The standard deviation of the height distribution is approximately 6 inches (since 6 is half of 12), which corresponds to option (C).
The distribution of the heights of students in a large class is roughly Normal, with an average height of 68 inches, and approximately 95% of the heights are between 62 and 74 inches.
The height distribution is approximately Normal, we can use the empirical rule, which states that approximately 95% of the data falls within 2 standard deviations of the mean, to estimate the standard deviation.
The range of heights within which approximately 95% of the students fall is from 62 to 74 inches.
This range is 12 inches wide, and it corresponds to 2 standard deviations from the mean.
Thus, we have:
2 standard deviations = range of 95% of the data = 74 - 62 = 12 inches
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Chester has 49 CDs. Tony has 1/7 as many as Chester. How many CDs does Tony have?
Answer:7
Step-by-step explanation: you divide 49 by 7 which gives you 7
Answer:
7
Step-by-step explanation:
1/7 of 49 would be equal to divided 49 by 7 to find 1 seventh of 49
49/7 = 7
so 1/7 of Chesters 49 CDS is equal to 7 CDS that Tony has.
hope this helps :)
A park has a large circle painted in the middle of the playground area. The circle is divided into 4 equal sections, and each section is painted a different color. The radius of the circle is 10 meters.
What is the area A of each section of the circle?
The area A of each of the section of the circle would be =78.5m²
How to calculate the area of each section of the circle given?To calculate the area of each section of the circle given, the formula for the area of circle is used which is given as follows;
Area of circle = πr²
Where;
π = 3.14
r = 10m
area = 3.14× 10×10
= 314m
But the circle is divided into 4 sections. Therefore, the area of a section = 314/4 = 78.5m²
Therefore, the area of each sector of the circle after being divided into four would be= 78.5m².
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A circle has a center of (1, -1). The circumference passes through (1, 2). Find the length of the circumference of the circle. Use 3.14 for pi. Then, Find the area of the circle.
Answer:
The radius of the circle is 3, so
Circumference = 2(3)π = 6π = 18.84
Area = π(3^2) = 9π = 28.26
Read the screenshot please answer this ASAP!!!!!!!! PLEASEEEEE
According to the information, the surface area of the prism is approximately 777.868 square inches, and its volume is approximately 3156.846 cubic inches.
How to calculate the surface area and volume of this prism?Since the hexagonal bases are regular, we know that all the six triangles are congruent to each other.
Let's call the side length of the hexagon s. Then, the apothem of each triangular face is given as 9 inches, and the base of each triangular face is given as 10 inches. Using the Pythagorean theorem, we can calculate the side length of the hexagon as follows:
s^2 = (10/2)^2 + 9^2
s^2 = 25 + 81
s^2 = 106
s ≈ 10.2956 inches
The surface area of the prism can be calculated by adding up the areas of its faces. The hexagonal base has an area of:
A_base = (3√3/2) * s^2 ≈ 450.978 square inches
The area of each triangular face is:
A_tri = (1/2) * base * height = (1/2) * 10 * 9 = 45 square inches
So the total surface area of the prism is:
A_total = 2A_base + 6A_tri
A_total = 2(450.978) + 6(45)
A_total ≈ 777.868 square inches
The volume of the prism can be calculated by multiplying the area of the base by the height of the prism:
V = A_base * height
V = 450.978 * 7
V ≈ 3156.846 cubic inches
Therefore, the surface area of the prism is approximately 777.868 square inches, and its volume is approximately 3156.846 cubic inches.
Note: This question is incomplete. Here is the complete information:
Calculate the surface area and volume of this prism.
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There are three angles measured in degrees of a triangle where x is the largest angle, y is the middle angle, and z is the smallest angle.
The measure of the largest angle is 40 degrees less than twice the sum of the measure of the other two angles.
The measure of the largest angle is twice the smallest angle plus 10 degrees.
The sum of the angles of a triangle can be written as x + y + z = 180.
What are the other equations that represent this system of equations?
