Hello, I am Alyssa Ann Verrett.
Put the numbers in order:
City A: {2, 3.5, 4, 4, 5, 5.5}
City B: {3.5, 4, 5, 5.5, 6, 6}
a)
The mean monthly rainfall amount for city A: 4 in;
The mean monthly rainfall amount for city B: 5 in;
b)
The MAD monthly rainfall amount for city A: 0.8 in;
The MAD monthly rainfall amount for city B: 0.8 in;
c)
The median monthly rainfall amount for city A: 4 in;
The median monthly rainfall amount for city A: 5.25 in;
Step-by-step explanation:
a) The general definition of mean of a set X is:
mean = (x₁ + x₂ + x₃ + ... xₙ)/n
For City a:
mean = (4+3.5+5+5.5+4+2)/6 = 4
For City b:
mean = (5+6+3.5+5.5+4+6)/6 = 5
b) The general definition of mean absolute deviation of a set X is:
MAD = (|x₁-mean| + |x₂-mean| + |x₃-mean| + ... + |xₙ-mean|)/n
For City a:
MAD = ( |4-4| + |3.5-4| + |5-4| + |5.5-4| + |4-4| + |2-4| )/6 = (0 + 0.5 + 1 + 1.5 + 0 + 2)/6 = 5/6 =0.8
For City b:
MAD = ( |5-5| + |6-5| + |3.5-5| + |5.5-5| + |4-5| + |6-5| )/6 = (0 + 1 + 1.5 + 0.5 + 1 + 1)/6 = 5/6 = 0.8
c) The general definition of median depends on the quantity of elements in the set X and it represents the middlemost value of the set:
When the quantity is odd:
median= x₍ₙ₊₁₎/₂
When the quantity is even:
median= (xₙ/₂ + x ₙ₊₂/₂) /2
For City A:
median = 2, 3.5, 4, 4, 5, 5.5 = (4 + 4) / 2 = 4
For City B:
median = 3.5, 4, 5, 5.5, 6, 6 = (5 + 5.5) / 2 = 5.25
Students attending a technology summer camp were asked what technology class they would like to attend at the camp. They chose between one of the following classes: robotics, video game design, or website design. The camp director constructed a frequency table to analyze the students’ class choices.
Robotics Video Game Design Website Design Total
Females 116 94 152 362
Males 172 157 52 381
Total 288 251 204 743
A camp counselor says that about 68% of female students chose a design class and the camp director says that about 34% of female students chose a design class
The frequency table shows that 152 female students chose website design out of a total of 362 female students, which is about 0.421 or 42%.
The frequency table shows that out of the total 362 female students attending the technology summer camp, 152 chose website design, which is a design class. This means that the percentage of female students who chose a design class is 152/362 = 0.4202 or about 42%.
However, the camp counselor says that about 68% of female students chose a design class. It is unclear where the counselor obtained this information from as it is not reflected in the frequency table. It is possible that the counselor gathered this information from a different survey or observation.
On the other hand, the camp director's statement is more accurate as it is based on the frequency table.
The frequency table shows that 152 female students chose website design out of a total of 362 female students, which is about 0.421 or 42%. It is important to rely on data and accurate information when making statements or drawing conclusions.
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In the diagram below, congruent figures 1, 2 and 3 are drawn.
Which sequence of transformations maps figure 1 onto figure 2 and then figure 2 onto figure 3
A sequence of transformations that maps figure 1 onto figure 2 and then figure 2 onto figure 3 include the following: D. a translation followed by a rotation.
What is a translation?In Mathematics and Geometry, a translation can be defined as a type of rigid transformation which moves every point of the object in the same direction, as well as for the same distance.
This ultimately implies that, a translation is a type of rigid transformation that does not change the orientation of the original geometric figure (pre-image).
What is a rotation?In Mathematics, a rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.
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Complete Question:
Which sequence of transformations maps figure 1 onto figure 2 and then figure 2 onto figure 3?
a reflection followed by a translation
a rotation followed by a translation
a translation followed by a reflection
a translation followed by a rotation
To the nearest hundredth, what is the value of x?
Use a trigonometric ratio to compute a distance
Therefore, the value of x to the nearest hundredth is approximately 72.73 units.
