The time of the day when two vehicles will leave park at same time is 11:20 a.m.
Traffic can be controlled by adjust the departure times, use a reservation system, limit the number of vehicles , and promote carpooling.
To create the departure timetable,
Start by listing the times at which the first bus and minibus will leave the park.
From there, add 40 and 50 minutes respectively to each departure time to find the next departure time for each vehicle.
Here is the timetable,
Departure time Bus interval Minibus interval
8.00 a.m. 40min 50min
8.40 a.m. 40min 50min
9.20 a.m. 40min 50min
10.00 a.m. 40min 50min
10.40 a.m. 40min 50min
11.20 a.m. 40min 50min
12.00 p.m. 40min 50min
12.40 p.m. 40min 50min
1.20 p.m. 40min 50min
2.00 p.m. 40min 50min
2.40 p.m. 40min 50min
3.20 p.m. 40min 50min
4.00 p.m. 40min 50min
4.40 p.m. 40min 50min
To identify any time of the day when the two vehicles will leave the park at the same time.
When the time of the intervals of the two vehicles overlap.
The least common multiple LCM of 40 and 50 is 200.
The two vehicles will leave the park at the same time every 200 minutes, or 3 hours and 20 minutes.
The first time this happens is at,
8:00am + 200 mins = 11:20am
So, at 11:20am both vehicles will leave the park at the same time.
To control traffic jam the park manager can consider the following strategies,
Adjust the departure times,
If the departure times are causing congestion,
The manager can adjust the intervals or the departure times to spread out the flow of vehicles.
Use a reservation system,
The manager can use a reservation system to stagger the departure times of the vehicles.
Ensuring that there are no backlogs at the loading area.
Limit the number of vehicles,
The manager can limit the number of vehicles that are allowed in the park at any given time.
To reduce the number of vehicles on the road and prevent congestion.
Promote carpooling,
The manager can encourage visitors to carpool to the park to reduce the number of vehicles on the road.
This can be done through promotional campaigns or by offering incentives for carpooling.
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Given that a company lets you download songs for $0.99 each after you pay a $5 fee to be a member, evaluate f(4)
for the function of total cost for x songs.
Responses
3.96
21. 96
9.90
8.96
please help 30 points
Answer:
Step-by-step explanation:
just here for the points
a unit vector that points in the direction of the vector −4i+7j can be written as
So, the unit vector that points in the direction of the vector −4i+7j can be written as (-4/√65)i + (7/√65)j.
To find a unit vector that points in the direction of the vector −4i+7j, follow these steps:
1. Find the magnitude of the given vector: The magnitude of a vector (a, b) can be calculated using the formula √(a^2 + b^2). In this case, the vector is (-4, 7).
Magnitude = √((-4)^2 + (7)^2) = √(16 + 49) = √65
2. Divide each component of the vector by its magnitude to find the unit vector: A unit vector has a magnitude of 1. To obtain the unit vector, divide each component of the original vector by the magnitude calculated in Step 1.
Unit vector = (-4/√65)i + (7/√65)j , So, the unit vector that points in the direction of the vector −4i+7j can be written as (-4/√65)i + (7/√65)j.
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Find the length of AB. Leave
your answer in terms of pi.
Therefore, the length of arc AB is 3π units (or approximately 9.42 units if rounded to the nearest hundredth).
What is arc?An arc is a curved segment of a circle. It is defined by two endpoints on the circle and the curve connecting them. The length of an arc is determined by the size of the angle it subtends at the center of the circle and the radius of the circle. Arcs are used in many geometric and trigonometric calculations, such as finding the length of an arc, the area of a sector, or the measure of an angle formed by two intersecting chords. In addition, arcs are commonly used in the design of structures and objects, such as arches, bridges, and curves in roads and railways.
Here,
The formula to find the length of an arc is:
length of arc = (angle measure in degrees / 360) x 2πr
where r is the radius of the circle.
In this case, the radius is 27 units and the angle measure is 20 degrees, so we can substitute these values into the formula to get:
length of arc = (20/360) x 2π(27)
length of arc = (1/18) x 54π
length of arc = 3π
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Question 5 of 20
Euler's formula, V-E+F=2, relates the number of vertices V, the number of edges E, and the number of
faces F, of a polyhedron. Solve Euler's formula for E
O E=2-V+F
O E= -F-2+V
OE=V+F-2
O E=2+-F
The solution for E in the equation V - E + F = 2 is E = V + F - 2
Solving the Euler's formula for EFrom the question, we have the following parameters that can be used in our computation:
V - E + F = 2
The above equation relates the number of vertices V, the number of edges E, and the number of faces F, of a polyhedron.
