Using the ratio, we solve and get, Ben needs 0.8 litres of red paint, 0.64 litres of yellow paint, and 0.06 litres of white paint to make 1.5 litres of orange paint.
To make 1.5 litres of orange paint, Ben needs to mix the red, yellow, and white paint in the ratio of 20 : 16 : 1.5.
To calculate the amount of each color needed, you first need to find the total number of parts in the ratio.
The total number of parts is 20 + 16 + 1.5 = 37.5.
Next, you can calculate the amount of each color needed by dividing 1.5 litres by the total number of parts in the ratio, and then multiplying by the respective parts for each color.
So, the amount of red paint needed is:
(1.5/37.5) x 20 = 0.8 litres
The amount of yellow paint needed is:
(1.5/37.5) x 16 = 0.64 litres
And the amount of white paint needed is:
(1.5/37.5) x 1.5 = 0.06 litres
Therefore, Ben needs 0.8 litres of red paint, 0.64 litres of yellow paint, and 0.06 litres of white paint to make 1.5 litres of orange paint.
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Use the slope of a line formula to find the slope of the following points: (3, 9) and (8, 15)
Answer:
m = 6/5
Step-by-step explanation:
Slope = rise/run or (y2 - y1) / (x2 - x1)
Points (3, 9) and (8, 15)
We see the y increase by 6 and the x increase by 5, so he slope is
m = 6/5
Answer:
The slope of the points is 6/5.
Step-by-step explanation:
SOLUTION :
Using slope of a line formula to find the slope of the points :
[tex]\quad\dashrightarrow{\sf{m = \dfrac{y_2 - y_1}{x_2 - x_1}}}[/tex]
[tex]\pink\star[/tex] m = slope[tex]\pink\star[/tex] [tex](x_1, y_1)[/tex] coordinates of first point in the line[tex]\pink\star[/tex] [tex](x_2, y_2) [/tex] = coordinates of second point in the lineSubstituting all the given values in the formula to find the slope of the points :
[tex]\quad\dashrightarrow{\sf{m = \dfrac{y_2 - y_1}{x_2 - x_1}}}[/tex]
[tex]\blue\star[/tex] y_2 = 15[tex]\blue\star[/tex] y_1 = 9[tex]\blue\star[/tex] x_2 = 8[tex]\blue\star[/tex] x_1 = 3[tex]\quad\dashrightarrow{\sf{m = \dfrac{15 - 9}{8 -3}}}[/tex]
[tex]\quad\dashrightarrow{\sf{m = \dfrac{6}{5}}}[/tex]
[tex]\quad{\star\underline{\boxed{\sf{\red{m = \dfrac{6}{5}}}}}}[/tex]
Hence, the slope of the points is 6/5.
————————————————Suppose that the weekly profit, in dollars, of producing and selling x cars is P(x) = -0.005x*-0.2x2 + 1000x - 1300. and currently 80 cars are produced and sold weekly. Use P(80) and the marginal profit when x-SAP(80)) to estimate the weekly profit of producing and selling 81 cars. Round to the nearest dollar.
• $75,731 • $75,732 • $75,645 • $77,032
To estimate the weekly profit of producing and selling 81 cars, we first need to find the current weekly profit for producing and selling 80 cars using P(80):
P(80) = -0.005(80)^(2) - 0.2(80) + 1000(80) - 1300
P(80) = $75,800
Now we need to find the marginal profit at x = 80, which is the derivative of the profit function P(x):
P'(x) = -0.01x - 0.4x + 1000
P'(80) = -0.01(80) - 0.4(80) + 1000
P'(80) = $920
The marginal profit at x = 80 is $920. This means that for each additional car produced and sold beyond 80, the profit will increase by $920.
To estimate the weekly profit of producing and selling 81 cars, we can use the approximation formula:
ΔP ≈ P'(80)Δx
where ΔP is the change in profit, Δx is the change in the number of cars produced and sold, and P'(80) is the marginal profit at x = 80.
We want to find the change in profit when the number of cars produced and sold increases from 80 to 81, so Δx = 1. Plugging in the values we have:
ΔP ≈ $920(1)
ΔP ≈ $920
This means that the estimated weekly profit for producing and selling 81 cars is:
P(81) ≈ P(80) + ΔP
P(81) ≈ $75,800 + $920
P(81) ≈ $75,720
Rounding to the nearest dollar, the answer is $75,720. So the correct option is: $75,720.