What is triangle?A triangle is a geometrical shape that consists of three straight sides and three angles. It is a polygon with three vertices, and the sum of its interior angles always adds up to 180 degrees. Triangles are classified based on the length of their sides and the measure of their angles. The most common types of triangles are equilateral, isosceles, and scalene, based on the length of their sides, and acute, right, and obtuse, based on the measure of their angles. Triangles have a wide range of applications in mathematics, physics, engineering, and other fields.
Here,
Therefore, in this triangle, sin(67°) = 67/x, where x is the length of the hypotenuse.
We can rearrange this equation to solve for x:
x = 67 / sin(67°)
Using a calculator, we find that sin(67°) is approximately 0.921, so:
x = 67 / 0.921
x ≈ 72.73
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Math 7 pap cdb 2 2020-2021 / 7 of 1
rectangle qrst is dilated with the origin as the center of dilation to create rectangle q'r's't'.
o'
r
q
which rule best represents the dilation applied to rectangle qrst to create rectangle q'r's't'?
o a. (x, y) - (3x, 3y)
o b. (x,y) - (1/3x, 1/3y)
o c. (x, y) - (x+3, y + 3)
o d. (x, y) - (x + 1/3, y + 1/3)
The correct answer is option (d) (x, y) → (x + 1/3, y + 1/3).
What is the rule that best represents the dilation applied to rectangle qrst to create rectangle q'r's't'?The dilation is a type of transformation that changes the size of the object, but not the shape. It can be represented by a rule in which each point of the original object is multiplied or divided by a constant factor. In this case, since the center of dilation is the origin, we can find the constant factor by dividing the coordinates of the corresponding points of the two rectangles.
Let's take the point Q(x, y) in rectangle QRST and its corresponding point Q'(x', y') in rectangle Q'R'S'T'. Since the dilation is centered at the origin, we have:
x' = k * x
y' = k * y
where k is the constant factor of dilation. We can find k by dividing the corresponding sides of the rectangles. For example, the length of QR is 4 units, and the length of Q'R' is 4/3 units. Therefore, k = 4/3.
Using this value of k, we can find the coordinates of any point in rectangle QRST that corresponds to a point in rectangle Q'R'S'T'. For example, point R(6, 2) in rectangle QRST corresponds to point R'(6 + 1/3, 2 + 1/3) = (20/3, 7/3) in rectangle Q'R'S'T'.
Hence, the correct answer is (x, y) → (x + 1/3, y + 1/3).
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Hugo rides the bus to work every day, a distance of 18 miles. The distance on the route map between the station by Hugos house and the station by his work is 3 inches. What is the maps scale? 1 inch = _____ miles.
The maps scale is 1 inch = 6 miles. This means that for every inch on the map, it represents 6 miles in real-life distance.
To determine the scale, we need to know the relationship between the distance on the map and the actual distance. In this case, the distance on the route map between Hugo's house and his work is 3 inches, and the actual distance he travels by bus is 18 miles.
To find the scale, we can set up a proportion using the given information:
(distance on the map in inches) / (actual distance in miles) = (1 inch) / (x miles)
Now, we can plug in the known values:
(3 inches) / (18 miles) = (1 inch) / (x miles)
To solve for x, we can cross-multiply:
3 inches * x miles = 18 miles * 1 inch
3x = 18
Now, divide both sides by 3:
x = 6
So, the scale of the map is 1 inch = 6 miles.
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In triangle abc, point d is on side ac, ab=bd=dc=12 inches, and measurement of angle bdc= 2 times the measurement of angle abd. find ac
The length of AC in triangle ABC is 24 inches.
In triangle ABC, let point D be on side AC such that AB = BD = DC = 12 inches. We are given that the measure of angle BDC is twice the measure of angle ABD.
To find the length of AC, we can use the Law of Cosines. This law relates the lengths of the sides of a triangle to the cosine of one of its angles. In this case, we can apply the Law of Cosines to triangle ABD to find the length of AD:
AD^2 = AB^2 + BD^2 - 2 * AB * BD * cos(ABD)
Since AB = BD = 12 inches, we have:
AD^2 = 12^2 + 12^2 - 2 * 12 * 12 * cos(ABD)
AD^2 = 288 - 288 * cos(ABD)
Now, let's consider triangle BDC. We are given that the measure of angle BDC is twice the measure of angle ABD. Let's denote the measure of angle ABD as x. Therefore, the measure of angle BDC is 2x.
