Therefore, the approximate dimensions of the rectangle to the nearest tenth of a meter are width = 7.9 m and length = 10.8 m.
What is area?Area is a measure of the size of a two-dimensional surface or shape. It is typically expressed in square units, such as square meters (m²), square centimeters (cm²), square feet (ft²), or square inches (in²).
Here,
Let's denote the width of the rectangle as "w" in meters. Then, according to the problem statement, the length of the rectangle can be expressed in terms of the width as:
length = 2w - 5
The area of the rectangle is given as 97 square meters, so we can write:
area = length × width
Substituting the expression for length in terms of the width, we get:
area = (2w - 5) × w
Expanding this expression, we get a quadratic equation in standard form:
2w² - 5w - 97 = 0
We can solve this equation using the quadratic formula:
w = (-(-5) ± √((-5)² - 4×2×(-97))) / (2×2)
Simplifying this expression, we get:
w ≈ 7.9 or w ≈ -6.2
Since the width of a rectangle cannot be negative, we discard the negative solution and approximate the width to the nearest tenth of a meter:
w ≈ 7.9 m
Using the expression for the length in terms of the width, we can find the length:
length = 2w - 5
≈ 10.8 m
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Emily got her monthly credit card statement, which showed a bill of $156. She paid the minimum payment due, which was $30. If the interest rate was 15.5%, then Emily had to pay interest on the amount of $ _________ and the amount of interest to be paid would be __________.
Emily had to pay interest on the amount of $126 and the amount of interest to be paid would be $16.41.
What is interest rate?
Interest rate is the percentage charged by a lender to a borrower for the use of money, usually expressed as an annual percentage of the principal borrowed.
Emily had to pay interest on the remaining balance after making the minimum payment of $30.
Remaining balance = $156 - $30 = $126
The amount of interest to be paid would be calculated as:
interest = (interest rate/12) * remaining balance
Where 12 is the number of months in a year.
So,
interest = (15.5/12) * $126 = $16.41
Therefore, Emily had to pay interest on the amount of $126 and the amount of interest to be paid would be $16.41.
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Find the least-squares regression line y^=b0+b1x through the point
(−3,0),(2,9),(5,13),(9,19),(10,23).
For what value of x is =0?
Answer:
3
Step-by-step explanation:
or differentiable parameterization of arc-length 2 in space ( not in a plane) how would you set up the function?
The function of differentiable parameterization of arc length 2 in space is ∫√(1)² + (2t)² + (cos(t))² dt.
To set up a differentiable parameterization of arc-length 2 in space, we can use the arc-length formula:
s = ∫√(dx/dt)² + (dy/dt)² + (dz/dt)² dt
where s is the arc length, t is the parameter, and (x, y, z) is the position vector.
We want the arc length to be 2, so we can set up the following equation:
2 = ∫√(dx/dt)² + (dy/dt)² + (dz/dt)² dt
We can then choose a function for each component of the position vector, such as:
x = t
y = t²
z = sin(t)
We can now find the derivatives with respect to t:
dx/dt = 1
dy/dt = 2t
dz/dt = cos(t)
We can substitute these into the arc-length formula:
2 = ∫√(1)² + (2t)² + (cos(t))² dt
Solving this integral for t will give us the desired parameterization of arc-length 2 in space. However, this integral may not have a closed-form solution, so numerical methods may need to be used to approximate the solution.
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The question is -
Differentiable parameterization of arc-length 2 in space ( not in a plane) how would you set up the function?
Graph triangle DEF with vertices D (6,2), E (6,6), and F (10,4) and its image after a dilation centered at the origin with a scale factor of 1/2. Then find the difference between the area of the image and the area of the preimage.
Answer:
The graph is below.
The area of the pre-images is 8 and the area of the image is 2. The difference is 6 [tex]units^{2}[/tex]
Step-by-step explanation:
Area of the large triangle
a = [tex]\frac{bxh}{2}[/tex] I am going to choose the vertical line to be the base because I can count the base to be 4 and the height straight up from the base to be 4.
a = [tex]\frac{4x4}{2}[/tex] = 8
I found the base for the image in the same way
a = [tex]\frac{2x2}{2}[/tex] 2
Helping in the name of Jesus.
