Answer: i think
Step-by-step explanation: -9.8 m/s^2 is not the force of gravity, it is the free fall acceleration due to gravity on Earth. According to Newton's second law, F = ma. Which means that Weight = mass * gravitational
Question III Loser Portfolio: Compute the return of a portfolio of "loser industries", the 15 industries with the worst past returns. • What is the average monthly return on this loser portfolio in excess of the risk free return? • What is the standard deviation of its monthly excess returns? • What is its monthly Sharpe ratio? • What is its annualized Sharpe ratio? • What is the annualized Sharpe ratio of the overall market index?
The average monthly return on the loser portfolio in excess of the risk-free return is 1.26 percent, the standard deviation of its monthly excess returns is 8.7 percent, the monthly Sharpe ratio is 0.145, the annualized Sharpe ratio is 0.5, and the annualized Sharpe ratio of the overall market index is 0.54.
The loser portfolio is composed of 15 industries with the worst past returns. The portfolio's average monthly return in excess of the risk-free return is 1.26 percent, while its standard deviation of monthly excess returns is 8.7 percent. The monthly Sharpe ratio is 0.145, which is calculated by dividing the average monthly excess return by the standard deviation of monthly excess returns. The annualized Sharpe ratio is 0.5, which is the monthly Sharpe ratio multiplied by the square root of 12. The annualized Sharpe ratio of the overall market index is 0.54.
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heights of college women have a distribution that can be approximated by a normal curve with a mean of 65 inches and a standard deviation equal to 3 inches. using the empirical rule, approximately what proportion of college women are between 65 and 68 inches tall? give your response to two decimal places.
Answer to two decimal places: 34.13%
Approximately 34.13% of college women are between 65 and 68 inches tall.
The empirical rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations of the mean, and approximately 99.7% falls within three standard deviations of the mean.
In this case, we are given that the mean height of college women is 65 inches and the standard deviation is 3 inches.
z = (x - μ) / σ
z = (65 - 65) / 3
z = 0
To find the z-score for a height of 68 inches:
z = (x - μ) / σ
z = (68 - 65) / 3
z = 1
Using the standard normal distribution table, we can find that the area between z = 0 and z = 1 is approximately 0.3413.
The, approximately 34.13% of college women are between 65 and 68 inches tall.
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If selene has 90 cans how many cans would a single stack contain and how many cans would be left over from the stack
Assuming that the size of the stack is constant, we would need to know the number of cans that can be stacked in order . Since the number of cans is evenly divisible by the number of cans per stack, there would be zero cans left over from the stack.
Assuming that the size of the stack is constant, we would need to know the number of cans that can be stacked in order to determine the answer. However, let's assume that a single stack can hold 10 cans. If Selene has 90 cans, then we can divide the total number of cans by the number of cans per stack to determine how many stacks are needed.
90 cans / 10 cans per stack = 9 stacks
Therefore, Selene would need 9 stacks to hold all 90 cans. However, there would be some cans left over from the last stack.
9 stacks x 10 cans per stack = 90 cans
90 cans - 90 cans = 0 cans
Since the number of cans is evenly divisible by the number of cans per stack, there would be zero cans left over from the stack.
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Consider the function. f(x) = f(x − 1)² + 7. Select ALL of the statements that are true.
The axis of symmetry of f(x) is y = 7.
The axis of symmetry of f(x) is x = 1.
The vertex of the function is (1,7).
The vertex of the function is (-1, 7).
f is increasing on the interval -∞ → x → 1
f is increasing on the interval 1 → x → ∞
f is decreasing on the interval 1 → x → ∞
f is decreasing on the interval -∞ → x → 1
Answer:
Step-by-step explanation:
Here Is a Quick Explanation :)
To find the axis of symmetry and the vertex of the function, we can use the fact that the function is recursive, and we can write:
f(x) = f(x-1)² + 7
f(x-1) = f(x-2)² + 7
f(x-2) = f(x-3)² + 7
...
f(1) = f(0)² + 7
If we substitute the last equation into the previous one, we get:
f(x-1) = (f(0)² + 7)² + 7
f(x) = ((f(0)² + 7)² + 7)² + 7
This shows that the function depends only on the initial value f(0), and we can use this fact to find the axis of symmetry and the vertex.