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Ms. Redmon gave her theater students an assignment to memorize a dramatic monologue to present to the rest of the class. The graph shows the times, rounded to the nearest half minute, of the first 10 monologues presented.
A number line going from 0.5 to 5. 0 dots are above 0.5 0 dots are above 1. 2 dots area above 1.5. 1 dot is above 2. 3 dots are above 2.5. 1 dot is above 3. 2 dots are above 3.5. 1 dot is above 4. 0 dots are above 2.5. 0 dots are above 5.
The next student presents a monologue that is about 0.5 minutes long. What effect will this have on the graph?
The median will decrease.
The mean will decrease.
The median will increase.
The mean will increase.
The effect of the student presenting such a monologue would be B. The mean will decrease.
How to find the effect ?Order the data points:
1. 5, 1. 5, 2, 2. 5, 2. 5, 2. 5, 3, 3. 5, 3. 5, 4
Find the mean ;
= (1. 5 + 1. 5 + 2 + 2. 5 + 2. 5 + 2. 5 + 3 + 3. 5 + 3. 5 + 4) / 10
= 27 / 10
= 2. 7
Then find the new mean after the student presents the monologue:
= ( 0. 5 + 1. 5 + 1. 5 + 2 + 2. 5 + 2. 5 + 2. 5 + 3 + 3. 5 + 3. 5 + 4) / 11
= 2. 5
The mean therefore reduced.
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Answer:
b
Step-by-step explanation:
In which of the following situations does order matter? Select all that apply
Answer:
Locker and Phone number
Step-by-step explanation:
Gym student grouped together with no thought doesnt matter, lunch menu doesn't need order, and a classroom seating chart doesn't really matter
Question 7(Multiple Choice Worth 2 points)
(Creating Graphical Representations MC)
A random sample of 100 middle schoolers were asked about their favorite sport. The following data was collected from the students.
Sport Basketball Baseball Soccer Tennis
Number of Students 17 12 27 44
Which of the following graphs correctly displays the data?
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
Question 8(Multiple Choice Worth 2 points)
(Circle Graphs MC)
A New York City hotel surveyed its visitors to determine which type of transportation they used to get around the city. The hotel created a table of the data it gathered.
Type of Transportation Number of Visitors
Walk 120
Bicycle 24
Car Service 45
Bus 30
Subway 81
Which of the following circle graphs correctly represents the data in the table?
circle graph titled New York City visitor's transportation, with five sections labeled walk 80 percent, bus 16 percent, car service 30 percent, bicycle 20 percent, and subway 54 percent
circle graph titled New York City visitor's transportation, with five sections labeled walk 40 percent, bicycle 8 percent, car service 15 percent, bus 10 percent, and subway 27 percent
circle graph titled New York City visitor's transportation, with five sections labeled subway 40 percent, bus 8 percent, car service 15 percent, bicycle 10 percent, and walk 27 percent
circle graph titled New York City visitor's transportation, with five sections labeled subway 80 percent, bicycle 20 percent, car service 30 percent, bus 16 percent, and walk 54 percent
The correct graph to display the data is: C. Bar graph with the title "favorite sport" and the x-axis labeled "sport" and the y-axis labeled....
Why is a Bar Graph appropriate?A bar graph is an appropriate choice for displaying the data collected from the middle school students because it allows us to compare discrete categories (in this case, sports) and their corresponding frequencies (number of students).
In this case, the data is as follows:
Basketball: 17 studentsBaseball: 12 studentsSoccer: 27 studentsTennis: 44 studentsThe correct bar graph has the title "Favorite Sport" to indicate the subject of the data being represented.
The x-axis is labeled "Sport" and lists the four sports - basketball, baseball, soccer, and tennis - in separate, distinct categories. The y-axis is labeled "Number of Students" and displays the frequency or count of students who chose each sport as their favorite.
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Here is a data set: 51, 47, 48, 51, 50, 8
Answer true or false for the following statements.
If you remove the outlier: 8
- the range will stay the same: false
- the mean will decrease: false
- the median will increase: true
The statements are classified as follows:
- the range will stay the same: false- the mean will decrease: false- the median will increase: true.How to obtain the features of the data-set?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.
8 is a low outlier, hence it is a value lower than the mean, meaning that the mean increases if we remove the observation of 8.
The range of a data-set is calculated as the difference between the highest value and the lowest value in the data-set, thus if we remove the low value of 8, the next low value is of 47, meaning that the range decreases.
The ordered data-set is given as follows:
8, 47, 48, 50, 51, 51.