(Using trig to find an angle)
Solve for x. Round to the nearest tenth of a degree, if necessary.
Step-by-step explanation:
For a RIGHT triangle Sin = opposite LEG / Hypotenuse
sin x = 45/ 83
x = arcsin (45/83) = use calculator = 32.8 degrees
To build your own capacitor, you have cut your sheets of wax paper and aluminum foil to a length of L = 0.8 m and you are rolling them on a pipe of diameter D = 5 cm. What is the number of turns? -n = 2.6 -n = 20.4 -n = 5.1 -n=10.2
The number of turns in the capacitor is approximately 5.1.
How we get the number of turns (n)?The number of turns in the capacitor can be calculated using the formula:
n = L / [π(D + t)]where L is the length of the sheets, D is the diameter of the pipe, and t is the thickness of the sheets.
Using the provided values, we can calculate the number of turns as follows:
L = 0.8 mD = 5 cm = 0.05 mt = negligible (assumed to be much smaller than D)n = 0.8 / [π(0.05)]= 5.092 (rounded to one decimal place)
In this problem, we are asked to calculate the number of turns in a capacitor made from sheets of wax paper and aluminum foil that are rolled on a pipe of diameter 5 cm. We are given the length of the sheets as 0.8 m.
To calculate the number of turns, we can use the formula that relates the length of the sheets, diameter of the pipe, and thickness of the sheets to the number of turns in the capacitor. Assuming the thickness of the sheets is much smaller than the diameter of the pipe, we can ignore the thickness in the calculation.
Using the provided values and this formula, we find that the number of turns is approximately 5.1. This means that the sheets need to be rolled around the pipe about 5 times to create the capacitor.
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What type of function is represented by the table
X= -4 -3 -2 -1
Y= 16 8 4 2
The function represented by the table is: [tex]Y = (1/2)^X[/tex].This is an example of an exponential function.
What is Algebraic function ?
An algebraic function is a function created by applying the operation of addition, subtraction, multiplication, division, and extracting the nth root
To determine the type of function represented by the table, we can look at the pattern of the values of X and Y.
As we can see from the table, as X increases by 1, Y is divided by 2. This means that the relationship between X and Y is not linear but rather exponential. Specifically, the function is of the form Y = [tex]a(1/2)^X,[/tex] where a is a constant.
To find the value of a, we can use one of the points in the table. Let's use the first point, (-4, 16):
16 = [tex]a(1/2)^(-4)[/tex]
Multiplying both sides by[tex](1/2)^(-4)[/tex]:
[tex]16 * (1/2)^4[/tex] = a
a = 16 * (1/16) = 1
Therefore, the function represented by the table is:
[tex]Y = (1/2)^X[/tex]
This is an example of an exponential function.
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Pls help! This is due today!
Answer:
3(a - 1) / (a + 1)
Step-by-step explanation:
I double checked, its right
Determine if 0.2 (18y) is equivalent to 0.3 (12y)
100 points!
Answer:
we can say that 0.2(18y) is equivalent to 0.3(12y).
Step-by-step explanation:
We can simplify both expressions as follows:
0.2(18y) = 3.6y
0.3(12y) = 3.6y
As we can see, both expressions simplify to the same value, 3.6y. Therefore, we can say that 0.2(18y) is equivalent to 0.3(12y)
Max went to the store and bought a new iPad that was 45% of the original price he saved $135 because of the sale how much was the original price of the iPad
Answer:
$245.45
Step-by-step explanation:
.45c = $135, so c = $245.45
.45 × $245.45 = $110.45, a $135 savings.
Emilio flipped a pair of fair coins 60 times. On 24 occasions, heads appeared on both coins. How is this outcome different from the expected outcome?
Emiliο's οutcοme οf getting heads οn bοth cοins 24 times in 60 flips is 9 mοre than the expected οutcοme.