Since the sum of angles in a triangle is 180 degrees, we can write:
x + 2x + angle BCD = 180
3x + angle BCD = 180
angle BCD = 180 - 3x
Now, let's apply the Law of Cosines to triangle BDC to find the length of BC:
BC^2 = BD^2 + CD^2 - 2 * BD * CD * cos(BDC)
BC^2 = 12^2 + 12^2 - 2 * 12 * 12 * cos(2x)
BC^2 = 288 - 288 * cos(2x)
Since AD = DC, we have AD = 12 inches. Now we can write the equation for the total length AC:
AC = AD + DC
AC = 12 + 12
AC = 24 inches
Therefore, the length of AC in triangle ABC is 24 inches.
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PLEASE HELP!! LIKE ASAPP
Answer:
12(8) + (1/2)(13)(20) + (1/4)π(8^2)
= 96 + 130 + 4π = 226 + 16π ft^2
= about 276.27 ft^2
can someone help me please
Answer:
3. 254.34 mm^2
4. 615.44 cm^2
5. 314 in^2
6. 7.065 in^2
7. 3.14 cm^2
8. 1.76625 ft^2
Step-by-step explanation:
AREA FORMULA: π * r^2
This question is asking to use 3.14 or 22/7 for x.
The following steps will use 3.14.
3. r = 9 mm (r^2 = 81 mm)
A = 81 * 3.14 = 254.34 mm^2
4. r = 14 cm (r^2 = 196 cm)
A = 196 * 3.14 = 615.44 cm^2
5. r = 10 in (r^2 = 100 in)
A = 100 * 3.14 = 314 in^2
Questions 6-8 show the diameter of the circle.
Divide by 2 to find the radius, then plug that into the area formula
6. r = 1.5 in (r^2 = 2.25 in)
A = 2.25 * 3.14 = 7.065 in^2
7. r = 1 cm (r^2 = 1 cm)
A = 1 * 3.14 = 3.14 cm^2
8. r = 0.75 ft (r^2 = 0.5625 ft)
A = 0.5625 * 3.14 = 1.76625 ft^2
Maria records random speeds from three different Internet providers in the table. ProviderDownload Speed (megabits per second)CityNet3. 6, 3. 7, 3. 7, 3. 6, 3. 9Able Cable3. 9, 3. 9, 4. 1, 4. 0, 4. 1Tel-N-Net3. 9, 3. 7, 4. 0, 3. 6, 3. 8 Which company offers the fastest mean downloading speed?  00:00 CityNet  00:00 Able Cable  00:00 Tel-N-Net  00:00 Impossible to determine from the information given
Able Cable offers the fastest mean downloading speed among the three providers with a speed of 4.0 Mbps.
How to determine the fastest internet provider?We can calculate the mean (average) download speed for each provider and compare them to determine which company offers the fastest mean downloading speed.
Based on the given data, the mean download speed for each provider is:
City Net: (3.6 + 3.7 + 3.7 + 3.6 + 3.9) / 5 = 3.7 megabits per second (Mbps)
Able Cable: (3.9 + 3.9 + 4.1 + 4.0 + 4.1) / 5 = 4.0 Mbps
Tel-N-Net: (3.9 + 3.7 + 4.0 + 3.6 + 3.8) / 5 = 3.8 Mbps
Therefore, Able Cable offers the fastest mean downloading speed among the three providers with a speed of 4.0 Mbps.
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A 2-column table with 6 rows. the first column is labeled years with entries 1, 2, 3, 4, 5, 6. the second column is labeled value(dollar sign) with entries 5,250; 5,512.50; 5,788.13; 6,077.54; 6,381.42; 6,700.49. the data in the table represents the value of a savings account at the end of each year for 6 years. the relationship between the increasing years and the increasing value of the account is exponential. there is rate of change in an exponential relationship. after each year, the value of the account is times as large as the previous year.
The value of the account is 1.05 times as large as the previous year
There is a 2-column table with 6 rows representing the value of a savings account at the end of each year for 6 years. The relationship between the years and the value of the account is exponential, and there is a rate of change in this exponential relationship.
To find the rate of change in this exponential relationship, you can follow these steps:
1. Divide the value of the account in the second year by the value of the account in the first year: 5,512.50 / 5,250 = 1.05.
2. Since the relationship is exponential and the rate of change is constant, the account's value will increase by the same factor every year. In this case, the rate of change is 1.05, which means that after each year, the value of the account is 1.05 times as large as the previous year.