The data-set has an even cardinality of 6, hence the median is calculated as the mean of the two middle elements as follows:
Median = (48 + 50)/2
Median = 49.
Removing 8, the data-set is given as follows:
47, 48, 50, 51, 51.
Hence the median increases, as it will be the middle value of 50.
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the average time it takes a salesperson to finish a sale on the phone is exponentially distributed with a mean of 18 minutes. find the probability that more than 2 minutes pass before a sale is completed.
The probability that more than 2 minutes pass before a sale is completed is approximately 0.895 or 89.5%.
The CDF of the exponential distribution is given by:
F(x) = 1 - e^(-λx)
where λ is the rate parameter, which is the reciprocal of the mean, λ = 1/18 in this case. The variable x is the time it takes for a sale to be completed.
To find the probability that more than 2 minutes pass before a sale is completed, we need to find the complement of the probability that a sale is completed within the first 2 minutes. That is:
P(X > 2) = 1 - P(X ≤ 2)
Substituting into the CDF formula:
P(X > 2) = 1 - F(2) = 1 - [tex](1 - e^{(-\lambda_2)} = e^{(-\lambda_2)}[/tex]
Plugging in the value of λ:
P(X > 2) = [tex]e^{(-(1/18)\times2)}[/tex] ≈ 0.895
This means that there is a high chance that it will take more than 2 minutes for a sale to be completed on the phone.
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Two sides of a parallelogram are 9. 5 feet and 6. 1 feet. The measure of the angle between these sides is 20°. Find the area of the parallelogram to the nearest 10th of a square foot
The area of the parallelogram is approximately 21.2 square feet, rounded to the nearest tenth of a square foot.
To find the area of a parallelogram, we need to multiply the base by the height. In this case, the two sides given (9.5 feet and 6.1 feet) are the base and height respectively, because they are perpendicular.
To find the area, we first need to find the length of the other two sides. Since a parallelogram has opposite sides that are equal in length, we know that the other two sides are also 9.5 feet and 6.1 feet.
Next, we can use the given angle (20°) to find the height of the parallelogram. We can use trigonometry, specifically the tangent function, to do this:
tan(20°) = height / 6.1 feet
height = 6.1 feet * tan(20°)
height ≈ 2.23 feet
Now we can find the area:
area = base * height
area = 9.5 feet * 2.23 feet
area ≈ 21.185 square feet
Rounding to the nearest tenth of a square foot, the area is approximately 21.2 square feet.
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Here is the income statement for Teal Mountain Inc.
TEAL MOUNTAIN INC.
Income Statement
For the Year Ended December 31, 2022
Sales revenue
$431,600
Cost of goods sold
234,300
Gross profit
197,300
Expenses (including $16,200 interest and $22,500 income taxes)
75,200
Net income
$ 122,100
Additional information:
1. Common stock outstanding January 1, 2022, was 26,700 shares, and 36,000 shares were outstanding at December 31, 2022.
2. The market price of Teal Mountain stock was $13 in 2022.
3. Cash dividends of $24,200 were paid, $6,600 of which were to preferred stockholders.
Compute the following measures for 2022. (Round all answers to 2 decimal places, e. G. 1. 83 or 2. 51%)
(a) Earnings per share
$enter earnings per share in dollars
(b) Price-earnings ratio
enter price-earnings ratio in times
times
(c) Payout ratio
enter payout ratio in percentages
%
(d) Times interest earned
enter times interest earned
times
Using the given information we can compute several financial ratios that help us evaluate the company's financial performance.
To calculate these ratios, we need to use information from the income statement and the additional information provided.
One important financial ratio is earnings per share (EPS), To compute EPS, we divide net income by the average number of common shares outstanding during the year. To find the average number of shares outstanding, we add the beginning and ending shares and divide by 2.
Net income = $122,100
Average number of common shares outstanding = (26,700 + 36,000) / 2 = 31,350
EPS = $122,100 / 31,350 = $3.89
Another important financial ratio is the price-earnings (P/E) ratio, To compute the P/E ratio, we divide the market price per share by the EPS.
Market price per share = $13
EPS = $3.89
P/E ratio = $13 / $3.89 = 3.34 times
The payout ratio measures the proportion of earnings that is paid out as dividends. To compute the payout ratio, we divide total dividends by net income. However, we need to adjust for the fact that some of the dividends were paid to preferred stockholders. To do this, we subtract the preferred dividends from the total dividends before dividing by net income.