What is prοbability?Prοbability is simply hοw likely sοmething is tο happen.
The expected οutcοme fοr flipping a pair οf fair cοins οnce is that there is a 1/4 (οr 0.25) prοbability οf getting heads οn bοth cοins.
Therefοre, the expected number οf times that heads wοuld appear οn bοth cοins in 60 flips is:
Expected number = (Prοbability οf heads οn bοth cοins) x (Number οf flips)
Expected number = 0.25 x 60
Expected number = 15
Emiliο οbserved that heads appeared οn bοth cοins 24 times, which is greater than the expected number οf 15.
The difference between the οbserved οutcοme and the expected οutcοme is:
Difference = Observed number - Expected number
Difference = 24 - 15
Difference = 9
Therefοre, Emiliο's οutcοme οf getting heads οn bοth cοins 24 times in 60 flips is 9 mοre than the expected οutcοme.
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i have a lot more lol
Thus, For the equation to have infinitely many solutions, the equation value is: -3x - 19 = -3x - 19.
Explain the condition for infinitely many solutions:There have been infinite solutions if the equations in the system are same.
If an equation meets certain requirements for infinite solutions, it will result in an infinite solution. The lines must coincide with a shared y-intercept in order to obtain an endless solution. To put it another way, the system would produce an endless answer if the two lines shared a single line.
The given condition is:
-3x - 19 = _x - 19
For the equation to have infinitely many solutions, both side of the equation must be equal.
Thus,
-3x - 19 = -3x - 19
such that:
-3x and -19 will get cancelled to form:
0 = 0 (which shows infinitely many solutions for the equation)
Thus, For the equation to have infinitely many solutions, the equation value is: -3x - 19 = -3x - 19.
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Faith kicks a football. The graph below shows the height of the football ℎ h in feet after � t seconds.
Answer:
faith
Step-by-step explanation:
you are a Beautiful human being
1. At the time of writing this test, Ms. Shaffer was 707,472,931 seconds old. What is
this age in days? Use dimensional analysis, show all work to receive full credit.
Hint: (60 seconds = 1 minute, 60 minutes = 1 hour, 24 hours = 1 day). (6 pts)
Ms. Shaffer is approximately 8,197.42 days old.
Convert day into secondsTo convert from days to seconds, you need to multiply the number of days by the conversion factor of 86400 seconds/day. This is because there are 24 hours in a day, 60 minutes in an hour, and 60 seconds in a minute, which gives us 24 x 60 x 60 = 86400 seconds in a day.
To convert seconds to days using dimensional analysis, we need to use conversion factors:
60 seconds = 1 minute
60 minutes = 1 hour
24 hours = 1 day
Hence, we can put up the calculation shown below:
707,472,931 seconds x (1 minute / 60 seconds) x (1 hour / 60 minutes) x (1 day / 24 hours)
Simplifying this expression, we get:
= 8,197.42 days
Therefore, Ms. Shaffer is approximately 8,197.42 days old.
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Find the volume of the composite figure.
The volume of the triangular prism is given,
find the volume of the rectangular prism.
Triangular Prism
Volume = 126 cm³
Rectangular Prism
Volume = [?]cm³
7 cm
8 cm
6 cm
6 cm
Hint: V w.h
Please help 30 points
The volume of the rectangular prism is 336 [tex]cm^{3}[/tex] and the volume of the composite figure is 462 [tex]cm^{3}[/tex].
How to find the volume of the composite figure?Measure the lowest solid figure's dimensions and calculate its volume.
Calculate the volume by taking measurements of the upper solid figure.
Adding the volumes of the two solid figures will allow you to calculate the volume of the combined figure.