It is called the Euler's formula
So, we have
V - E + F = 2
Add E to both sides
V + F = 2 + E
Subtract 2 from both sides
V + F - 2 = E
So, we have
E = V + F - 2
Hence, the solution for E is E = V + F - 2
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according to national surveys, slightly more than of the adults in the united states drink alcohol. group of answer choices 50% 60% 70% 80%
According to national surveys conducted in current years, slightly more than 60% of adults within the united states of america drink alcohol.
Whilst this percentage may fluctuate slightly from year to year, it has remained pretty constant nowadays. it's crucial to be aware, however, that no longer all adults who drink alcohol do so in the same manner. some may additionally drink alcohol only on occasion or in moderation, even as others may engage in heavy or binge consuming.
Heavy alcohol consumption can have extreme health results, along with liver disorder, most cancers, and mental fitness issues, so it's critical for humans to reveal their consuming habits and are seeking help if important. additionally, it is essential for public health officers to hold tracking alcohol intake charges and promoting secure and responsible alcohol use.
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(e) The radius of the semi-circle centre O is 5 cm. A square is fitted into the semi-circle as shown in the diagram. Calculate the area of the square. (Hint: Let the length of the square equal x)
The length of the square is derived to be √20 using the Pythagoras rule and the area of the square is 20 cm²
What is the Pythagoras rule?The Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Let the length of the square be x, thus considering the triangle formed with the radius as the hypotenuse, x as the height and x/2 as the base, then By Pythagoras rule we can evaluate for x as follows:
x² + (x/2)² = 5²
(4x² + x²)/4 = 25
5x² = 100 {cross multiplication}
x² = 20
x = √20
Area of the square = (√20)²
Area of the square = 20 cm²
Therefore, the length of the square is derived to be √20 using the Pythagoras rule and the area of the square is 20 cm²
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The histograms display the frequency of temperatures in two different locations in a 30-day period.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 14. A shaded bar stops at 2 above 60 to 69, at 4 above 70 to 79, at 12 above 80 to 89, at 6 above 90 to 99, at 4 above 100 to 109, and at 2 above 110 to 119. The graph is titled Temps in Desert Landing.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 16. A shaded bar stops at 2 above 60 to 69, at 4 above 70 to 79, at 9 above 80 to 89, at 9 above 90 to 99, at 4 above 100 to 109, and at 2 above 110 to 119. The graph is titled Temps in Flower Town.
When comparing the data, which measure of center should be used to determine which location typically has the cooler temperature?
Mean, because Flower Town is symmetric
Mean, because Flower Town is skewed
Median, because Desert Landing is skewed
Median, because Desert Landing is symmetric
The answer is either A. IQR, because Sunny Town is symmetric or B. IQR, because Beach Town is skewed.
We know that,
A distribution refers to the pattern of how data is spread out or distributed across different values or intervals. It is a way to describe and analyze the shape, center, and spread of a set of data.
According to question:
To determine the location with the most consistent temperature, we need to measure the variability of the temperature data in both locations. The measure of variability that is appropriate for this purpose is the interquartile range (IQR), which measures the spread of the middle 50% of the data.
Therefore, the answer is either A. IQR, because Sunny Town is symmetric or B. IQR, because Beach Town is skewed, depending on the shape of the distributions. If the temperature data in Sunny Town is symmetric, then the IQR would be appropriate to measure the spread of the data. If the temperature data in Beach Town is skewed, then the IQR would also be appropriate to measure the spread of the data. However, if the temperature data in either location is not skewed, then the range would not be an appropriate measure of variability.
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how many unique slip planes of the {110} type are in a bcc metal?how many unique slip planes of the {110} type are in a bcc metal?2468122448
As per the mentioned informations, there are 4 slip planes associated with each of the 3 unique <111> directions, giving a total of 12 unique {110} slip planes in a body-centered cubic (BCC) crystal
In a body-centered cubic (BCC) crystal, there are 12 slip systems of the {110} type. Each of these slip systems is associated with a unique slip plane.