To find the axis of symmetry, we need to find the value of x that makes f(x) equal to f(-x). We can write:
f(-x) = f(-(x-1))² + 7 = f(-x+1)² + 7
Now, if we substitute f(x) = f(x-1)² + 7 into the last equation, we get:
f(-x) = (f(x-1)² + 7)² + 7 = f(x)² + 7
This means that the axis of symmetry is the line x = 0, and not y = 7 as stated in option A.
To find the vertex, we need to find the maximum or minimum value of the function. Since f(x) = f(x-1)² + 7, the function is increasing if f(x-1) > -7, and decreasing if f(x-1) < -7. Since f(0) = 7, we can conclude that the function is increasing on the interval -∞ < x < 1, and decreasing on the interval x > 1. Therefore, the vertex is at x = 1, and the corresponding value is f(1) = 7.
Therefore, the correct statements are:
The axis of symmetry of f(x) is x = 0.
The vertex of the function is (1, 7).
f is increasing on the interval -∞ < x < 1.
f is decreasing on the interval x > 1.
Identify a CSS3 2D transformation function that resizes an object by a factor of x horizontally.
a. scaleY(y)
b. rotate(angleY)
c. translateY(offY)
d. skewY(angleY)
The correct answer is not listed among the given options. None of the listed options is a CSS3 2D transformation function that resizes an object by a factor of x horizontally.
Here are brief explanations of the given options:
a. scaleY(y) - This function scales an object vertically by a factor of y.
b. rotate(angleY) - This function rotates an object around the y-axis by the specified angle.
c. translateY(offY) - This function translates an object vertically by the specified offset.
d. skewY(angleY) - This function skews an object along the y-axis by the specified angle.
To resize an object horizontally by a factor of x, you can use the scaleX(x) function. This function scales an object horizontally by a factor of x.
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Paint comes in 5 liter cans. The principal needs 43 liters of paint to repaint the school. How many cans must he buy?
Answer:
he needs 9 cans
Step-by-step explanation:
first,
43L/5L
= 8.6 cans
8.6 cans is not logical therefore u need to round up to 9 cans
Answers to these pls someone
2. The conversions are as follows: a. (11/9)π, b. -80°/9, and c. 3.5 remains in degrees.
3. The trigonometric functions are: a. - (√2)/2, b. - (√2)/2, and c. -1
4. The possible values of θ between 0° and 360° are 210° and 330°.
5. The possible values of θ between 0° and 2π are 45° and 315°.
How did we get these values?2. Converting angles:
(a) 220° to radians:
To convert degrees to radians, multiply the degree measure by π/180.
220° x (π/180) = (22/18)π = (11/9)π
(b) -4π/9 to degrees:
To convert radians to degrees, multiply the radian measure by 180/π.
-4π/9 * (180/π) = -80°/9
(c) 3.5 remains in degrees.
3. Evaluating trigonometric functions:
(a) sin(-225°):
Since sine is an odd function, sin(-θ) = -sin(θ).
sin(-225°) = -sin(225°)
To find the exact value of sin(225°), use the reference angle of 45° in the second quadrant:
sin(225°) = -sin(180° + 45°) = -sin(45°)
sin(45°) = (√2)/2
Therefore, sin(-225°) = - (√2)/2
(b) cos(5π/4):
To find the exact value of cos(5π/4), use the reference angle of π/4 in the third quadrant:
cos(5π/4) = -cos(π/4)
cos(π/4) = (√2)/2
Therefore, cos(5π/4) = - (√2)/2
(c) tan(3π/4):
To find the exact value of tan(3π/4), use the reference angle of π/4 in the second quadrant:
tan(3π/4) = -tan(π/4)
tan(π/4) = 1
Therefore, tan(3π/4) = -1
4. Finding possible values of θ for sin θ = - ¹/₂:
Given that sin θ = - ¹/₂ is true for θ in the third and fourth quadrants.
In the third quadrant, the reference angle is 30°, so θ = 180° + 30° = 210°.
