your garage, grab the 20 ft ladder and place it so that it reaches exactly to your bedroom window. What is the angle of elevation needed to reach your window? How far away will the bottom of the ladder be from your house?
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A diagram of the situation is shown below:
In order to determine the angle of elevation x, use the sine function, as follow:
sin x = opposite side/hypotenuse
the opposite side is the distance from the ground to the wi
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What is the domain of the function graphed below?
x<7
x_<7
-2_< X_<3
all real numbers
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The given function is defined everywhere except at x = 7 and a higher value than 7 thus x < 7 will be the domain of the function so option (A) is correct.
What is the range and domain of a function?A function's range is the set of all values that the function accepts, and its domain is the set of all values for which the function is defined.
The domain is for the independent variable while the range is for the dependent variable.
As per the given graph of the function,
The value of the function at x = -1 is -2.
In another place, the graph is not breaking before x = 7.
So, at x > 7 the function is not defined.
The domain of the function will be (-∞ ,7).
Hence "The given function is defined everywhere except at x = 7 and a higher value than 7 thus x < 7 will be the domain of the function".
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The given question is incomplete, the complete question follows with the graph below;
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?
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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.
The one-to-one function f is defined below.
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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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Find the area of the figure.A. 57 square yardsB. 66 square yardsC. 180 square yards D. 234 square yards
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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
Segment EF is rotated 90° clockwise around the origin and then translated by (-6, y + 7).
The resulting segment E" F" has coordinates E" (-4, 5), F"(-1,-2).
What are the coordinates of the segment EF?
does anyone know this??
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Answer:
E = 2,2 F = 5,-9
Step-by-step explanation:
First, you have to add (6, -7) to both coordinates (that being (-4,5)(-1,-2)
This results in E = 2,-2 and F = -5,-9
Next, you need to rotate both coordinates 90 counterclockwise, resulting in: E being (2,-2) and F being (5,-9)
Hope this helped!
5 In nahiangle Bcm. Ireos B = / 13 which function also cauals
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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.
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.
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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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Determine whether the graph represents a function.
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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
What is the range of f(x) = 3x + 9?
{y | y < 9}
{y | y > 9}
{y | y > 3}
{y | y < 3}
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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
Find the perimeter of rectangle given below and drop the appropriate expression. DRAG & DROP THE ANSWER 2s - 6 38 - 12 Perimeter = 264
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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
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.
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.
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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]
Find the solutions of the following equations in the interval [0, 2π).
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In order to solve this equation, we can first do the following steps to simplify it:
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.
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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]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
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.
a. 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?
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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]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
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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.]
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.
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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
212385758487✖️827648299199375
Answers
Answer:
1.7578071e+26
Step-by-step explanation:
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]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?
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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 meetingwhat 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
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
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]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
Eliminate the y in the following system of equations. What is the result when you add the two equations? [tex]x + y = 8 \\ 5x - 3y = 24[/tex]A: 6x = 32B: 8x = 32 C: x = 0D: 8x = 48
Answers
EXPLANATION
x + y = 8 ----------------------------------------(1)
5x - 3y = 24 ------------------------------------------(2)
If we are to eliminate y in the equations, we first need to multiply through equation (1) by 3.
3x + 3y = 24 ----------------------------------------(3)
Add equation (2) and equation (3).
If we add equation(1) and equation(3) together, -3y will cancel-out 3y.
(5x + 3x) = (24 + 24)
8x = 48
Therefore, the correct option is D. 8x = 48
A ball is thrown from an initial height of 1 meter with an initial upward velocity of 7 m/s. The balls height h (in meters) after t seconds is given by the following. h=1+7t-5t^2Find all values of t for which the balls height is 2 meters.Round the answer(s) to the nearest hundredth
Answers
Solution
To find the values of t for which the ball's height is 2 meters
we set h = 2
=> 2 = 1 + 7t - 5t^2
=>5t^2 - 7t + 1 = 0
Using the quadratic formula,
[tex]\begin{gathered} t=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ \\ \Rightarrow t=\frac{7\pm\sqrt{\left(-7\right)^2-4\left(5\right)\left(1\right)}}{2\cdot5} \\ \\ \Rightarrow t=1.24s\text{ or }0.16s \end{gathered}[/tex]Therefore, t = 1.23s or 0.16s
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
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.