Select each correct answer.
a.) x=2y+10
b.) x=2z+10
c.) x=40-2(y+z)
d.) x=2z+y-40
e.) 2(y+z)-40
An angle is a polyhedron made up of two rays with a shared terminal, often known as sides or legs (called the vertex). Angles are used to express how much rotation or inclination there is between second line or planes and are commonly described in degrees or radians.
From the given information, we have the following equations:
[tex]x = 2(y+z) - 40[/tex] (the largest angle is 40 degrees less than twice the sum of the other two angles)
[tex]x = 2z + 10[/tex] (the largest angle is twice the smallest angle plus 10 degrees)
[tex]x + y + z = 180[/tex] (the sum of the angles of a triangle is 180 degrees)
To simplify the system of equations, we can use the second equation to substitute for x in the first equation:
[tex]2z + 10 = 2(y+z) - 40[/tex]
Simplifying this equation, we get:
[tex]y = z + 25[/tex]
Now we can substitute x and y in terms of z into the third equation:
[tex]x + (z+25) + z = 180[/tex]
Simplifying this equation, we get:
[tex]x + 2z = 155[/tex]
Finally, we can substitute x in terms of z from the first equation into this last equation:
[tex]2(y+z) - 40 + 2z = 155[/tex]
Simplifying this equation, we get:
[tex]y + 3z = 97[/tex]
Therefore, the equations that represent this system are:
[tex]x = 2(y+z) - 40\\y = z + 25\\x + 2z = 155\\y + 3z = 97[/tex]
So the correct answers are:
[tex]a.) x=2y+10\\d.) x=2z+y-40\\e.) 2(y+z)-40[/tex]
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The equations that represent this system are:
a.) x=2y+10
d.) x=2z+y-40
e.) 2(y+z)-40
What is angles ?
An angle is a polyhedron made up of two rays with a shared terminal, often known as sides or legs (called the vertex). Angles are used to express how much rotation or inclination there is between second line or planes and are commonly described in degrees or radians.
From the given information, we have the following equations:
=> x=2(y+z)-40 (the largest angle is 40 degrees less than twice the sum of the other two angles)
=> x=2z+10 (the largest angle is twice the smallest angle plus 10 degrees)
=> x+y+z=180 (the sum of the angles of a triangle is 180 degrees)
To simplify the system of equations, we can use the second equation to substitute for x in the first equation:
=> 2z+10=2(y+z)-40
Simplifying this equation, we get:
y=z+45
Now we can substitute x and y in terms of z into the third equation:
x+z+25+z=180
Simplifying this equation, we get:
=> x+2z=155
Finally, we can substitute x in terms of z from the first equation into this last equation:
2(y+z)-40+2z=155
Simplifying this equation, we get:
y+3z=97
Therefore, the equations that represent this system are:
a.) x=2y+10
d.) x=2z+y-40
e.) 2(y+z)-40
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A line passes through the points (−4, 50) and (5, −31). What is the equation of the line in slope-intercept form?
Answer:
y = - 9x + 14
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 4, 50 ) and (x₂, y₂ ) = (5, - 31 )
m = [tex]\frac{-31-50}{5-(-4)}[/tex] = [tex]\frac{-81}{5+4}[/tex] = [tex]\frac{-81}{9}[/tex] = - 9 , then
y = - 9x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (5, - 31 )
- 31 = - 9(5) + c = - 45 + c ( add 45 to both sides )
14 = c
y = - 9x + 14 ← equation of line
Use point-slope form to write the equation of a line that passes through the point (16,−14) with slope 1.
The equation of the line that passes through the point (16, -14) with slope 1 is y = x - 30.
What is meant by equation?
An equation is a mathematical statement that shows that two expressions are equal. It contains an equals sign and can include variables, constants, and mathematical operations. Equations are used to represent relationships between quantities and to solve problems in mathematics and science.
What is meant by slope?
Slope refers to the measure of the steepness of a line. It is calculated by dividing the change in the y-coordinate (vertical distance) by the change in the x-coordinate (horizontal distance) between two points on the line.
According to the given information
The point-slope form of the equation of a line is given by:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line and m is the slope of the line.