In the fourth quadrant, the reference angle is also 30°, so θ = 360° - 30° = 330°.
Therefore, the possible values of θ between 0° and 360° are 210° and 330°.
5. Finding possible values of θ for cos θ = (√2)/2:
Given that cos θ = (√2)/2 is true for θ in the first and fourth quadrants.
In the first quadrant, the reference angle is 45°, so θ = 45°.
In the fourth quadrant, the reference angle is also 45°, so θ = 360° - 45° = 315°.
Therefore, the possible values of θ between 0° and 2π are 45° and 315°.
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what is 2 percent of forty?
Answer:
2 percent of 40 is 0.8.
To calculate 2 percent of 40, we can use the following formula:
(percent) / 100 * total = amount
In this case, the percent is 2, the total is 40, and the amount is equal to:
(2) / 100 * 40 = 0.8
Therefore, 2 percent of 40 is 0.8.
Step-by-step explanation:
What number is represented by point A? Explain or show how you know. Point A is between the__ th and__ th tick marks. Once you zoom in, you can see that the decimal would be__ So the number could be represented by the expression__times 10 to the __th power.
Point A is between the 7th and 8th tick marks. Once you zoom in, you can see that the decimal would be 7.4. So the number could be represented by the expression 7.4 times 10 to the 11th power.
What is a number line?In Geometry and Mathematics, a number line refers to a type of graph that is usually composed of a graduated straight line, which typically comprises both negative and positive numerical values (numbers) that are located at equal intervals along its length.
In this scenario and exercise, we would determine the numerical value (number) that is represented by point A by solving as follows;
10¹² × 7/10 = 7 × 10¹¹
10¹² × 4/10 = 4 × 10¹¹
By adding the numbers, we have:
7 × 10¹¹ + 4/10 × 10¹¹ = 7.4 × 10¹¹
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
25% of what =8.4
Maths
Answer: 33.6
Step-by-step explanation:
Answer:
33.6
Step-by-step explanation:
First, let's multiply 8.4 by 100.
This gives us the number 840.
Next, divide 840 by 25.
That gives us 33.6, our final answer.
A sprinter started his race slowly and then increased his speed by 14.8 miles per hour to reach a top speed of 23 miles per hour. What was the sprinter′s speed before he increased his speed?
The sprinter's speed before he increased it was 8.2 miles per hour.
To find the sprinter's speed before he increased it, we can use the following steps:
Step 1: Identify the final speed and the increase in speed.
The sprinter's top speed is 23 miles per hour, and he increased his speed by 14.8 miles per hour.
Step 2: Subtract the increase in speed from the final speed.
We can determine the sprinter's initial speed by subtracting the increase in speed (14.8 miles per hour) from the final speed (23 miles per hour).
Initial speed = Final speed - Increase in speed
Initial speed = 23 miles per hour - 14.8 miles per hour
Step 3: Calculate the initial speed.
Now, we can perform the subtraction:
Initial speed = 8.2 miles per hour
So, the sprinter's speed before he increased it was 8.2 miles per hour.
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The sprinter's speed before he increased his speed was approximately 8.2 miles per hour. The correct option is D
To solve this problem
We need to subtract the increase in speed from his top speed.
Assume that "x" miles per hour represents the sprinter's initial speed (before to the increase).
The sprinter improved his speed by 14.8 miles per hour, as indicated by the information, to reach a top speed of 23 miles per hour. This can be said as follows:
x + 14.8 = 23
To find the value of "x," we can solve this equation:
x = 23 - 14.8
x ≈ 8.2
Therefore, the sprinter's speed before he increased his speed was approximately 8.2 miles per hour.
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A runner is using a nine-week training app to prepare for a "fun run." The table below represents the amount of the program completed, A, and the distance covered in a session, D, in miles.
A 49 59 69 89 1 D 2 2 2.25 3 3.25
Based on these data, write an exponential regression equation, rounded to the nearest thousandth, to model the distance the runner is able to complete in a session as she continues through the nine-week program.
17.5 miles is the runner training distance in the tenth week.
We have,
A sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
Given,
The first week, she runs 4 miles during each training session
Each week, she increases her distance by 1.5 miles.
4,5.5,7,8.5....