To understand why there are 12 slip systems, consider that the {110} plane has two perpendicular <111> directions, which are the directions of maximum atomic density in a BCC crystal. Each of these <111> directions can be associated with four equivalent {110} slip planes, which intersect at a line that lies along the <111> direction.
Therefore, there are 4 slip planes associated with each of the 3 unique <111> directions, giving a total of 12 unique {110} slip planes in a BCC metal.
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a model car has a scale of 1:100, find the scale length in cm if the car is 4.32m long
Answer: Therefore, the scale length of the model car is 4.32 cm.
Step-by-step explanation:
If the scale of the model car is 1:100, this means that every 1 unit on the model represents 100 units in real life. Let's use x to represent the scale length in cm.
Since the car is 4.32m long in real life, and 1m = 100cm, the length of the car in cm is:
4.32m x 100cm/m = 432cm
According to the scale, 1 unit on the model car represents 100 units in real life. Therefore:
1 unit on the model car = 100 units in real life = 100cm
So we can set up a proportion:
1 unit on the model car / x cm = 100 units in real life / 432 cm
Simplifying this expression, we get:
1 / x = 100 / 432
Cross-multiplying, we get:
x = 432 / 100
x = 4.32 cm
a new car is offered with eleven different optional packages. the dealer claims that there are more than 2,000 different combinations available. is this claim justified? explain. there are incorrect: your answer is incorrect. different ways to choose which of the packages you get, so the claim is changed: your submitted answer was incorrect. your current answer has not been submitted. justified.
The dealer's claim that there are "more than 1,000 different combinations" of the 10 optional packages available for the new car is justified, as there are actually 1024 possible combinations.
To determine whether the dealer's claim is justified, we need to calculate the total number of possible combinations of packages that can be selected.
Since there are 10 optional packages, there are 2^10 (or 1024) possible combinations of packages. This is because for each package, there are two possible choices: either it is selected or it is not selected.
Therefore, the dealer's claim that there are "more than 1,000 different combinations" is indeed justified. The actual number of possible combinations is 1024, which is greater than 1,000.
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Please help me with this question
The depth of the water if the speed of the tsunami is 10 m/s is approximately 0.34 meters, or 34 centimeters, given by the equation d = s / (3v).
What is speed?Speed is the rate at which an object moves through a distance per unit of time. It is often expressed in meters per second (m/s) or kilometers per hour (km/h).
What is equation?An equation is a mathematical statement that shows that two expressions are equal. It usually contains variables, constants, and mathematical operations, and can be solved to find the value of the variables.
According to the given information:
The equation relating the speed of a tsunami and the depth of the water is s = 3vd, where s is the speed of the wave (in m/s), v is the velocity of gravity (which is approximately 9.8 m/s²), and d is the depth of the water (in meters).
We can rearrange the equation to solve for d, which gives us:
d = s / (3v)
Plugging in the given values, we get:
d = 10 m/s / (3 × 9.8 m/s²)
Simplifying, we get:
d = 10 / 29.4
Therefore, the depth of the water is approximately 0.34 meters, or 34 centimeters.
So, if the speed of the tsunami is 10 m/s, the depth of the water is approximately 0.34 meters.
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The box plots display measures from data collected when 20 people were asked about their wait time at a drive-thru restaurant window.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 10 to 14.5 on the number line. A line in the box is at 12.5. The lines outside the box end at 5 and 20. The graph is titled Fast Chicken.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 8.5 to 15.5 on the number line. A line in the box is at 12. The lines outside the box end at 3 and 27. The graph is titled Super Fast Food
Which drive-thru typically has more wait time, and why?
Fast Chicken, because it has a larger median
Fast Chicken, because it has a larger mean
Super Fast Food, because it has a larger median
Super Fast Food, because it has a larger mean
Super Fast Food typically has more wait time, because although its box is wider than Fast Chicken's, its median is lower, indicating a shorter typical wait time.
The median is a measure of central tendency that represents the value at which half of the data falls below and half falls above.
A higher median indicates that the data is more dispersed, and thus there is likely to be more wait time at that drive-thru.
The median wait time for Fast Chicken in this case is 12.5 minutes, while the median wait time for Super Fast Food is 12 minutes. As a result, Fast Chicken typically has a longer wait time.