In this case, the line passes through the point (16, -14) and has a slope of 1. Plugging these values into the point-slope form, we get:
y - (-14) = 1(x - 16) y + 14 = x - 16 y = x - 30
So, the equation of the line that passes through the point (16, -14) with slope 1 is y = x - 30.
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Need help ASAP!!!
Jordyn likes to practice dancing while preparing for a math tournament. She spends 60 minutes every day practicing dance and math. To help her concentrate better, she dances for 20 minutes longer than she works on math.
Part A: Write a pair of linear equations to show the relationship between the number of minutes Jordyn practices math every day (x) and the number of minutes she dances every day (y). (5 points)
Part B: How much time does Jordyn spend practicing math every day? Show your work. (3 points)
Part C: Is it possible for Jordyn to have spent 60 minutes practicing dance if she practices for a total of exactly 80 minutes and dances for 20 minutes longer than she works on her math? Explain your reasoning. (2 points)
Answer:
A: x +y = 60; y = x +20
B: 20 minutes on math
C: no
Step-by-step explanation:
You have some relations and some questions about dance times and math practice times with dance times longer than math practice by 20 minutes.
A. EquationsThe given relations can be written as two equations:
x + y = 60 . . . . . total time is 60 minutes
y = x + 20 . . . . . dance time is 20 minutes longer than math time
B. SolutionWe want the value of x. We can find that by using the second equation to substitute for y in the first equation:
x + (x +20) = 60
2x = 40 . . . . . . . . . subtract 20
x = 20 . . . . . . . . divide by 2
Jordyn practices math 20 minutes every day.
C. More practiceIf Jordyn dances for 60 minutes, then she will practice math for 60 -20 = 40 minutes. That brings her total practice time to 60 +40 = 100, which is more than 80.
It is not possible to spend 80 minutes total if she spends 60 minutes dancing.
(She could spend 50 minutes dancing, 30 minutes on math, and have a total practice time of 80 minutes.)
Jordyn spends 20 minutes each day practicing math. However, if her total practice time is 80 minutes, it would not be possible for her to spend 60 minutes practicing dance.
Explanation:The total time Jordyn spends practicing both dancing and math is 60 minutes. If we establish the time she spends on math as 'x' and the time she spends dancing as 'y', we can establish the following and equations:
y = x + 20: This equation represents the fact that Jordyn dances 20 minutes longer than she works on math. x + y = 60: This equation represents the total time Jordyn spends on dancing and math combined.To solve for 'x', substitute the first equation into the second to get x + (x + 20) = 60. Simplify to get 2x + 20 = 60. Subtract 20 from each side to get 2x = 40, and finally divide by 2 to get x = 20. Therefore Jordyn spends 20 minutes practicing math each day.
To answer Part C, if Jordyn practices for a total of exactly 80 minutes and dances 20 minutes longer than she does math, it would not be possible for her to spend 60 minutes practicing dance. The most amount of time she could spend dancing is 50 minutes (80 total minutes- 30 minutes for math).
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what is the area under the sine curve from 0 to pi?
Work Shown:
[tex]\displaystyle \int \sin(x) dx = -\cos(x)+C\\\\\displaystyle \int f(x)dx = g(x)+C\\\\\displaystyle \int_{a}^{b} f(x)dx = g(b)-g(a)\\\\\displaystyle \int_{0}^{\pi} f(x)dx = g(\pi)-g(0)\\\\\displaystyle \int_{0}^{\pi} \sin(x) dx = -\cos(\pi)-(-\cos(0))\\\\[/tex]
[tex]\displaystyle \int_{0}^{\pi} \sin(x) dx = -\cos(\pi)+\cos(0)\\\\\displaystyle \int_{0}^{\pi} \sin(x) dx = -(-1)+1\\\\\displaystyle \int_{0}^{\pi} \sin(x) dx = 1+1\\\\\displaystyle \int_{0}^{\pi} \sin(x) dx = 2\\\\[/tex]
The area is 2 square units. You can use WolframAlpha or GeoGebra to confirm.
HELPPPPPPPPPPPP PLSSSSSSS
Suppose the ages of cars driven by employees at a company are normally distributed with a mean of 8 years and a standard deviation of 3.2 years.