Total dividends = $24,200
Preferred dividends = $6,600
Common dividends = $24,200 - $6,600 = $17,600
Net income = $122,100
Payout ratio = $17,600 / $115,500 = 15.24%
The times interest earned (TIE) ratio, To compute the TIE ratio, we divide earnings before interest and taxes (EBIT) by interest expense.
Interest expense = $16,200
EBIT = Gross profit - Expenses + Interest expense = $197,300 - $75,200 + $16,200 = $138,300
TIE ratio = $138,300 / $16,200 = 8.54 times
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2. Kyle submits a design for the contest, but his
explanation was misplaced. How can Figure A be
mapped onto Figure B? Can any other transformation be
used to map Figure A onto Figure B?
Note that in order to map A onto B, Kyle would have to dilate the given figure by a scale factor or 3.
What is a scale factor?The scale factor is a metric for figures with similar appearances but differing scales or measurements. Assume two circles appear similar but have different radii. The scale factor specifies how much larger or smaller a figure is than the original figure.
The original point of figure A which has 4 points are
(0,02)
(-1, 2)
(0, 1)
(1, 2)
Multiply all th e points by 3, and you get,
(0,02) x 3 = (0, -6) =
(-1, 2) x 3 = (-3, 6)
(0, 1) x 3 = (0, 3)
(1, 2) x3 = (3, 6)
Plotting the new values will give us the transformation (dilation) required. See the attached image.
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Circle W has a center at (15,–2) and has a radius of 4. Circle W' has a center of (–5,–5) with a radius of 4. What is the transformation of circle W to circle W'?
The correct answer is "Translated to the left 10 and down 3 and then reflected about the y-axis."
Understanding Transformation of CircleTransformation is a process that changes the position, orientation, size, or shape of a geometric object. Transformations are often described using matrices, vectors, or other mathematical operations.
Types of Transformations
Translation - moving object on a straight lineRotation - turning an object around a fixed point by a certain angleScaling - changing the size of an object by a fixed factor.Reflection - flipping an object over a fixed lineFrom the problem statement, to move the center from (15,-2) to (-5,-5), we need to translate the circle to the left by 10 units and down by 3 units. So the first transformation is a translation to the left 10 units and down 3 units.
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Find the coordinates of a point P on the line and a vector v parallel to the line. X-7 - Y + 2 = 2 + 6 = 5 4 P(x, y, z) = V ="
To find the coordinates of point P on the line, we can solve for x and y in the equation X-7 - Y + 2 = 2 + 6 = 5. Adding 7 to both sides, we get X - Y + 2 = 12. Subtracting 2 from both sides, we get X - Y = 10. We can choose any value for x, and then solve for y using this equation. For example, if we choose x = 0, then y = -10.
So the coordinates of point P on the line could be (0, -10, z), where z is any real number.
To find a vector v parallel to the line, we can take two points on the line and find the vector between them. For example, we could use the points (0, -10, 0) and (1, -9, 0). The vector between these points is (1-0, -9-(-10), 0-0) = (1, 1, 0).
So a vector v parallel to the line is v = (1, 1, 0).
To find the coordinates of a point P on the line and a vector v parallel to the line, we first need to rewrite the given equation in a more standard form. The equation provided seems to be incorrect, but let's assume it's meant to be in the format of Ax + By = C, then we can proceed as follows:
1. Identify the normal vector of the line (A, B): Since the given equation is X - Y = 3 (combining the constants), the normal vector is (1, -1).
2. Determine the direction vector of the line, which is perpendicular to the normal vector. One possible direction vector is the one obtained by swapping the components and negating one of them, so v = (1, 1).
3. To find a point P on the line, we can choose a value for either x or y and solve for the other coordinate. Let's choose x = 0, then we have 0 - Y = 3, which gives Y = -3. Therefore, P(x, y) = (0, -3).
In summary, the point P on the line is (0, -3), and a vector v parallel to the line is (1, 1).
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A 32" flat screen television measures 32 inches across its diagonal. the diagonal makes a 35° angle with the bottom of the television
32"
h
a
35°
select all equations that can be used to solve for the height, h, of the television screen
The trignometric equation h = (32 inches) x tan(35°) can be used to solve for the height, h, of the television screen.
We can use trigonometry to solve for the height, h, of the television screen. From the given information, we can form a right triangle with the diagonal of the television screen as the hypotenuse, and the height of the screen as one of the legs.
Since we are given the angle between the diagonal and the bottom of the television, we can use the trigonometric function tangent to relate the height and the diagonal.