In summary, the rate of change in the exponential relationship between the increasing years and the increasing value of the account is 1.05, meaning that after each year, the value of the account is 1.05 times as large as the previous year.
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Determine whether the geometric series is convergent or divergent. If it is convergent, find the sum. (If the quantity diverges, enter DIVERGES.) 00 7 80 3| n n = 1
|r| = 7/80 < 1, the series is convergent. The sum = 0/(1-7/80) = 0. the sum of the geometric series is 0.
The geometric series with first term 0 and common ratio 7/80 is given by 0, 7/80, (7/80)², (7/80)³, ... In general, the nth term is (7/80)ⁿ⁻¹.
To determine whether this series is convergent or divergent, we can use the formula for the sum of an infinite geometric series:
sum = a/(1-r)
where a is the first term and r is the common ratio. In this case, a = 0 and r = 7/80.
If |r| < 1, then the series converges to the sum given by the above formula. If |r| ≥ 1, then the series diverges.
In this case, |r| = 7/80 < 1, so the series is convergent. The sum is given by:
sum = 0/(1-7/80) = 0
Therefore, the sum of the geometric series is 0.
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3 cm
H
8 cm
12 cm
What is the volume of the table tent?
The volume of the table tent 3 cmH8 cm12 cm is 288 cubic cm.
How to determine the volume of the table tentThe volume of the table tent can be found by multiplying the length, width, and height of the tent.
Volume = length x width x height
In this case, the length is 12 cm, the width is 8 cm, and the height is 3 cm.
Volume = 12 cm x 8 cm x 3 cm
Volume = 288 cubic cm
Therefore, the volume of the table tent is 288 cubic cm.
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Yvette cuts a hole from a rectangular panel to make a window. She wants to determine how
much of the panel is left after she cuts the hole. She writes:
(fraction left)
(area of panel) - (area of hole)
(area of panel)
If the panel is 3 feet by 2 feet, and the hole is 1 foot by foot, what is the fraction left?
The area of the panel left after she cuts the hole is 5.215 ft²
Given that a circular hole of 1 foot by foot has been cut out of a rectangular panel of 3 feet by 2 feet,
We need to find the area of the remaining part after the cutting of the hole,
So, we will find the same by subtracting the area of the hole from the area of the panel.
So, area of the hole = π×radius² = 3.14×0.5² = 0.785 ft²
Area of the panel = length × width = 3 × 2 = 6 ft²
Area remaining part = 6-0.785 = 5.215 ft²
Hence the area of the panel left after she cuts the hole is 5.215 ft²
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Find the value of X of the circle
The circle's x value will continue to be the same as the arc ST. So, x has a value of 40 degrees.
What is circle?A circle's centre is the point from which all of the distances to the other points on the circle are equal. The radius of the circle is the measurement at issue.
Every point on a circle is a geometric shape that is equally separated from the centre.
The location of any point that is evenly separated from the fixed point known as the circle's centre can also be characterised as it.
The distance from any point on a circle to the centre is known as the radius of the circle.
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Rectangle ABCD shown below is a scale drawing of rectangle UVWX. the scale is 1:2 1/2
fill in the blanks below
someone please help
Using area formula for rectangles, we can find the new area of the rectangle to be 7350m².
The new dimensions are:
Length = 105m
Breadth = 70m
Define a rectangle?A rectangle is a quadrilateral with parallel opposite sides and equal angles. There are a lot of rectangular objects all around us. Each rectangle's two defining characteristics are its length and breadth. A rectangle's longer and shorter sides are its width and length, respectively.
Here in the question,
Dimensions of the rectangle are as follows:
Length, l = 42m.
Width, w = 28m.
Scale factor here is 1: 5/2
Now,
Let the new width be x.
The new width will be:
28/x = 1/ (5/2)
Cross multiplying:
⇒ 28 × 5/2 = x
⇒ x = 70m.
So, new width = 70m.
Now, let new length be x.
So,
42/x = 1/ (5/2)
Cross multiplying:
⇒ x = 42 × 5/2
⇒ x = 105m.
So, the new length = 105m.
Now new area will be:
70 × 105
= 7350m².
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A velociraptor runs 5m [e] , 10 m [w], 3m [s], & 2m [w] in 10 seconds. calculate speed & velocity.
The velociraptor's speed is 2 m/s, and its velocity is -0.3 m/s [w].
What is the total distance covered?
To calculate the speed and velocity of the velociraptor, we need to first find the total distance it covered and the displacement.