What is the z-score of a car that is 6 years old?
Responses
−1.6
negative 1.6
−0.625
negative 0.625
0.625
0.625
1.6
The z-score of a car that is 6 years old is -0.625.
To find the z-score of a car that is 6 years old, we can use the formula:
z = (x - μ) / σ
where x is the value we are interested in (in this case, 6 years old), μ is the mean of the distribution (8 years), and σ is the standard deviation (3.2 years).
Plugging in the values, we get:
z = (6 - 8) / 3.2 = -0.625
Therefore, the z-score of a car that is 6 years old is -0.625. This indicates that the car is 0.625 standard deviations below the mean age of cars driven by employees at the company. Since the distribution is normal, we can use this z-score to find the probability of finding a car with an age of 6 years or less, using a z-table or a calculator.
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Explain how to plot the point (3, -7) on the coordinate plane.
Answer:
Starting at the origin (0, 0), go right 3 units, then down 7 units. You will end at (3, -7).
8.) Jesenia is standing on a pedestrian bridge that is 9.5 feet above a lake. She looks down and sees a
duck in the water. The duck is 4.5 feet away from Jesenia's position on the bridge. What is the angle of
depression from Jesenia to the duck? Round to the nearest degree.
Answer: The angle of depression from Jesenia to the duck is 25.17°. The solution has been obtained by using trigonometry.
What is trigonometry?
Right-angled triangles, their sides, angles, and connections are the main topics of the mathematical field of trigonometry.
We are given that that Jesenia is standing on a pedestrian bridge that is 9.5 feet above the lake and the duck is 4.5 feet away from jesenias position on the bridge.
This means that perpendicular is 9.5 and base is 4.5.
We know that tan θ is value of opposite side to adjacent side.
So, we get
⇒ Tan θ =
⇒ Tan θ = 0.47
⇒ θ = 25.17°
Hence, the angle of depression from Jesenia to the duck is 25.17°.
Step-by-step explanation:
Welcome!
Which line is represented by y=3/2x-3 ? A. B. C. D.
Answer:
B
Step-by-step explanation:
the equation y=3/2x-3 has a slope of 3/2 and a y intercept of -3
So, first find the graph(s) that have the y intercept of -3. The only options would be B and C.
Next, from the y-intercept of -3, go UP 3, and to the RIGHT 2 to find your next point. This eliminates option C for the slope. The slope of option C is 2/3, not 3/2.
So, option B is correct. Hope this helps ;)
Answer:
B
Step-by-step explanation:
y = mx + b
y = mx (slope) + b (y-intercept)
The y-intercept of y = 3/2x - 3 is -3, so the graph needs to have a point at (0, -3). The slope is 3/2, if you go up 3 times and to the right twice from the point (0, -3), it will point (2, 0).
Find the exact value of cos (2theta), given tan A = -8/15, and theta lies in Quadrant II.
Please show steps and thank you in advance!
The value of cos (2tetha) is 161/289
What is trigonometric ratio?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.
sin(tetha) = opp/hyp
cos(tetha) = adj/hyp
tan(tetha) = opp/adj
Therefore if tan(tetha) = -8/15, therefore opposite is 8 and adj is 15
hyp = √8²+15²
= √ 64+225
= √ 289
= 17
therefore cos (tetha) = 8/17 and since theta is in second quadrant, cos tetha will be negative
cos (tetha) = -15/17
cos²(tetha) = 225/289
sin(tetha) = 8/17
sin²(tetha) = 64/289
cos(2tetha) = cos²(tetha) -sin²(tetha)
= 225/289 - 64/289
= 161/289
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Edge lengths are given in units. Find the surface area of each prism in square units.
the area of given figure made from two part Parallelogram and Triangle is 288sq cm
what is Parallelogram and Triangle?A parallelogram is a four-sided shape with opposite sides that are parallel and equal in length. The opposite angles of a parallelogram are also equal in measure. Parallelograms can have various orientations, but their opposite sides will always be parallel.