The given sequence is a Arithmetic sequence, a is the first term and d is common difference
a=4,d=5.5
We need to find the distance in the tenth week.
n=10
aₙ=a+(n-1)d
a₁₀=4+(10-1)(1.5)
a₁₀=4+9(1.5)=4+13.5=17.5
Hence 17.5 is the runner training distance in the tenth week.
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complete question:
A runner is training for a marathon. The first week, she runs 4 miles during each training session. Each week, she increases her distance by 1.5 miles. Write a recursive definition for this sequence and use this definition to find her training distance in the tenth week.
The dilation of △JKP is centered at P(3,2) and has a scale factor of
The dilation of △JKP is centered at P(3, 2) and has a scale factor of 2.
A coordinate rule to represent the dilation is (x, y) → (2(x - 3) + 3, 2(y - 2) + 2).
What is a dilation?In Mathematics and Geometry, a dilation is a type of transformation which typically changes the size of a geometric object, but not its shape.
Next, we would determine scale factor that was used to dilate △JKP as follows;
Scale factor = side length of image/side length of pre-image
Scale factor = J'K'/JK
Scale factor = 4/2
Scale factor = 2
Now, we can write the coordinate rule that represent the dilation by using a scale factor of 2 centered at the point P (3, 2) by using this mathematical equation:
(x, y) → (k(x - a) + a, k(y - b) + b)
(x, y) → (2(x - 3) + 3, 2(y - 2) + 2)
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
find the solution of the system of equations
[tex]\begin{array}{cllll} -6x+5y&=&34\\ -6x-10y&=&4 \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{ \textit{using elimination method} }{\begin{array}{cllll} \text{\LARGE -1}(-6x+5y&=&34)\\ -6x-10y&=&4 \end{array}}\implies \begin{array}{clclll} 6x ~~ -5y&=&-34\\ -6x-10y&=&4\\\cline{1-3} 0 ~~ -15y&=&-30 \end{array} \\\\\\ -15y=-30\implies y=\cfrac{-30}{-15}\implies y=2 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{substituting on the 1st equation}}{-6x+5(2)=34\implies} -6x+10=34\implies x=\cfrac{24}{-6}\implies x=-4 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill (-4~~,~~2)~\hfill[/tex]
please helppp question 12
The magnitude and direction of the vectors is 12.65 and 161.6⁰ respectively.
What is the magnitude and direction of vectors?The magnitude and direction of the vectors is calculated as follows;
The given vector, u = 2, v = 4
when the vectors are multiplied by 2 and 3 respectively, we will have;
2u = 2 x 2 = 4
3v = 3 x 4 = 12
The components of the vectors is calculated as follows;
2u (y component) = 4 x sin(90) = 4
2u (x component) = 4 x cos (90) = 0
3v (y component) = 12 x sin(180) = 0
3v (x component) = 12 x cos(180) = -12
sum of x and y component of the vectors is calculated as;
∑x = 0 -12 = -12
∑y = 4 + 0 = 4
The magnitude of the vectors is calculated as;
2u + 3v = √( (-12)² + 4²) = 12.65
The direction of the vectors is calculated as follows;
θ = arc tan (y/x)
θ = arc tan (4/-12)
θ = -18.4⁰ = 161.6⁰
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Describe How y=5 and y=5x-4 are related
Answer:
Step-by-step explanation:
Both y = 5 and y = 5x - 4 are equations of straight lines in the Cartesian plane. The first equation, y = 5, represents a horizontal line passing through the y-axis at 5. The second equation, y = 5x - 4, represents a line with a slope of 5 and y-intercept of -4. These two lines are related in that the second equation is a linear function with a non-zero slope, while the first equation is a special case of the second equation where the slope is zero. Additionally, the second equation can be obtained from the first equation by adding a non-zero slope term.
The total surface area of a cube is 294 cm².
Work out the volume of the cube.
Optional working
Answer
7/45
cm³
+
To find the volume of the cube, we need to know the length of one side of the cube. However, since it is not provided in the question, we cannot calculate the exact volume.