Total distance = 5m + 10m + 3m + 2m = 20m
Displacement = Final position - Initial position
Displacement = (2m [w]) - (5m [e])
Displacement = -3m [w]
Velocity is defined as displacement per unit time, while speed is defined as distance per unit time.
Velocity = Displacement / Time
Velocity = -3m [w] / 10s
Velocity = -0.3 m/s [w]
Speed = Total distance / Time
Speed = 20m / 10s
Speed = 2 m/s
Therefore, the velociraptor's speed is 2 m/s, and its velocity is -0.3 m/s [w].
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The box plot displays the number of push-ups completed by 9 students in a PE class.
A box plot uses a number line from 12 to 58 with tick marks every 2 units. The box extends from 27.5 to 42.5 on the number line. A line in the box is at 37. The lines outside the box end at 15 and 55. The graph is titled Push-Ups In PE and the line is labeled Number of Push-Ups.
Which of the following represents the value of the lower quartile of the data?
27.5
37
42.5
55
the answer is Q1 = 27.5
h(t) = -16t^2 +90t
how many seconds will it take for the ball to reach its maximum height
The amount of time it would take for the ball to reach its maximum height is 2.1825 seconds.
How to determine the time when the ball would reach its maximum height?Based on the information provided, we can logically deduce that the height (h) in feet, of this ball above the ground is related to time by the following quadratic function:
Next, we would determine the maximum height of this ball by taking the first derivate in order to determine the time (t) it takes as follows;
h(t) = -16t² + 90t
h'(t) = -32t + 90
90 = 32t
t = 90/32 = 2.1825 seconds.
h(2.1825) = -16(2.1825)² + 90(2.1825)
h(2.1825) = 120.21 feet.
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Piotr has run the first 24 miles of a race which means he is 85% finished. How long is the race?
The total length of the race is approximately 28.24 miles.
To determine the total length of the race, we can use the given information: Piotr has completed 24 miles, which represents 85% of the race. We can set up a proportion to find the total length. Let 'x' represent the full length of the race:
(24 miles) / x = 85% / 100%
To solve for 'x', we can first convert the percentage to a decimal by dividing 85 by 100, resulting in 0.85:
24 / x = 0.85
Next, we can cross-multiply:
0.85 * x = 24
Now, we can solve for 'x' by dividing both sides by 0.85:
x = 24 / 0.85
x ≈ 28.24 miles
Therefore, the total length of the race is approximately 28.24 miles. Piotr has completed 85% of this distance, which means he has run 24 miles and has around 4.24 miles remaining to finish the race.
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What is the cost of 0. 7 kg of apples, if 1 kg of apples cost 89. 50
In the proportion, the cost of 0.7kg apple is Rs.62.65 .
What is proportion?
A percentage is created when two ratios are equal to one another. We write proportions to construct equivalent ratios and to resolve unclear values. a comparison of two integers and their proportions. According to the law of proportion, two sets of given numbers are said to be directly proportional to one another if they grow or shrink in the same ratio.
Here cost of 1kg apples = 89.50
Then cost of 0.7 kg apple = x.
Now using proportion,
=> 1 = 89.50
0.7= x
=> x = [tex]\frac{89.50\times0.7}{1}[/tex]
=> x = 62.65.
Hence the cost of 0.7kg apple is Rs.62.65 .
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Consider a metal plate on [0,1] ×[0,1] with density rho(x,y) = αx
+ βy g/cm2, where α and β are positive constants. Show that the
center of mass must lie on the line x + y = 7/6 .
The center of mass of the metal plate with density rho(x,y) = αx+ βy g/cm2 must lie on the line x + y = 7/6.
To find the center of mass of the metal plate, we need to calculate the coordinates of its centroid (X, Y). The coordinates of the centroid are given by:
X = (1/M) ∬(R) x ρ(x,y) dA, Y = (1/M) ∬(R) y ρ(x,y) dA
where M is the total mass of the plate, R is the region of integration (0 ≤ x ≤ 1, 0 ≤ y ≤ 1), and dA is the differential area element.
We can calculate the total mass M of the plate as follows:
M = ∬(R) ρ(x,y) dA = α/2 + β/2 = (α + β)/2
Using the given density function, we can calculate the integrals for X and Y:
X = (1/M) ∬(R) x ρ(x,y) dA = (2/αβ) ∬(R) x(αx+βy) dA = (2/3)(α+β)
Y = (1/M) ∬(R) y ρ(x,y) dA = (2/αβ) ∬(R) y(αx+βy) dA = (2/3)(α+β)
Thus, the coordinates of the centroid are (X, Y) = ((2/3)(α+β), (2/3)(α+β)).