A triangle, on the other hand, is a three-sided shape with three angles and three vertices. The sum of the angles in a triangle is always 180 degrees. Triangles can come in various shapes and sizes, such as equilateral (all sides and angles are equal), isosceles (two sides and two angles are equal), and scalene (all sides and angles are different).
According to given informationgiven that
1st part:
Base=6cm
height=8cm
Area=1×Base×Height/2
Area=(1×6×8)cm²/2
Area=24cm²
it have two part so, Area=2×24=48sq cm
2nd part:
if we assume Parallelogram
Area=Base×Height
Area=15cm×8cm
Area=120 sq unit
it have two part so,2×120sq cm
240sq unit
total area of given figure is 48 sq cm+240sq cm=288 sq unit.
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Question 9(Multiple Choice Worth 2 points)
(Creating Graphical Representations LC)
A teacher was interested in the subject that students preferred in a particular school. He gathered data from a random sample of 100 students in the school and wanted to create an appropriate graphical representation for the data.
Which graphical representation would be best for his data?
Stem-and-leaf plot
Histogram
Circle graph
Box plot
The most useful visual representation of the teacher's data on the preferred subjects of 100 kids at the school would be a histogram. answer is option (a).
What is a histogram?In a histogram, which is a graphical depiction of the distribution of a set of continuous or discrete data, the height of a bar above the bin on the x-axis represents the frequency or count of the data falling within each bin. On the y-axis of the histogram, the frequency or count of the data points that fall into each bin is displayed.
The most useful visual representation of the teacher's data on the preferred subjects of 100 kids at the school would be a histogram. In a histogram, bars are used to illustrate the frequency distribution of a group of continuous or discrete data points.
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I don't get it... please help thanks in advance
Answer:
Set your calculator to degree mode.
[tex] \tan( \alpha ) = \frac{23}{35} [/tex]
[tex] \alpha = {tan}^{ - 1} \frac{23}{35} = 33.31[/tex]
The angle of elevation of the sun is about 33°.
Solids $A$ and $B$ are similar. Use the given information and scale factor $k$ from solid $A$ to solid $B$ to find the volume of solid $B$ to the nearest thousandth. Cylinder $A$ has a volume of $112\pi$ cubic meters and $k=$ $\frac{1}{4}$. The volume of solid $B$ is about
cubic meters
The volume of solid B is about 7π cubic meters, which is approximately 21.99 cubic meters when rounded to the nearest thousandth.
The volume of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height. Since solids A and B are similar, they have the same shape, but different sizes.
Let V₁ be the volume of solid A, and V₂ be the volume of solid B. The scale factor k from solid A to solid B is 1/4, which means that the dimensions of solid B are 1/4 of the dimensions of solid A.
We can find the radius and height of solid B by multiplying the radius and height of solid A by 1/4. Therefore, we have:
V₂ = π(r/4)²(h/4) = (π/16)rh²
We are given that V₁ = 112π cubic meters, so we can solve for rh²:
112π = πr²h
rh² = 112
Substituting into the formula for V₂, we get:
V₂ = (π/16)rh² = (π/16)(112) = 7π
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The advantage of making a stem-and-leaf display instead of a dotplot is that a stem-and-leaf display
A. is for quantitative data, while a dotplot shows categorical data.
B. none of these
C. satisfies the area principle.
D. preserves the individual data values.
E. shows the shape of the distribution better than a dotplot.
Which of the following is not an equation?
Answer:
Option (3)
Step-by-step explanation:
Option (3) is not an equation. It is an expression. An equation is a mathematical statement where two expressions are equal to each other connected by an equal sign. In option (1), 3+1 is equal to 4+0 so it is an equation. In option (2), x2-2x is equal to 8, so it is also an equation. In option (4), 1+3 is equal to 6, so it is an equation, though it is not a true statement. However, in option (3), there is no equal sign, so it is not an equation. It is an expression that simplifies to 8x+2.
What is the value of line 1 and2 in y=mx+b form?Help please!!!
1. The equation of the line in graph 1 in slope-intercept form is
y = (2/3)x + 2/3.
