The tower is leaning at an angle of approximately 86.41 degrees.
To find the angle the tower is leaning, we can use trigonometry. Let's assume the tower is leaning towards the right.
We have a right triangle formed by the tower, the ground, and the rope. The side opposite the angle we're looking for is the height of the tower (54 feet), and the adjacent side is the distance from the base of the tower to the rope (3 feet).
The tangent function relates the opposite and adjacent sides of a right triangle:
tan(angle) = opposite/adjacent
In this case, we can plug in the values:
tan(angle) = 54/3
To find the angle, we need to take the inverse tangent (arctan) of both sides:
angle = arctan(54/3)
Using a calculator, we can find that the angle is approximately 86.41 degrees.
Therefore, the tower is leaning at an angle of approximately 86.41 degrees.
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The grams of fiber from 1,000 different breakfast cereals sold in the United States were collected.
Which graphical representation would be most appropriate for the data, and why?
Bar chart, because the data is categorical
Histogram, because there is a large set of data
Stem-and-leaf plot, because you can see the shape of the data
Line plot, because you can see the mode of the data
The graphical representation that would be most appropriate for the data, given the number of different breakfast cereals sold, is B. Histogram, because there is a large set of data.
Why are histograms used for large sets of data ?Histograms are used for large sets of data because they provide a visual representation of the distribution of the data. They are particularly useful for understanding the distribution of continuous variables, such as measurements or time series data.
One of the main advantages of histograms is that they allow for easy comparison of large sets of data. The use of bars to represent the data makes it easy to see the overall shape of the distribution and identify patterns or outliers. Additionally, histograms can be used to compare multiple sets of data at once, allowing for easy comparison of different groups or changes over time.
Another advantage of histograms is that they can be used to identify the underlying probability distribution of a dataset, which is useful for statistical analysis and modeling.
This is why, given the fact that the data contains information from 1, 000 different cereals, a histogram is best to show this as the data is large.
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Answer: B Histogram
Step-by-step explanation:
PLS HELP!! 15 points!
The origin's coordinates are as follows: (0, 0). A pair of ordered numbers contains one point's coordinates in the coordinate system.
What do you meant by ordered pair ?To accomplish this, convert the total number of liters of fuel you purchased into gallons (multiply by 0.219). the initial mileage is subtracted from the total. Then, multiply the distance traveled by the number of gallons of fuel used. Miles per gallon are provided. The concept of proportionality refers to a graphed proportional relationship in which the independent variable is represented by x and the dependent variable by y.
Independent variables describe the input values in a relationship and are typically represented by the x coordinate in the ordered pairs (x, y). When two or more parameters are directly or indirectly proportional to one another, the relationship is denoted by the symbols a=kb or a = k/b, where k denotes the direction of the relationship between the two variables.
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maya wants to be able to take a series of four triangles and place them in a mobile design where all four triangles are attached at one point and are balanced so that they stay horizontal. Which statement best describes where she should attach each triangle?
A) Where the medians intersect
B) where the altitudes intersect
C) where perpendicular bisectors intersect
D) at any vortex
The correct statement is (D) at every vertex.
What is a vertex?The vertex of a triangle is the intersection of two sides. Vertices is the term used to describe objects with several vertices.
The ability to write an equation for a line given two points is a prerequisite. The intersection of two lines will then need to be solved, which will give you the intersection's coordinates.
One of the triangle's vertices is at this intersection of two lines.
So, we know that 4 triangles are joined to make them horizontal.
This can be done when the vertex is attached to all 4 triangles.
Then, statement (D) will be a correct statement.
Therefore, the correct statement is (D) at every vertex.
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A milk truck delivers 459 dozen gallons of milk to stores in 1 day. Write and solve an equation to find g, the number of gallons of milk the milk truck delivers in 1 day I don't get it help!