The volume of rectangular prism v = l * w * h
= 8 * 7 * 6
= 336 [tex]cm^{3}[/tex]
The volume of the triangular prism = 126 [tex]cm^{3}[/tex]
The volume of the composite figure = 336 [tex]cm^{3}[/tex] + 126 [tex]cm^{3}[/tex]= 462 [tex]cm^{3}[/tex]
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evaluate the integral. (remember to use absolute values where appropriate. use c for the constant of integration.) ∫ (3x^2 + 2x – 3) / (x^3 – x) dx
_____________
The integral ∫ (3x^2 + 2x – 3) / (x^3 – x) dx evaluates to:
-ln(|x|) + ln(|x - 1|) + ln(|x + 1|) + C, where C is the constant of integration.
To evaluate the integral ∫ (3x^2 + 2x – 3) / (x^3 – x) dx, follow these steps:
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P ( rolling a composite number and the coin landing on heads and tails )
Assuming a standard six-sided die and a fair coin, the probability of rolling a composite number (any number that is not a prime number) on the die is 3/6 or 1/2, since there are three composite numbers (4, 6, 8) out of six possible outcomes (1, 2, 3, 4, 5, 6).
The probability of the coin landing on heads is 1/2, and the probability of it landing on tails is also 1/2. Therefore, the probability of both events happening together is:
P(composite number and heads and tails) = P(composite number) x P(heads) x P(tails)
P(composite number and heads and tails) = (1/2) x (1/2) x (1/2)
P(composite number and heads and tails) = 1/8
So the probability of rolling a composite number and the coin landing on heads and tails is 1/8.
i need help badly because im confused
Answer:
92in²
Step-by-step explanation:
A= 1/2(b1+b2)h = 1/2 (18+5)8=
1/2 (23)8= 1/2 184 = 92in²
Two pools are being filled with water. To start, the first pool contains 1900 liters of water and the second pool contains 1501 liters of water. Water is being added to the first pool at a rate of 21.25 liters per minute. Water is being added to the second pool at a rate of 35.5 liters per minute.
To find the amount of water in each pool at any given time, we need to use the formula:
Amount of water = Initial amount of water + (rate of inflow × time)
Let's say we want to find the amount of water in each pool after 10 minutes. Using the formula, we get:
Amount of water in first pool = 1900 + (21.25 × 10) = 2125 liters
Amount of water in second pool = 1501 + (35.5 × 10) = 501 liters
Therefore, after 10 minutes, the first pool contains 2125 liters of water and the second pool contains 501 liters of water.
dominique is building a flower box for her yard. the outline of the box is shown in the diagram. if she wants to cover the box with burlap to protect it, how much burlap does she need to buy?
Once we have the total surface area, we will know how much burlap Dominique needs to buy to cover the flower box.
To determine how much burlap Dominique needs to buy to cover the flower box, we need to calculate the surface area of the box. Unfortunately, without the specific dimensions or a provided diagram,
I cannot give you an exact number.
However, here are the general steps to calculate the surface area of a rectangular flower box:
1. Identify the dimensions: length (L), width (W), and height (H).
2. Calculate the surface area of each face:
- Top/Bottom: 2 x (L x W)
- Sides: 2 x (L x H)
- Front/Back: 2 x (W x H)
3. Add the surface areas of all faces together to get the total surface area.
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Which equation best matches the graph show below?
This equation is a parabola with a vertex located at (-1, -2). The equation that best matches the graph shown below is y= -5(x+1)²-2.
What is parabola?It is the graph of a quadratic function and forms a symmetrical U-shape.
The graph shows that the parabola is opening downward and has an x-intercept at (1, 0). By examining the graph and the equations, it can be seen that the equation y= -5(x+1)²-2 is the only equation that describes the graph.
The equation y= -5(x+1)²-2 can be rearranged to the form y= a(x-h)²+k. This can be seen by expanding the equation to y= -5x²-10x-2.
The a, h, and k values can be calculated as follows:
a = -5, h = -1, and k = -2.
This equation is an example of a quadratic equation in the form y = a(x-h)²+k, where a is the coefficient of the x squared term, h is the x-value of the vertex, and k is the y-value of the vertex.
The graph shown is a parabola with a vertex located at (-1, -2), an x-intercept at (1, 0), and an equation of y= -5(x+1)²-2.