2. The equation of the line in graph 2 is
y = (1/3)x + 4/3.
How to find the equation of the linea. To find the equation of the line passing through (3, 4) and (0, 2) (points obtained from the graph) in slope-intercept form, we need to first find the slope of the line.
slope = (y2 - y1) / (x2 - x1)
Substituting the given values, we get:
slope = (2 - 4) / (0 - 3) = -2 / (-3) = 2/3
The point-slope form of the equation of a line passing through a point (x1, y1) with slope m is given by:
y - y1 = m(x - x1)
y - 4 = (2/3)(x - 3)
y = (2/3)x + 2/3
b. points obtained from the graph (-3, 1) and (-6, 0)
slope = (y2 - y1) / (x2 - x1)
slope = (0 - 1) / (-6 - (-3)) = -1 / (-3) = 1/3
y - y1 = m(x - x1)
y - 1 = (1/3)(x - (-3))
y = (1/3)x + 4/3
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Is the event independent or dependent? You toss a penny and you toss a
dime.
O dependent
O independent
Answer:
the event would be independent.
Step-by-step explanation:
because the penny and dime are two seperate variables
Choose all of the two-dimensional shapes that result from a vertical, horizontal, or angled cross section of a cone.
A- Rectangle
B- Triangle
C- Circle
D- Parabola
E- Ellipse
The cross section across a conic section would produce:
Triangle, Circle and Parabola
What are the properties of conic sections?Looking at the given options, we can say that ellipse, circle and parabola are all conic sections and as such they are possible figures that can be made if we intersect a plane and a cone.
However, rectangle is not a conic section.
A cylinder which could have a rectangular cross section if the plane is perpendicular to the base or A tetrahedron could have a square cross section, which is a special case of a rectangle.
In forming a conic section , we could also form an ellipse.
Now, when we cut a cross section across a cone, we can get a circle, triangle or parabola
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bruce has a pet worm that fell into a well. the well is 26 feet deep. each day, the worm climbs up 8 feet, but each night, it slides back down 2 feet. how many days will it take for bruce’s worm to get to the top of the well
A Ray's pizza party each pizza was cut into 8 slices. There were 7 groups of children. Each group ate 2\frac{1}{2} pizzas. How many pizzas were eaten at the party in all?
18 pizzas were eaten at the party in total.
What is total number?The term "total number" refers to the complete count or sum of a set of numbers or objects. It is the result of adding up all the individual numbers or objects in a set to get a final value that represents the entire set.
According to question:If each pizza was cut into 8 slices, then 2 and 1/2 pizzas is equivalent to 20 slices of pizza because:
2\frac{1}{2} \times 8 = 20
Since there were 7 groups of children, the total number of slices of pizza eaten at the party is:
20 slices/pizza x 7 groups = 140 slices
To convert this to the number of pizzas eaten, we divide the total number of slices by the number of slices per pizza:
140 slices ÷ 8 slices/pizza = 17.5 pizzas
Therefore, 17.5 pizzas were eaten at the party in total. However, since a pizza cannot be divided into fractions, we should round up to the nearest whole number, giving us a final answer of 18 pizzas.
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Matt is painting the trim in his living room. He leans a ladder against the wall so that it forms an angle
elevation with the floor of 56°. If it is a 12-foot ladder, how high up on the wall does it reach? Round to
the nearest tenth.
Answer:
9.9 inches
Step-by-step explanation:
Visualize the scenario for a second. If the ladder is leaning against the wall, we can assume that it is the hypothenuse of the triangle that is forming here. The angle of elevation in this scenario is the angle formed by the ladder and ground.
Next, recall each trig function and determine which best belongs. We have the hypothenuse and we need the side opposite the angle. Therefore, we use sine. (probably using a calculator for trig questions)
Therefore, we can now set up our equation and solve. (x is the height of the wall)
sin 56 = [tex]\frac{x}{12}[/tex] Initial equation
12 sin 56 = x Multiply each side by 12 so that we get x by itself.
x ≈ 9.9 Punch 12 sin 56 into a calculator and your done!