The equation we can use to solve for the height is:
tan(35°) = [tex]\frac{h }{ (32 inches)}[/tex]
Rearranging this equation, we get:
h = (32 inches) x tan(35°)
Therefore, the equation that can be used to solve for the height, h, of the television screen is:
h = (32 inches) x tan(35°)
So, the equation h = (32 inches) x tan(35°) can be used to solve for the height, h, of the television screen.
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Given two events E and F with Pr(E) = 0. 4, Pr(F) = 0. 5, and Pr(EnF) = 0. 3, a) Pr(E|F) = b) Pr(F|E) = c) Are E and F independent? (Enter YES or NO)
Given two events E and F with Pr(E) = 0. 4, Pr(F) = 0. 5, and Pr(EnF) = 0. 3 then:
a) Pr(E|F) = 0.6
b) Pr(F|E) = 0.75
c) NO, E and F are not independent.
a) To find Pr(E|F), we use the formula: Pr(E|F) = Pr(EnF)/Pr(F). Substituting the given values, we get Pr(E|F) = 0.3/0.5 = 0.6.
b) Similarly, to find Pr(F|E), we use the formula: Pr(F|E) = Pr(EnF)/Pr(E). Substituting the given values, we get Pr(F|E) = 0.3/0.4 = 0.75.
c) We can check for independence by seeing if Pr(E) = Pr(E|F) or Pr(F) = Pr(F|E). However, since Pr(E) ≠ Pr(E|F) and Pr(F) ≠ Pr(F|E), we can conclude that E and F are not independent.
In other words, the occurrence of one event affects the probability of the other event occurring. Specifically, the fact that Pr(EnF) ≠ Pr(E)Pr(F) indicates that the events are dependent.
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Airline passengers pay $439 to fly to california. for this price, customers may check 2 pieces of luggage. there is a fee of $25 for each additional piece of luggage a passenger wants to check. which function can be used to find the amount in dollars a passenger has to pay to fly with p pieces of luggage, where p >2
The function that can be used to find the amount in dollars a passenger has to pay to fly with `p` pieces of luggage, where `p > 2` is: `C(p) = 439 + 25(p-2)`
- The base cost of the flight is $439.
- Customers may check 2 pieces of luggage without any additional fee.
- For each additional piece of luggage beyond 2, there is a fee of $25.
- If `p` is the number of pieces of luggage checked, then the number of additional pieces of luggage beyond 2 is `p - 2`.
- Therefore, the additional fee for `p` pieces of luggage beyond the first 2 is `25(p - 2)`.
- Adding this fee to the base cost gives the total cost `C(p)`:
C(p) = base cost + additional fee for (p-2) pieces of luggage
= 439 + 25(p-2)
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Which angle in AXYZ has the largest measure? 4 Y A. LX B. LY C.
(A) ∠X is the largest angle in the given triangle as the side opposite is also the largest.
What are angles?An angle is formed when two straight lines or rays meet at a single terminal.
The place where two points converge is known as an angle's vertex. The name "angle" comes from the Latin word "angulus," which means "corner."
Two lines that meet at the same point or two planes that meet at the same line form a geometric figure.
The angle in degrees separates these lines or planes.
So, we know that:
The side opposite to the largest angle is also the largest side of the triangle and vica-versa.
Remembering this we can easily conclude that ∠X is the largest angle as the largest is 9 units and X is opposite of the side YZ which measures 9 units.
Therefore, (A) ∠X is the largest angle in the given triangle as the side opposite is also the largest.
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Correct question:
Which angle in AXYZ has the largest measure?
A. ∠X
B. ∠Y
C. ∠Z
D. Cannot be determined
Please Help! A water cup is in the shape of the cone. The diameter of the cup is 4 inches and the height is 6 inches.
What is the volume of water the cup could hold?
Use 3.14 for pi. (Enter your answer, as a decimal.)
The volume of water the cup can hold is 25.12 inches³.
How to find the volume of the cup?A water cup is in the shape of the cone. The diameter of the cup is 4 inches and the height is 6 inches.