Now, if we substitute X + Y = (4/3)(α+β) into the equation x + y = 7/6, we get:
x + y = 7/6
2x + 2y = 7/3
2(x+y) = 4/3(α+β)
x+y = (2/3)(α+β)
which shows that the centroid lies on the line x + y = 7/6. Therefore, the center of mass must also lie on this line.
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PLEASE HELP THIS A FRESHMEN QUESTION
Answer:
The total area of the "t" figure is 20 square units.
The figure is made up of a triangle, a square, and a rectangle.
The area of the triangle is (1/2)(base)(height) = (1/2)(4)(3) = 6 square units.
The area of the square is 4^2 = 16 square units.
The area of the rectangle is 2(4)(3) = 24 square units.
The total area of the figure is 6 + 16 + 24 = 46 square units.
However, the question asks for the area of the composite region, which is the shaded region in the figure. The shaded region is a triangle with base 4 units and height 3 units. The area of this triangle is (1/2)(base)(height) = (1/2)(4)(3) = 6 square units.
Therefore, the area of the composite region is 6 square units.
Here is a diagram of the figure with the areas of each shape labeled:
[Image of the "t" figure with the areas of each shape labeled]
Answer:
Step-by-step explanation:
I don't have enough information to answer this.
The high temperature in Jackson, WY, on July 13 was 80°F. Use the formula, C = (F - 32), where C is Celsius degrees and
Fis Fahrenheit degrees, to convert 80°F to Celsius degrees. Round to the nearest tenth of a degree
The temperature of 80°F is equivalent to 48°C.
How to convert temperature from Fahrenheit to Celsius using a specific formula?To convert 80°F to Celsius degrees using the formula C = (F - 32), we substitute the given Fahrenheit temperature into the formula.
C = (80 - 32) = 48
Therefore, the temperature of 80°F is equivalent to 48°C.
The Celsius scale is commonly used in scientific and international contexts, while the Fahrenheit scale is more prevalent in the United States. The conversion formula allows us to convert temperatures between these two scales.
Rounding to the nearest tenth of a degree, we find that 48°C remains unchanged.
It's worth noting that the Celsius scale sets the freezing point of water at 0°C and the boiling point at 100°C at standard atmospheric pressure. In contrast, on the Fahrenheit scale, water freezes at 32°F and boils at 212°F.
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Quickly
Triangle XYZ- triangle JKL. Use the image to answer the question.
K to j is10.44
K to L = unknown
L to J = 9.84
X to Y = 8.7
X to Z = 8.2
Y to Z = 7.8
Determine the measurement of KL.
A: KL = 8.58
B: KL = 6.36
The value of KL as shown in the image is 12 units
What is an equation?An equation is an expression that shows how numbers and variables using mathematical operators.
Two triangles are said to be similar, if the ratio of their corresponding sides are in the same proportion.
For the triangle shown, since triangle XYZ is similar to triangle JKL, hence:
KL/XY = KJ / XZ
substituting, KJ = 10.44:
KL / 8.7 = 11.31 / 8.2
KL = 12
The value of KL is 12 units
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Draw a triangle with side lengths that are 3 inches, 5 inches, and 6 inches long. Is this the only triangle that you can draw using these side lengths? Explain
The combination of these side lengths uniquely determines the shape of the triangle.
Hi! To draw a triangle with side lengths 3 inches, 5 inches, and 6 inches, make sure that the sum of any two sides is greater than the third side. In this case, 3 + 5 > 6, 3 + 6 > 5, and 5 + 6 > 3, so a triangle can be formed.
Yes, this is the only triangle you can draw using these side lengths.
The reason is that the side lengths are fixed, and according to the triangle inequality theorem, the combination of these side lengths uniquely determines the shape of the triangle.
The combination of these side lengths uniquely determines the shape of the triangle.
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Which statement could be made based on the diagram below?