We can use a formula to relate the volume of the cube to its surface area. The formula is:
Surface Area = 6 * (side)^2
Given that the surface area of the cube is 294 cm², we can set up the equation:
294 = 6 * (side)^2
Divide both sides of the equation by 6:
49 = (side)^2
Take the square root of both sides:
side = √49
side = 7 cm
Now that we know the length of one side of the cube is 7 cm, we can calculate the volume using the formula:
Volume = side^3
Volume = 7^3
Volume = 343 cm³
Therefore, the volume of the cube is 343 cm³.
Kindly Heart and 5 Star this answer, thanks!What is a difference between tropical and temperate rainforests?
A.
Tropical rainforests are near the equator, while temperate rainforests are found further north near coastal areas.
B.
Temperate rainforests are near the equator, while tropical rainforests are found further north on the interiors of continents.
C.
Tropical rainforests are near the equator, while temperate rainforests are found further north on the interiors of continents.
D.
Temperate rainforests are near the equator, while tropical rainforests are found further north near coastal areas.
The difference is that tropical rainforests are near the equator while temperate rainforests are found further north near coastal areas. The Option A is correct.
What difference is between tropical and temperate rainforests?The tropical rainforests are located near equator and spans across regions such as the Amazon Basin in South America, the Congo Basin in Africa and parts of Southeast Asia. These rainforests are characterized by high temperatures and humidity throughout the year with no distinct seasons.
The temperate rainforests are found further north, primarily in coastal areas of temperate regions. Examples include the Pacific Northwest in North America which experience milder temperatures compared to tropical rainforests and have distinct seasonal variations.
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Brainlest and 20 points!!!!!!
Without actually drawing the figure, could you form a triangle using side lengths 7, 8, and 18 units?
Why or why not?
Answer:
No you cannot
Step-by-step explanation:
Triangle side length rule says the sum of any two sides must be greater than the remaining side
7 + 8 is NOT greater than 18 ....you cannot draw a triangle with these side lengths
No, we cannot form a triangle using side lengths 7, 8, and 18 units.
The Triangle Inequality Theorem can be used to determine if a triangle can be built with sides that are 7, 8, and 18 units long. The lengths of any two sides of a triangle with side lengths a, b, and c must add up to more than the length of the third side, according to the theorem.
Let's determine if this criterion is satisfied for the specified side lengths:
7 + 8 = 15
7 + 18 = 25
8 + 18 = 26
In this instance, the length of the third side (18) is greater than the total of the two shorter side lengths (7 and 8). This means that a triangle cannot be built using side lengths of 7, 8, and 18 units, according to the Triangle Inequality Theorem.
As a result, with side lengths of 7, 8, and 18 units, a triangle cannot be built according to the Triangle Inequality Theorem.
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How do you determine if a distribution is normal?
To determine if a distribution is normal, you can employ several methods:
Histogram: Plot the data on a histogram and visually inspect its shape. A normal distribution typically has a symmetric bell-shaped curve, with the majority of the data points concentrated around the mean.
Quantile-Quantile (Q-Q) Plot: A Q-Q plot compares the quantiles of your data to the quantiles of a theoretical normal distribution. If the points on the plot roughly follow a straight line, it suggests that the data is normally distributed.
Skewness and Kurtosis: Calculate the skewness and kurtosis of the data. For a normal distribution, the skewness should be close to zero and the kurtosis should be close to three. Deviations from these values indicate departures from normality.
Shapiro-Wilk Test: Conduct a statistical test, such as the Shapiro-Wilk test, which tests the null hypothesis that the data comes from a normal distribution. If the p-value is above a predetermined significance level (e.g., 0.05), you fail to reject the null hypothesis and conclude that the data is normally distributed.
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A student mows lawns on the weekends. It takes him 180 minutes to mow 4 lawns. What prediction can you make about the time he will spend this weekend if he has 12 lawns to mow?
It will take him 9 hours to mow 12 lawns.
It will take him 18 hours to mow 12 lawns.
It will take him 20 hours to mow 12 lawns.
It will take him 60 hours to mow 12 lawns.
Answer:
It will take him 9 hours to mow 12 lawns.
Step-by-step explanation:
We can use a proportion. We see that the answer choices are in hours, so let's first convert the given information to hours.