Thus, its upper whisker (ending at 27) is longer than Fast Chicken's (ending at 20), indicating that some customers had to wait much longer at Super Fast Food.
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Surface of triangle is 305 inches and area of base is 55 inches. Each face has a base of 9 inches. What is the slant
Note that where the above is given, the slant is 18.52 inches
How is this so?Given the above, we can use the formula for the surface area of a triangular pyramid, which is given by...
Surface area = base area + (1/2) × perimeter × slant
where the perimeter is the sum of the lengths of the three sides of the base, and the slant is the height of each triangular face.
We are given that the base area is 55 square inches and the perimeter is 3 × 9 = 27 inches. We are also given that the total surface area is 305 square inches. Substituting we have
305 = 55 + (1/2) × 27 × slant
Simplifying and solving for the slant, we get:
250 = 13.5 × slant
slant = 18.52 inches
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please answer this question . when you solve it please explain how you got the answer . thank you.
Answer:
210°
Step-by-step explanation:
You want the angle in standard position to the point (-√3, -1).
AngleThe angle θ in standard position to a point (x, y) can be found from ...
tan(θ) = y/x
θ = arctan(y/x)
The arctangent function gives an angle between -90° and +90°, so will give the value of the reference angle in this case. To find the angle in quadrant III, we must add 180° to the reference angle.
θ = arctan(-1/-√3) + 180° = 210°
The angle shown is 210°.
__
Additional comment
If you draw a vertical line from the point to the x-axis, you have a right triangle with side lengths 1 and √3. You know from your memory of special right triangles that this is a 30°-60°-90° triangle, whose smallest angle is 30°. This is the reference angle, so the angle of interest is 180° +30° = 210°.
I need the axis of symmetry and the vertex of the following y=x^2+6x+4
y=-2x^2+8x-5
y=x^2-2x
y=-x^2-8x-9
1. axis of symmetry = -3
vertex = ( -3,-5)
2. axis of symmetry = -2
vertex = ( -2,-13)
3. axis of symmetry = 1
vertex = ( 1,-1)
4. axis of symmetry = 4
vertex = (4,-5)
What is axis of symmetry and vertex?The vertex is the highest point if the parabola opens downward and the lowest point if the parabola opens upward.
The axis of symmetry is the line that cuts the parabola into 2 matching halves and the vertex lies on the axis of symmetry.
The vertex is calculated as -b/2a and we substitute the value in the equation to get the y axis. The equation must be in the form ax²+bx + c
The axis of symmetry is calculated as -b/2a
1. x²+6x+4
axis of symmetry = -6/2 = -3
the y cordinate vertex = -3)²+6(-3)+4 = 9-18+4 = -5
therefore the vertex = ( -3,-5)
2. 2x²+8x-5
axis of symmetry= -8/2(2) = -8/4 = -2
the y cordinate of vertex = 2(-2)² + 8(-2) -5
= 8-16-5 = -13
therefore the vertex = ( -2,-13)
3. x²-2x
axis of symmetry = -(-2)/2 = 2/2 = 1
the y cordinate of vertex = 1²-2(1) = 1-2 = -1
vertex = ( 1,-1)
4. x²-8x-9
axis of symmetry = -(-8)/2 = 8/2 = 4
the y cordinate of the vertex= 4²-8(4) -9 = 16-12-9 = -5
therefore the vertex = (4,-5)
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which of the three confidence intervals provides the most precise estimation? group of answer choices (3, 4) (2, 5) (2.5, 4.5)
Confidence interval (3,4) will provides the most precise estimation.
To determine which of the three confidence intervals provides the most precise estimation, we need to calculate the width of each interval. The width of a confidence interval is determined by the confidence level, the standard deviation of the population, and the sample size.
Assuming all three intervals have the same confidence level and population standard deviation, the interval with the smallest width will be the most precise.
Therefore, we can calculate the width of each interval as follows:
Interval (3,4): Width = 4 - 3 = 1
Interval (2,5): Width = 5 - 2 = 3
Interval (2.5,4.5): Width = 4.5 - 2.5 = 2
From the calculations, we can see that the interval (3,4) has the smallest width, and thus provides the most precise estimation.