Therefore, the volume of water the water cup can hold can be calculated as follows:
Hence,
volume of the cup = 1 / 3 πr²h
where
r = radiush = height of the coneTherefore,
r = 4 / 2 = 2 inches
h = 6 inches
Therefore,
volume of the cup = 1 / 3 × 3.14 × 2² 6
volume of the cup = 1 / 3 × 3.14 × 4 × 6
volume of the cup = 75.36 / 3
volume of the cup = 25.12 inches³
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A telephone line hangs between two poles 14 m apart in the shape of the catenary y = 17 cosh x 17 − 12, where x and y are measured in meters. A telephone line hanging between two poles is on the x y coordinate plane. The left pole is located at x = −7 and the right pole is located at x = 7. The line hangs between the poles crossing the y-axis at y = 5. The acute angle formed by the right pole and the hanging line is labeled theta. (a) Find the slope of this curve where it meets the right-hand pole. (Round your answer to four decimal places. ) (b) Find the angle theta (in degrees) between the line and the pole. (Round your answer to two decimal places. ) theta = °
(a) To find the slope of the curve where it meets the right-hand pole, we need to differentiate the given equation with respect to x. y = 17cosh(x/17) - 12.
Using the chain rule, we get dy/dx = (17/17)sinh(x/17) = sinh(x/17). Therefore, at x = 7, the slope of the curve is sinh(7/17) ≈ 0.6968.
(b) To find the angle theta between the line and the pole, we can use trigonometry. The slope of the curve at the right-hand pole is the same as the tangent of the angle theta.
Therefore, tan(theta) = 0.6968. Taking the inverse tangent of both sides, we get theta = arctan(0.6968) ≈ 34.33 degrees. Therefore, the acute angle formed by the right pole and the hanging line is approximately 34.33 degrees.
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The president of the student council wants to survey the student population about parking. She decides to use a
random number table to take a random sample of 100 of the 1,020 students at the school. What is the smallest number
of digits that should be used to label the population?
The smallest number of digits that should be used to label the population is 4, since there are 1,020 students in the school.
To determine the smallest number of digits needed to label the population, we will follow these steps:
1. Determine the total number of students in the population.
2. Identify the number of digits needed to represent the largest student number.
3. Apply this number of digits to all student labels.
Let's apply these steps to your question:
1. The total number of students is 1,020.
2. The largest student number is 1,020, which requires 4 digits (since it has four numbers: 1, 0, 2, and 0).
3. To label the entire student population consistently, use 4 digits for all student labels.
So, the smallest number of digits that should be used to label the population is 4.
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Suppose that Uranus rotates on its axis once every 17. 2 hours. The equator lies on a circle with a radius of 15,881 miles. (a) Find the angular speed of a point on its equator in radians per day (24 hours). (b) Find the linear speed of a point on the equator in miles per day. Do not round any intermediate computations, and round your answer to the nearest whole number. (a) Angular speed: radians per day (b) Linear speed : miles per day
Rounding to the nearest whole number, the linear speed of a point on Uranus' equator is approximately 139,424 miles/day.
(a) To find the angular speed of a point on Uranus' equator, we need to convert the rotation period from hours to days and then calculate the angle rotated in one day.
In one day (24 hours), Uranus rotates:
24 hours ÷ 17.2 hours/rotation ≈ 1.3953 rotations
The angle rotated in one day is:
1.3953 rotations × 2π radians/rotation ≈ 8.7674 radians/day
So the angular speed of a point on Uranus' equator is approximately 8.7674 radians/day.
(b) To find the linear speed of a point on Uranus' equator, we can use the formula:
linear speed = radius × angular speed
where the radius is given as 15,881 miles and the angular speed is 8.7674 radians/day (from part (a)).
Substituting these values, we get:
linear speed = 15,881 miles × 8.7674 radians/day ≈ 139,424 miles/day
Rounding to the nearest whole number, the linear speed of a point on Uranus' equator is approximately 139,424 miles/day.
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Pls help I don’t get how to do this
Answer:
Step-by-step explanation:
explanation in image
Which expression is equivalent to 6\cdot 6^{-2}\normalsize?6⋅6
−2
?
The expression 6 * 6^(-2) is equivalent to 1/6.
Simplify this expression using the rule of exponents?We can simplify this expression using the rule of exponents that states a^m / a^n = a^(m-n), which gives:
6 * 6^(-2) = 6 / 6^2 = 6 / 36 = 1/6
Let's break down the expression and simplify it step by step:
6 * 6^(-2)
We start by evaluating the exponent, which means we take the reciprocal of 6^2:
6 * (1/6^2)
Now we simplify the denominator of the fraction:
6 * (1/36)
Finally, we can simplify the expression by dividing 6 by 36:
1/6
So, the expression 6 * 6^(-2) is equivalent to 1/6. This means that if we multiply 6 by 6 raised to the power of -2 (or 1/6^2), we get the same result as dividing 6 by 6^2 (or 36), which is 1/6.