A) m∠3 + m∠6 = 90
B) ∠3 = ∠6
C) ∠3 = ∠5
D) m∠4 + m∠5 = 180
Need help please show work
Answer:
Add the lengths:
5x - 16 + 2x - 4 = 7x - 20
009 10.0 points Let f be a function defined on (-1, 1] such that f(-1) = f(1) = . Consider the following properties that f might have: A. f(1) = 2; x | | B. f continuous on (-1, 1]; C. Which properties ensure that there exists cin (-1, 1) at which f'(c) = 0? - f(x) = 22/3 = x2 1. B and C only 2. none of them 3. all of them 4. B only 5. C only 6. A and C only 7. A only 8. A and B only
Properties B and C together ensure that there exists a 'c' in (-1, 1) at which f'(c) = 0.
Your answer: 1. B and C only
Which properties ensure that there exists ?
a 'c' in (-1, 1) at which f'(c) = 0, given f(-1) = f(1) = and the properties A, B, and C.
First, let's define the properties:
f(1) = 2
f is continuous on (-1, 1]
f(x) = (22/3) - x^2
To ensure that there exists a 'c' in (-1, 1) at which f'(c) = 0, we will use the Mean Value Theorem (MVT). MVT states that if a function is continuous on a closed interval and differentiable on an open interval, then there exists at least one 'c' in the interval where the derivative is 0.
Looking at property B, it states that f is continuous on (-1, 1], which satisfies the first condition of the MVT. Property C provides a specific function for f(x), which is differentiable on (-1, 1) since it is a polynomial function. Therefore, properties B and C together ensure that there exists a 'c' in (-1, 1) at which f'(c) = 0.
Your answer: 1. B and C only
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WILL MARK BRAINLIEST QUESTION IS IN THE PHOTO
The value of measure of RU is,
⇒ 149°
We have to given that;
In circle,
m RS = 88 degree
m ST = 35 degree
Hence, We can formulate;
The value of measure of RU is,
⇒ 360° - ( 88° + 35° + 88°)
⇒ 360° - 211°
⇒ 149°
Thus, The value of measure of RU is,
⇒ 149°
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Sand falls from an overhead bin and accumulates in a conical pile with a radius that is alwavs two times its heiaht. Suppose the height of the pile increases at a rate of 2 cm/s when the pile is 11 cm high. At what rate is the sand leaving the bin at that instant?
To solve this problem, we need to use related rates. Let's start by drawing a diagram:
```
/\
/ \
/ \
/ \
/ \
/__________\
```
We know that the radius of the conical pile is always two times its height, so we can label the diagram as follows:
```
/\
/ \
/ \
/ \
/ \
/__________\
/| r=2h \
/ |___________\
```
Now we need to find an equation that relates the height of the pile to its radius. We can use the formula for the volume of a cone:
```
V = (1/3)πr^2h
```
We want to solve for h in terms of r:
```
V = (1/3)πr^2h
3V/πr^2 = h
```
Now we can differentiate both sides of this equation with respect to time:
```
d/dt (3V/πr^2) = d/dt h
0 = (3/πr^2) dV/dt - (2/πr^3) dr/dt
```
We're given that the height is increasing at a rate of 2 cm/s when the pile is 11 cm high, so we know that:
```
dh/dt = 2 cm/s
h = 11 cm
```
We want to find the rate at which sand is leaving the bin, which is given by `dV/dt`. We can solve for this using the equation we derived:
```
0 = (3/πr^2) dV/dt - (2/πr^3) dr/dt
dV/dt = (2/3)πr^2 (dh/dt) / r
```
Now we just need to plug in the values we know:
```
dh/dt = 2 cm/s
h = 11 cm
r = 2h = 22 cm
dV/dt = (2/3)π(22)^2 (2) / 22
dV/dt = 264π/3
```
So the rate at which sand is leaving the bin when the pile is 11 cm high is `264π/3 cm^3/s`.
To solve this problem, we can use the relationship between the radius and height of the conical pile, as well as the given rate of height increase.
Since the radius (r) is always two times the height (h), we have r = 2h. The volume (V) of a cone is given by the formula V = (1/3)πr^2h. We can substitute r with 2h, so V = (1/3)π(2h)^2h.
Now, let's differentiate both sides with respect to time (t):
dV/dt = (1/3)π(8h^2)dh/dt
When the height is 11 cm, the rate of height increase (dh/dt) is 2 cm/s. We can substitute these values into the equation:
dV/dt = (1/3)π(8(11)^2)(2)
Solving for dV/dt:
dV/dt ≈ 2046.92 cm³/s
At that instant, the sand is leaving the bin at a rate of approximately 2046.92 cm³/s.
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