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Givenf(x)=-x-1find,f(5)
Answer: -6
Step-by-step explanation:
f(5) means plug in 5 for x
f(5) = -5 - 1
=-6
Which images show rotations of one shape onto another? Select all that apply.
Answer:
C
Step-by-step explanation:
Find the 96th term of the arithmetic sequence 1,−12,−25
[tex]1~~,~~\stackrel{1-13}{-12}~~,~~\stackrel{-12-13}{-25}~~,~~...\hspace{5em}\stackrel{\textit{common difference}}{-13} \\\\[-0.35em] ~\dotfill\\\\ n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ d=\textit{common difference}\\[-0.5em] \hrulefill\\ a_1=1\\ d=-13\\ n=96 \end{cases} \\\\\\ a_{96}=1+(96-1)(-13)\implies a_{96}=1+(-1235)\implies \boxed{a_{96}=-1234}[/tex]
Leandro currently lets his chickens roam free, but he has lost a few chickens during nighttime to predators. Consequently, Leandro plans to use an 80-foot roll of
wire fencing to build a rectangular pen for his chickens to stay in at night. The fencing is 10-feet tall and Leandro will cover the top of the pen.
• The minimum side length will be 180 inches.
• The entire 80 feet of wire fencing will be used.
that is the greatest possible area, in square feet, for Leandro's chicken pen that satisfies these conditions?
A. 225 square feet
B. 400 square feet
C. 375 square feet
D. 1,600 square feet
According to the information, the answer is (C) 375 square feet, which is the closest option to 300 square feet.
How to calculate the greatest possible area for Leadro's chicken?Let's start by drawing a rectangle and labeling its dimensions. Since the perimeter is 80 feet and the minimum side length is 180 inches, we can set up the following equations:
2L + 2W = 80 (perimeter equation)L ≥ 180/12 = 15 feet (minimum side length)H = 10 feet (height of fence)Simplifying the perimeter equation, we get:
[tex]L + W = 40[/tex]Solving for one variable in terms of the other, we get:
[tex]L = 40 - W[/tex]Substituting into the area equation:
[tex]A = LW + 2LH + 2WH[/tex][tex]A = W(40 - W) + 2(10)(W) + 2(10)(40 - W)[/tex][tex]A = -W^2 + 60W + 800[/tex]To find the maximum area, we need to find the vertex of the parabolic equation[tex]A = -W^{2} + 60W + 800[/tex]. The x-coordinate of the vertex is given by x = -b/2a, where a = -1 and b = 60:
[tex]W = -b/2a = -60/-2 = 30[/tex]So the width of the pen is 30 feet, and the length is:
[tex]L = 40 - W = 40 - 30 = 10 feet[/tex]
Therefore, the area of the pen is:
[tex]A = LW = 10 x 30 = 300 square feet[/tex]
Since the pen has a height of 10 feet, we can also calculate the volume of the pen:
[tex]V = LH = 10 x 10 x 30 = 3,000 cubic feet[/tex]
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(4) The weight of 4 bags of almonds and 3 bags of peanuts is 750g. The
weight of 3 bags of almonds and 5 bags of peanuts is equal to the
weight of 14 bags of peanuts. How many grams does each bag of
almonds and peanuts weigh?
Thank you in advance for any help!
Answer:
Let x be the weight of a bag of almonds (in grams) and y be the weight of a bag of peanuts (in grams).
From the first statement, we have the equation:
4x + 3y = 750
From the second statement, we have:
3x + 5y = 14y
Simplifying the second equation, we get:
3x - 9y = 0
Now we have two equations:
4x + 3y = 750
3x - 9y = 0
We can use elimination to solve for one variable. Multiplying the second equation by 4, we get:
12x - 36y = 0
Adding this to the first equation, we get:
16x = 750
x = 46.875
Now we can substitute this value of x back into one of the equations to solve for y. Using the second equation, we get:
3(46.875) + 5y = 14y
140.625 = 9y
y = 15.625
Therefore, each bag of almonds weighs approximately 46.875 grams, and each bag of peanuts weighs approximately 15.625 grams.
Two angles are supplementary. If the m∠A is five times the sum of the m∠B plus 7.2°, what is m∠B?
°
Answer:
24
Step-by-step explanation:
If two angles are supplementary, they add up to 180.
Let's say m∠A = a and m∠B = b.