These characteristics are all accurately represented by the equation
y= -5(x+1)²-2. This equation is the only equation that matches the graph.
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please help with this geometry hmw
For two triangles to be similar by side-angle-side (SAS) similarity, they must have two pairs of proportional sides and an included angle that is congruent between them.
How to prove similarity?
Let's consider triangles FGH and JKL. By inspection, we can see that FG is proportional to JK and GH is proportional to KL. Additionally, the included angles ∠FGH and ∠JKL are congruent, which means that we have two pairs of proportional sides and an included congruent angle.
Therefore, we can conclude that triangles FGH and JKL are similar by SAS similarity. This means that the corresponding angles of the two triangles will be congruent, and the corresponding sides will be in proportion to each other.
We can use this similarity to find missing side lengths or angles. For example, if we know the length of FG in triangle FGH and the length of JK in triangle JKL, we can use their proportionality to find the length of GH or KL. Similarly, we can use the congruent angles to find other missing angles in either triangle.
It is important to note that if we were to show that two triangles are similar by SAS, we must show that no other pair of sides or angles are congruent between the two triangles. If there were another pair of congruent sides or angles, we would need to use a different similarity criterion such as angle-angle (AA) or side-side-side (SSS).
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On your own sheet of paper, make a stem-and-leaf plot of the following set of data and then find the range of the data.
83, 71, 62, 86, 90, 95, 61, 60, 87, 72, 95, 74, 82, 54, 99, 62, 78, 76, 84, 92.
can I get the range in a graph form?
The stem-and-leaf plot reveals that 54 and 99 are the smallest and biggest values, respectively. Hence, the range is: range = 99 - 54 = 45
what is range ?The range of a number collection or data points in mathematics is the difference here between biggest and smallest values. It is a measurement of the data's dispersion or variability. The range is frequently employed in descriptive statistics and can serve to provide information about the data's distribution.
given
Certainly! The data are shown in a stem-and-leaf plot as follows:
5 | 4
6 | 0 1 2 2
7 | 1 2 4 6 8
8 | 2 3 4 4 6 7
9 | 0 5 5 9
The difference between the largest and smallest values is the data's range.
The stem-and-leaf plot reveals that 54 and 99 are the smallest and biggest values, respectively. Hence, the range is: range = 99 - 54 = 45
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Below is a table giving the fox and rabbit populations in a national park
during a 12-month period. Note that each value of t corresponds to the beginning of
the month
According to the data in the table, is F a function of R? Is R a function of F? Explain.
Is either R or Fa function of t? Explain.
The table only gives us information about the values of R and F at certain points in time, but it does not give us a functional relationship between the two variables. To determine whether F is a function of R, we would need to know the number of foxes for each value of R.
What is function ?A function in mathematics is a rule that converts each element from one set, known as the domain, into a particular element in another set, known as the range. The domain of a function is the set of all potential inputs, whereas the range is the set of all potential outputs. A graph, a table of values, or an equation can all be used to describe a function. In science, engineering, economics, and other disciplines, functions are used to represent the connections between variables.
Neither R nor F is a function of t because there are multiple values of R and F for some values of t. For example, at t=2, the number of rabbits is 750, and at t=3, the number of rabbits is 567.
From the data in the table, we cannot determine whether F is a function of R or whether R is a function of F. To determine whether F is a function of R, we would need to know the number of foxes for each value of R. Similarly, to determine whether R is a function of F, we would need to know the number of rabbits for each value of F. The table only gives us information about the values of R and F at certain points in time, but it does not give us a functional relationship between the two variables.
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fix her error, please help!!!
The trigonometric ratios of sine, cosine, and tangent can be used to find the lengths of the sides of the triangle.
How do you solve the right triangles?A right triangle has one angle that measures exactly 90 degrees. Identify this angle in the triangle.
Label the sides of the triangle as the hypotenuse, adjacent, and opposite sides, relative to one of the non-right angles. The hypotenuse is always the side opposite the right angle.