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A right triangle with a height measuring
4.75 inches contains a hypotenuse
measuring 7.42 inches. What is the
measure of the area of the triangle to the
nearest tenth of a square inch?
Engineers built an arch bridge across a river. The arch bridge
makes a parabola shape that has the equation
y=-0. 1(x – 5)2 + 12, where x and y are measured in
meters. If the bridge makes contact with both banks at a height
of 4 meters, how long is the distance between the two banks
of the river where the bridge is? Round your answer to the
nearest whole number.
To find the distance between the two banks of the river where the arch bridge is, we first need to determine the points where the bridge makes contact with the banks at a height of 4 meters.
We are given the parabola shape of the arch with the equation y = -0.1(x - 5)^2 + 12.
1. Set the height y equal to 4 meters:
4 = -0.1(x - 5)^2 + 12
2. Subtract 12 from both sides:
-8 = -0.1(x - 5)^2
3. Divide both sides by -0.1:
80 = (x - 5)^2
4. Take the square root of both sides:
sqrt(80) = x - 5
5. Now, we find the two x-values where the bridge contacts the banks:
x1 = sqrt(80) + 5
x2 = -sqrt(80) + 5
6. Calculate the distance between the two banks by subtracting x2 from x1:
Distance = x1 - x2 = (sqrt(80) + 5) - (-sqrt(80) + 5)
7. Simplify the expression:
Distance = 2 * sqrt(80)
8. Round your answer to the nearest whole number:
Distance ≈ 18 meters
The distance between the two banks of the river where the arch bridge is, is approximately 18 meters.
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What is the difference in minutes between the shortest collection.
The difference in the shortest collection times before and after the well installation is 20 minutes, calculated by subtracting the shortest time after installation (25 minutes) from before (45 minutes), as shown in the box and whiskers plot.
This is calculated by subtracting the shortest collection time after well installation (25 minutes) from the shortest collection time before well installation (45 minutes):
45 - 25 = 20 minutes.
This can be seen in the box and whiskers plot provided, where the lowest value for each distribution is denoted by the beginning of the whiskers.
So, the difference is before and after the well installation is 20 minutes.
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--The given question is incomplete, the complete question is given
" What is the difference in minutes between the shortest collection times before and after the well was installed"--
There's a question I've been trying for 2 days to get solved but either I'm missing something or maybe I haven't been using the right method but I hope someone will help me here. ________________________________________
Substitution, Manipulation, Elimination
Solve Simultaneously. Use the method you find easiest. (title of the question)
________________________________________
4x-3y=11
5x-9y=-2
Answer:
(x, y) = (5, 3)
Step-by-step explanation:
You want the solution to the system of equations ...
4x -3y = 115x -9y = -2SolutionIt is convenient to subtract the second equation from 3 times the first:
3(4x -3y) -(5x -9y) = 3(11) -(-2)
12x -9y -5x +9y = 33 +2
7x = 35 . . . . . . . simplify
x = 5 . . . . . . . . . . divide by 7
4(5) -3y = 11 . . . . . substitute into the first equation
9 = 3y . . . . . . . . add 3y-11 to both sides
y = 3 . . . . . . . . divide by 3
The solution is (x, y) = (5, 3).
__
Additional comment
We find using a graphing calculator to be the easiest way to solve a pair of simultaneous equations. The attachment shows the solution is the one we found above.
The approach of "substitution" is straightforward, if error-prone. Basically, you solve one equation for either variable, then use that expression in the other equation. Here, for example, you can solve the first for x:
x = (11 +3y)/4
Then use that in the second equation:
5(11 +3y)/4 -9y = -2
5(11 +3y) -36y = -8 . . . . eliminate the denominator
55 +15y -36y = -8 . . . . . eliminate the parentheses
-21y = -63 . . . . . . . . . . . simplify, subtract 55
y = 3 . . . . . . . . . . . . divide by -21
x = (11 +3(3))/4 = 20/4 = 5 . . . . find x
In the above, we used "elimination." We took advantage of the fact that the y-coefficients were related by a factor of 3. To cancel y-terms, we need to have the equations we "add" have opposite signs for the y-terms. Here, we do that by multiplying the first by 3 (to make -9y), then subtracting the second equation (which has -9y, so will cancel). We could have subtracted 3 times the first from the second, but that would make all the resulting coefficients be negative, which we like to avoid.