Therefore, the answer is about 9.9 inches. (If you got something different, make sure that your calculator is in degrees and not radians! Some calculators abbreviate it as DEG and RAD respectively.)
perry como fans fifty-six percent of respondents to an online poll said that they were perry como fans. if 982 randomly selected people responded to this poll, what is the true proportion of all local residents who are perry como fans? estimate at the 95% confidence level.
Perry como fans fifty-six percent of respondents to an online poll said that they were perry como fans. if 982 randomly selected people responded to this poll.
By use the sample proportion to estimate the true proportion of all local residents who are Perry Como fans.
Let p be the true proportion of all local residents who are Perry Como fans. Then, the sample proportion is 0.56 and the sample size is n = 982.
We construct a 95% confidence interval for p by using the formula
Sample proportion ± z*standard error
Where z is the critical value from the standard normal distribution for a 95% confidence level, which is 1.96. The standard error is the estimated standard deviation of the sample proportion which is defined as
[tex]\sqrt{p*(1-p)/n} \\}[/tex]
By putting the values we get
Standard error = [tex]\sqrt{0.56*(1-0.56)/982)[/tex] = 0.018.
95% confidence interval = 0.56 ± 1.96*0.018 = (0.525, 0.595).
Hence, we can say with 95% confidence that the true proportion of all local residents who are Perry Como fans is between 0.525 and 0.595.
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Find the quotient. Assume that no denominator has a value of 0.
(6x-24)÷x^2-16/6x
The quotient of the expression (6x-24)÷x^2-16/6x is 36x/(x + 4)
Finding the quotient of the expressionFrom the question, we have the following parameters that can be used in our computation:
(6x-24)÷x^2-16/6x
Assume that no denominator has a value of 0, we have
(6x-24)÷x^2-16/6x = 6(x - 4) ÷ (x - 4)(x + 4)/6x
Express as products
So, we have the following representation
(6x-24)÷x^2-16/6x = 6(x - 4) * 6x/(x - 4)(x + 4)
When the factors are evaluated, we have
(6x-24)÷x^2-16/6x = 36x/(x + 4)
Hence, the solution is 36x/(x + 4)
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2 Bea counts the number of red pencils in 7 boxes of pencils. The list shows her
data: 22, 28, 30, 28, 35, 30, 28. The mean is 26 red pencils per box. Based on
the MAD for the data set, would it be unlikely to get a box with 31 red pencils?
Show your work. Explain your reasoning.
2.29 is less than the MAD of 2.53, it would not be unlikely to get a box with 31 red pencils based on the MAD for the given data set.
What is the data set?To determine whether it would be unlikely to get a box with 31 red pencils based on the Mean Absolute Deviation (MAD) for the given data set, we first need to calculate the MAD.
Step 1: Calculate the mean of the data set
The given data set is: 22, 28, 30, 28, 35, 30, 28
The mean is calculated by adding up all the numbers and dividing by the total number of values:
Mean = (22 + 28 + 30 + 28 + 35 + 30 + 28) / 7 = 201 / 7 = 28.71 (rounded to two decimal places)
Step 2: Calculate the absolute deviations
The absolute deviation for each data point is calculated by finding the absolute difference between the data point and the mean:
|22 - 28.71| = 6.71
|28 - 28.71| = 0.71
|30 - 28.71| = 1.29
|28 - 28.71| = 0.71
|35 - 28.71| = 6.29
|30 - 28.71| = 1.29
|28 - 28.71| = 0.71
Step 3: Calculate the MAD
The MAD is the mean of the absolute deviations:
MAD = (6.71 + 0.71 + 1.29 + 0.71 + 6.29 + 1.29 + 0.71) / 7 = 17.71 / 7 = 2.53 (rounded to two decimal places)
Now, to determine whether it would be unlikely to get a box with 31 red pencils, we can compare 31 with the MAD. If the difference between 31 and the mean (28.71) is greater than the MAD (2.53), then it would be unlikely.
Difference = 31 - 28.71 = 2.29
Since 2.29 is less than the MAD of 2.53, it would not be unlikely to get a box with 31 red pencils based on the MAD for the given data set.
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