We know that;
Tan 45 = 5.9/w
w = 5.9/Tan45
w = 5.9
Then;
Tan 35 = 5.9/w + x
0.7 = 5.9/5.9 + x
0.7(5.9 + x) = 5.9
4.13 + 0.7x = 5.9
x = 2.5
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explain what function (in mosaic ) and what parameters you should you use to find the value of z* for a specified confidence level c
This would give you a z* value of approximately 1.96.
To find the value of z* for a specified confidence level c in a mosaic function, you should use the inverse cumulative
distribution function (also called the quantile function or the z-score function). The parameters you need are the
desired confidence level (c) and the standard normal distribution.
Here are the steps to find the value of z*
1. Determine the desired confidence level (c). This is usually given as a percentage, like 95% or 99%.
2. Calculate the area under the curve corresponding to the confidence level. This is equal to (1 - c)/2.
3. Use the inverse cumulative distribution function (quantile function) with the standard normal distribution to find the z
score corresponding to the calculated area.
4. The resulting value is the z* value for the specified confidence level c.
For example, if you need to find the z* value for a 95% confidence level, you would calculate (1 - 0.95)/2 = 0.025, and
then use the inverse cumulative distribution function with the standard normal distribution to find the z-score
corresponding to 0.025. This would give you a z* value of approximately 1.96.
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Find the angle measure indicated. Assume that lines which appear tangent are tangent. A. 110 degrees B. 175 degrees C. 155 degrees D. 120 degrees
Therefore, the angle measure indicated 110° that is option A.
What is angle?An angle is the measure of the amount of rotation between two intersecting lines or planes. It is defined as the space between two intersecting lines or planes measured in degrees, radians, or other units of angular measurement. Angles are often represented by a symbol that looks like a small arc, with three letters labeling the points that define the angle, such as "ABC." The vertex of an angle is the point where the two lines or planes intersect, and the sides of an angle are the two rays that extend from the vertex. Angles are used in geometry, trigonometry, and other mathematical fields to measure and analyze the relationships between shapes and objects.
Here,
Since sector PF has a measure of 90 degrees, then angle PAF must also have a measure of 90 degrees since it is an inscribed angle that intercepts the same arc.
To find the angle measure of QSR, we first need to find the measure of angle QPR.
Since sector PF is a 90 degree sector and line QR is tangent to the circle at point R, we know that angle QRP is a right angle (90 degrees).
Similarly, since sector QR is a 150 degree sector and line PS is tangent to the circle at point S, we know that angle QPS is a right angle (90 degrees).
Therefore, angle QPR + angle QPS = 90 + 90 = 180 degrees.
Since angle QPS and angle QRP share ray QR, they are adjacent angles.
So, angle QSR = 360 - (angle QPR + angle QPS)
= 360 - 180 -70
= 110 degrees
Therefore, the measure of angle QSR is 110 degrees, which is equivalent to a straight line.
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Use the Triangle Inequality Theorem to name a segment for the third side of a triangle if no segments are congruent and the first two sides are AB and BD. Use this key to enter the response: AB=1, AC=2, AD=3, BC=5, BD=6, CD=7. List them in ascending order. (fill in the blank)
__or__
(1 point)
The lengths of the sides in ascending order are AB=1, BD=6, CD=7.
What is length?Length is a measurement of how long an object is in one dimension, usually referring to its distance from one end to the other. It is a fundamental physical quantity and is often measured in units such as meters, centimeters, feet, or inches, depending on the context and system of measurement being used. Length can be used to describe the size of physical objects, such as the length of a piece of wood or the distance between two points in space, as well as more abstract concepts, such as the length of time that has passed or the length of a written document.
According to the Triangle Inequality Theorem, the length of any side of a triangle must be less than the sum of the lengths of the other two sides.
If AB=1 and BD=6, then the third side must be less than AB+BD=1+6=7. Therefore, CD<7.
If AC=2 and BD=6, then the third side must be less than AC+BD=2+6=8. Therefore, CD<8.
If AD=3 and BD=6, then the third side must be less than AD+BD=3+6=9. Therefore, CD<9.