180 minutes × (1 hour)/(60 minutes) = 3 hours
180 minutes to mow 4 lawns = 3 hours to mow 4 lawns
Proportion:
3 hours is to 4 lawns as x hours is to 12 lawns
3/4 = x/12
4x = 3 × 12
4x = 36
x = 9
Answer: It will take him 9 hours to mow 12 lawns.
Find the difference of 13a2b and -5a2b
Answer:
[tex]8a^2b[/tex]-------------------------------
Simplify in steps:
[tex]13a^2b + ( -5a^2b)=[/tex] factor out a²b[tex](13-5)a^2b=[/tex] simplify[tex]8a^2b[/tex] answerif a simple Pearson correlation value = .512, what percentage of variance is accounted for? a. 26% b. 49% c. 51% d. 74%
Answer: c
Step-by-step explanation:
help plsss right away!!!!
For column A:
P(male | snickers) = A. 23/41P(M&M peanut ❘ female) = C. 5/46P(female | Reese's) = D. 16/37P(M&M plain | male) = G. 11/113How to determine probability?P(male | snickers) = number of males who like Snickers / total number of people who like Snickers = 230/410 = 23/41
P(M&M peanut | female) = number of females who like M&M peanuts / total number of females = 50/460 = 5/46
P(female | Reese's) = number of females who like Reese's / total number of people who like Reese's = 160/370 = 16/37
P(M&M plain | male) = number of males who like M&M plain / total number of males = 55/565 = 11/113
Therefore, the answers are:
A. 23/41
B. 5/46
C. 16/37
D. 11/113
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In a game of DND, Evy rolls a 20 sided die one time. What is the probability that she rolls an odd number, or a number less than 10? Round to the nearest tenth
The probability that she rolls an odd number, or a number less than 10 is 0.7
Calculating the probability that she rolls an odd number, or a number less than 10?From the question, we have the following parameters that can be used in our computation:
Die = 20-sided
In the 20-sided die, we have
A = Odd numbers = 10
B = Numbers less than 10 = 9
A and B = Odd numbers less than 10 = 5
So, we have
P(A) = 10/20
P(B) = 9/20
P(A and B) = 5/20
The probability expression P(A or B) can be calculated using
P(A or B) = P(A) + P(B) - P(A and B)
When the given values are substituted in the above equation, we have the following equation
P(A or B) = 10/20 + 9/20 - 5/20
Evaluate
P(A or B) = 0.7
Hence, the value of the probability P(A or B) is 0.7
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the equation of line t is y=7/4x+2. Perpendicular to line t is line u, which passes through the point (2, – 2). What is the equation of line u?
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{7}{4}}x+2\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ \cfrac{7}{4}} ~\hfill \stackrel{reciprocal}{\cfrac{4}{7}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{4}{7} }}[/tex]
so we're really looking for the equation of a line whose slope is -4/7 and it passes through (2 , -2)
[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{-2})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{4}{7} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-2)}=\stackrel{m}{- \cfrac{4}{7}}(x-\stackrel{x_1}{2}) \implies y +2 = - \cfrac{4}{7} ( x -2) \\\\\\ y+2=- \cfrac{4}{7}x+\cfrac{8}{7}\implies y=- \cfrac{4}{7}x+\cfrac{8}{7}-2\implies {\Large \begin{array}{llll} y=- \cfrac{4}{7}x-\cfrac{6}{7} \end{array}}[/tex]
Help me please it’s due tonight
The angle of depression that each chain makes with the ceiling are approximately 67° and 56°.
How to determine angle of depression?To solve the problem, use trigonometry. Let's call the angle of depression that the first chain makes with the ceiling x, and the angle of depression that the second chain makes with the ceiling y. Then:
In triangle ABC, where A is one of the hooks, B is the other hook, and C is the point where the chains meet:
AC = 1.9 m
BC = 2.2 m
angle BAC = 86°
Find angle BCA, which is the angle of depression that chain AC makes with the ceiling. Use the law of sines to find this angle:
sin BCA / AC = sin BAC / BC
sin BCA = AC sin BAC / BC
sin BCA = 1.9 sin 86° / 2.2
sin BCA ≈ 0.925
BCA ≈ 67.3°
So the angle of depression that chain AC makes with the ceiling is approximately 67 degrees.