[tex]a=5(b+7.2)[/tex]
[tex]a= 5b + 36[/tex]
[tex]a-5b = 36[/tex]
We also still have [tex]a+b=180[/tex]
[tex]a-5b=36\\a+b=180[/tex]
Subtract,
[tex]-6b=-144[/tex]
[tex]b=24[/tex]
see if you can help me
We can see from the table and the graph that the relationship is proportional. Also, the line passes through the origin
What is a proportional relationship?A relationship between two variables is said to be proportionate if it causes both of the variables' values to rise or fall by the same amount.
To know if the relationship is proportional we have to look at the table so that we can be able to see the movement of the values and thus know whether or not we can classify what we see as a proportional relationship.
If the relationship is proportional, then the increase would be by fixed amounts as shown in the graph.
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PLEASE HELP!! determine asymptotes, intercepts, and multiplicities!!!
The vertical asymptotes of the function are -5 and 3, and the horizontal asymptote is 1.
What is the asymptotes of the function?
The asymptotes of the function, f(x) = (x² + 5x) / (x² + 2x - 15), is calculated as follows;
For vertical asymptotes;
x² + 2x - 15 = 0
(x + 5)(x - 3) = 0
x = -5 or 3, this is the vertical asymptotes.
The horizontal asymptotes is calculated as;
divide the numerator and denominator by x²;
f(x) = (x² + 5x) / (x² + 2x - 15)
= (1 + 5/x) / (1 + 2/x - 15/x²)
As x approaches infinity, both 5/x and 2/x become very small, and 15/x² becomes even smaller.
The limit of the function:
f(x) → 1 / 1 = 1
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what is 7/8 x 1/8 intion
fac
The product of 7/8 and 1/8 is 7/64. This can be obtained by multiplying the numerators together to get 7, and multiplying the denominators together to get 64.
To multiply two fractions, we simply multiply their numerators together and then multiply their denominators together. So, 7/8 x 1/8 would be
(7 x 1) / (8 x 8) = 7/64
Therefore, 7/8 x 1/8 equals 7/64.
In words, we can say that 7/8 represents 7 parts out of 8, while 1/8 represents 1 part out of 8.
To find the result of multiplying these fractions, we multiply the parts together: 7 x 1 = 7. Then, we multiply the total number of parts, which is
8 x 8 = 64.
So, the result is 7/64, which means that 7/8 x 1/8 represents 7 parts out of 64.
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WHAT ELSE WOULD NEED TO BE CCONGRUENT TO SHOW THAT ABC = XYZ BY ASA
the value of a building is currently 281000. if the value increase by 4.5%, what will the new be value
N Determine the size of all numbered angles
The size of all numbered angles are ∠1 = 80 degrees, ∠2 = 20 degrees and ∠3 = 80 degrees
Determining the size of all numbered anglesGiven that we have
The figure
Also, we have
GEF = 80 degrees
By the theorem of corresponding angles, we have
∠3 = 80 degrees
Next, we have
∠2 = 180 - 80 - 80 degrees --- sum of angles in a triangle
So, we have
∠2 = 20 degrees
Lastly, we have
∠1 = 80 degrees --- sum of angles in a triangle
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if tan theta=-3/2 and 90°
The value of cos Θ /2 and tan Θ /2 can be found to be:
cos Θ /2 = √((1 - √(4/13))/2) tan Θ /2 = √((1 + √(4/13))/(1 - √(4/13)))How to find the cosine and tangent ?We are given that 90° < Θ < 180°, which means that theta would be in the second quadrant.
We can therefore use half - angle formulas to find cos Θ /2 and tan Θ /2.
To find cos Θ /2, we have:
cos(Θ/2) = ±√((1 + cos(Θ))/2)
cos(Θ/2) = ±√((1 - √(4/13))/2)
cos(Θ/2) = √((1 - √(4/13))/2)
To find tan Θ /2, we have:
tan(Θ/2) = ±√((1 - cos(Θ))/(1 + cos(Θ)))
tan(Θ/2) = ±√((1 + √(4/13))/(1 - √(4/13)))
tan(Θ/2) = √((1 + √(4/13))/(1 - √(4/13)))
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The full question is:
Suppose that tan Θ = - 3/2 and 90 °< Θ < 180 °.
Find the exact values of cos Θ /2 and tan Θ /2