Or, we could have multiplied the first equation by -3 to make the y-coefficients opposite, then added the results. (Again, that would give negative coefficients in the sum.) Planning ahead can help avoid mistakes due to minus signs.
Jim is building a deck for his family to enjoy. Because of a big bay window that juts out next to the deck, he has to build an angled section for the steps going down to the yard. The section will be a parallelogram. Assuming that he cannot accurately prove that any two sides are parallel, how can he be assured that he has an actual parallelogram? Identify the theorem that he will use and how he will use it
By applying the Consecutive Angles Theorem, Jim can confirm that the angled section for the steps is indeed a parallelogram, even without accurately proving that any two sides are parallel.
Jim building a deck with an angled section in the shape of a parallelogram. To be assured that he has an actual parallelogram, Jim can use the Consecutive Angles Theorem.
This theorem states that if the consecutive angles of a quadrilateral are supplementary (add up to 180 degrees), then the quadrilateral is a parallelogram.
To use the Consecutive Angles Theorem, Jim should follow these steps:
1. Measure the four angles of the quadrilateral he has created for the angled section of the deck.
2. Check if the consecutive angles are supplementary (i.e., the sum of each pair of consecutive angles is equal to 180 degrees).
3. If all consecutive angles are supplementary, he can be assured that the quadrilateral is a parallelogram.
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Using a compass a ruler and a protractor draw a circle having
By using the compass a ruler and a protractor a circle having a Radius MO of 3 cm, Diameter OP of 6cm, Chord QR of 4cm, and Central angle <OMS of 60° has been Drawn.
Given data:
Radius MO = 3 cm
Diameter OP = 6cm
Chord QR = 4cm
Central angle <OMS = 60°
Steps to follow to draw the circle,
Step 1: Mark the M point as the center.
Step 2: Now take the compass and take a 3 cm reading on it by using the ruler.
Step 3: Draw the circle by using M as the center
Step 4: Mark a point O on the circle
Step 5: Draw a straight line segment OP passing through M
Step 6: Mark a point Q on the circle
Step 7: Using compass width and take a 3 cm reading on it and by taking Q as center cut the circle at R.
Step 8: Now join Q and R points.
Step 9: Using compass width and take a 3 cm reading on it and by taking O as the center cut the circle at S.
Step 10: Now join S and M points
Therefore, The circle, central angle on the circle, and chord on the circle are drawn.
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The complete question is,
1. Directions: Using a compass, ruler, and protractor, draw a circle having:
1.) M as the center
2.) radius MO of 3 cm
3.) diameter OP of 6cm
4.) chord QR of 4cm
5.) central angle:<OMS of 60°
Question 2 of 10
The graph of y=-2x + 10 is:
OA. a point that shows the y-intercept.
OB. a line that shows the set of all solutions to the equation.
OC. a line that shows only one solution to the equation.
D. a point that shows one solution to the equation.
Answer:
The graph of y = -2x + 10 is B) a line that shows the set of all solutions to the equation.------------------------------------------------
A linear equation is an equation of a straight line.
It describes the straight-line graph of a set of ordered pairs (x, y) that are solutions to the equation.
There are different forms of linear equations.
The slope-intercept form of a linear equation is y = mx + b.
The equation y = -2x + 10 is in slope-intercept form. Its graph is a line with slope -2 and y-intercept 10. It shows the set of all solutions to the equation.
As per description above, the correct answer choice is B, all the other options are false.
How many degrees are in the acute angle formed by the hands of a clock at 3:30?
The acute angle formed by the hands of a clock at 3:30 is 75 degrees. An acute angle is an angle that measures less than 90 degrees, and in this case, the hour hand is pointing at the 3, which is a 90-degree angle from the 12, while the minute hand is pointing at the 6, which is a 180-degree angle from the 12.
Find the number of degrees in the acute angle formed by the hands of a clock at 3:30, follow these steps:
Determine the position of the hour hand. At 3:30, the hour hand is halfway between 3 and 4, so it's at 3.5 hours. Convert this to degrees by multiplying by 30 (since there are 360 degrees in a circle and 12 hours on a clock, each hour represents 30 degrees).
So, the hour hand is at 3.5 x 30 = 105 degrees.
Determine the position of the minute hand. At 3:30, the minute hand is on 6, which is 180 degrees around the clock.
Find the difference between the two positions.
Subtract the smaller angle from the larger angle: 180 - 105 = 75 degrees.
The acute angle formed by the hands of a clock at 3:30 is 75 degrees.
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