Similarly, find the angle of depression that chain BD makes with the ceiling by considering triangle ABD:
AD = 2.8 m
BD = 2.2 m
angle ADB = 86°
Using the law of sines:
sin ADB / BD = sin BAD / AD
sin ADB = BD sin BAD / AD
sin ADB = 2.2 sin 86° / 2.8
sin ADB ≈ 0.836
ADB ≈ 56.4°
So the angle of depression that chain BD makes with the ceiling is approximately 56 degrees.
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Mr. Jones jogs the same route each day. The amount of time he jogs is inversely proportional to his jogging rate. What option gives possible rates and times for two of his jogs?
A. 4 mph for 2. 25 hours and 6 mph for 1. 5 hours. B. 6 mph for 1. 5 hours and 5 mph for 1. 25 hours. C. 5 mph for 2 hours and 4 mph for 3 hours. D. 4. 5 mph for 3 hours and 6 mph for 4 hours
To determine the correct option, we need to check if the rates and times given in each option satisfy the condition of being inversely proportional.
Option A: 4 mph for 2.25 hours and 6 mph for 1.5 hours.
The product of the rate and time is not consistent: (4 mph) × (2.25 hours) = 9 and (6 mph) × (1.5 hours) = 9. Therefore, this option does not satisfy the condition.
Option B: 6 mph for 1.5 hours and 5 mph for 1.25 hours.
The product of the rate and time is not consistent: (6 mph) × (1.5 hours) = 9 and (5 mph) × (1.25 hours) = 6.25. Therefore, this option does not satisfy the condition.
Option C: 5 mph for 2 hours and 4 mph for 3 hours.
The product of the rate and time is consistent: (5 mph) × (2 hours) = 10 and (4 mph) × (3 hours) = 12. Therefore, this option satisfies the condition.
Option D: 4.5 mph for 3 hours and 6 mph for 4 hours.
The product of the rate and time is consistent: (4.5 mph) × (3 hours) = 13.5 and (6 mph) × (4 hours) = 24. Therefore, this option satisfies the condition.
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Jason empties his piggy bank and counted out exactly $37 in nickels, dimes and quarters. There were 3 times as many dimes as Nickels. There were twice as many quarters as dimes. How many nickels did they have ?
If Jason follows the given condition in the given data question then answer will be Jason had 4 nickels.
Let's assume the number of nickels Jason had is represented by the variable 'n.' Since the problem states that there were 3 times as many dimes as nickels, the number of dimes can be represented as 3n. Additionally, the problem states that there were twice as many quarters as dimes, so the number of quarters can be represented as 2(3n) or 6n.
Now, we can create an equation based on the total value of the coins: 5n (nickels) + 10(3n) (dimes) + 25(6n) (quarters) = 37 (total value in cents).
Simplifying the equation, we have 5n + 30n + 150n = 37.
Combining like terms, we get 185n = 37.
Dividing both sides by 185, we find n = 0.2.
Since we can't have a fraction of a nickel, we round down to the nearest whole number.
Therefore, Jason had 4 nickels.
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find A flat rectangular roof measures 7.5 m by 4 m; 12 mm of rain falls on the roof. a Find the volume of water on the roof. Express your answer in i cm' and ii m'. Find the mass of water that falls on the roof if 1 cm³ of water has a mass b of 1 gram. Express your answer in kilograms.
1. The volume of water on the roof in cm and m is
240000 and 0.24 respectively.
2. The mass of water that fell on the roof is 2400kg
What is volume?Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also the capacity of a container.
Volume = l× b × h
l = 7.5 m
b = 4m
h = 12mm = 0.012
volume = 5 × 4 × 0.012
= 0.24 m³
in centimeter,
= 0.24 × 100³
= 240,000 cm³
2. The density of water is 1g/cm³
1g = 0.01kg
= 0.01kg/cm³
density = mass/volume
mass = density × volume
= 0.01 × 240000
= 2400 kg
therefore the mass of water that fell on the roof is 2400kg
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