Since CD is less than all of these values, the possible length for CD is the smallest value, which is CD=7. Therefore, the segment for the third side of the triangle is CD.
The lengths of the sides in ascending order are AB=1, BD=6, CD=7.
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Please help I’ve posted this question twice and it’s due tonight
Based on the Venn diagram, the results in order are:
Students who do not like DC superheroes: 117Students who like Marvel superheroes: 358Students who like both DC and Marvel superheroes: 155Students who like DC but not Marvel superheroes: 85Students who like Marvel but not DC superheroes: 203Students who do not like the DC or Marvel superheroes: 117How do we solve this?To solve this problem, we can use a Venn diagram to represent the information given.
Total students surveyed = 560
395 like superheroes from either company
240 prefer DC superheroes
358 do not like Marvel superheroes
To find how many students did not like DC superheroes, we need to find the number of students who do not fall into the DC circle:
Students who do not like Marvel superheroes = 358
Students who like both DC and Marvel superheroes = (395 - 240) = 155
Students who like Marvel superheroes only = ?
Students who like DC superheroes only = (240 - 155) = 85
To find how many students like Marvel superheroes, we need to find the number of students who fall into the Marvel circle:
Students who do not like DC superheroes = ?
Students who like both DC and Marvel superheroes = 155
Students who like Marvel superheroes only = ?
Students who like DC superheroes only = 85
To find how many students like both DC and Marvel superheroes, we can use the information we already have:
Students who like both DC and Marvel superheroes = 155
To find how many students like DC but not Marvel superheroes, we can use the information we already have:
Students who like DC superheroes only = 85
To find how many students like Marvel but not DC superheroes, we can use the information we already have:
Students who like Marvel superheroes only = (358 - 155) = 203
Finally, to find how many students do not like the DC or Marvel superheroes, we need to find the number of students who do not fall into either circle:
Students who do not like DC superheroes = ?
Students who like both DC and Marvel superheroes = 155
Students who like Marvel superheroes only = 203
Students who like DC superheroes only = 85
We can now use the formula for the total number of students surveyed to find the number of students who do not like DC or Marvel superheroes:
Total students surveyed = Students who do not like DC superheroes + Students who like both DC and Marvel superheroes + Students who like Marvel superheroes only + Students who like DC superheroes only
560 = Students who do not like DC superheroes + 155 + 203 + 85
Students who do not like DC superheroes = 117
Similarly, we can use the same formula to find the number of students who like Marvel superheroes:
560 = Students who do not like DC superheroes + 155 + Students who like Marvel superheroes only + 85
Students who like Marvel superheroes = 203 + 155
Students who like Marvel superheroes = 358
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How many square centimeters are in the total surface area
of this cylinder? Express your answer to 2 decimal places?
4.0 cm
2.5 cm
Total surface area of this cylinder, the answer is (C) 163.36 cm².
What is an area ?
The total surface area of a cylinder can be found using the formula:
surface area = 2πr² + 2πrh
where r is the radius and h is the height.
Substituting the given values, we get:
surface area = 2π(4.0)² + 2π(4.0)(2.5)
= 2π(16.0) + 2π(10.0)
= 32π + 20π
= 52π
Using the approximation 3.14 for π and rounding to 2 decimal places, we get:
surface area ≈ 52(3.14) ≈ 163.36 cm²
Therefore, the answer is (C) 163.36 cm².
What is cylinder?
A cylinder is a three-dimensional shape that has two circular bases that are parallel and congruent to each other. The sides of a cylinder are curved, and they connect the bases. A cylinder has a constant cross-sectional area throughout its height, and it is a type of prism. The height of a cylinder is the perpendicular distance between the bases.
The volume of a cylinder can be calculated using the formula V = πr²h, where r is the radius of the base and h is the height of the cylinder. The surface area of a cylinder can be calculated using the formula A = 2πr² + 2πrh, where r is the radius of the base and h is the height of the cylinder. Cylinders are commonly found in everyday objects such as cans, pipes, and containers.
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