If a milk truck delivers 459 dozen gallons of milk to stores in 1 day. the equation to show the quantity of milk delivered in one day is
459xand the amount of milk delivered in one day is
5508 gallons of milkHow to solve for the amount of milk truck delivered in one dayThe information necessary to find the quantity of milk delivered in one day is that 1 dozen is equal to 12 pieces
The total number of gallons of milk delivered
the equation is 459x
where x represents number in a dozen
amount delivered
= 12 * 459
= 5508 gallons of milks
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Construct one table that includes relative frequencies based on the frequency distributions shown below, then compare the amounts of tar in non filtered and filtered cigarettes. Do the cigarette filters appear to be effective? ( Hint: the filters reduce the amount of tar ingested by the smoker)
The table including relative frequencies based on the frequency distributions is as follows:
Tar(mg) Relative frequency Relative frequency
(Nonfiltered) (Filtered)
3-8 0% 4%
9-14 0% 12%
15-20 4% 24%
21-26 0% 60%
27-32 56% 0%
33-38 28% 0%
39-44 12% 0%
Yes, the cigarette filters appear to be effective.
What are relative frequencies?
The ratio (fraction or proportion) of the number of times a data value appears in the set of all outcomes to the total number of outcomes is known as the relative frequency.
Tar(mg) Frequency Relative Frequency Relative
frequency frequency
(Nonfiltered) (Filtered)
3-8 0 0% 1 4%
9-14 0 0% 3 12%
15-20 1 4% 6 24%
21-26 0 0% 15 60%
27-32 14 56% 0 0%
33-38 7 28% 0 0%
39-44 3 12% 0 0%
Hence, the cigarette filters appear to be effective because the relative frequency of the higher tar classes is greater for non filtered cigarettes.
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Find x if QT is an angle bisector. Round to the nearest tenth.
18
S
T
32
21
X
R
Rounding to the nearest tenth: x = 7.6
What is an angle bisector?
An angle bisector is a line or segment that divides an angle into two congruent angles. It is called an angle bisector because it bisects, or cuts in half, the measure of the angle. An angle bisector can also divide the angle into two angles of different measures if the angle is not congruent.
In order to find x, we can use the Angle Bisector Theorem which states that the ratio of the length of the segment from the vertex of the angle bisector to the sides of the angle is equal to the ratio of the length of the other two segments formed by the angle bisector.
In this case, we know that QT is an angle bisector of angle X, so we can set up the following proportion:
(ST/x) = (TR/XT)
We are given that ST = 21, TR = 32 and XT = 18
Solving for x:
x = (21*18) / (32+18) = 378 / 50 = 7.56
Hence, Rounding to the nearest tenth: x = 7.6
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What are the 3 coordinate systems you use for AutoCAD drawings?
The 3 coordinate systems you use for Auto CAD drawings are the Absolute coordinate system, Relative Rectangular coordinate system, and Relative Polar coordinate system.
Absolute Coordinates use the Cartesian System to specify a position in the X, Y, and Z axes to locate a point from the 0 and X, 0 and Y, and 0 and Z (0,0,0) points.
The relative coordinate started with the symbol telling Auto CAD it was a relative coordinate. Using relative coordinate points entered by typing x,y.
Polar coordinates are used when you need to draw the next points at a specific angle. The polar coordinates system in Auto CAD specifies the distance length at which angle. Using polar coordinate points entered by typing distance<angle.
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Solve the quadratic equation numerically (using tables of x- and y- values). X squared + 7 x + 12 = 0.
The quadratic equation numerically for [tex]x^{2} + 7x +12 = 0[/tex] is when
x = -4 and x =-3
The equation is [tex]x^{2} + 7x +12 = 0[/tex]
To solve this equation using the table, we change the equation into a function
So, the function is F(x) = y = [tex]x^{2} + 7x + 12[/tex]
We have to find the value of x which we can substitute to the equation to get the y value to become 0. Since it is a quadratic equation, x will have 2 values, on [tex]x^{2}[/tex] & 7x
X [tex]x^{2} + 7x + 12[/tex] = Y
-4 = [tex]-4^{2}[/tex] +7(-4) + 12 = 0
-3 = [tex]-3^{2}[/tex] +7(-3) + 12 = 0
-2 = [tex]-2^{2}[/tex] +7(-2) + 12 = 2
-1 = [tex]-1^{2}[/tex] +7(-1) + 12 = 6
0 = [tex]0^{2}[/tex] +7(0) + 12 = 12
1 = [tex]1^{2}[/tex] +7(1) + 12 = 20
2 = [tex]2^{2}[/tex] +7(2) + 12 = 30
Based on table above we can see Y = 0, when X = -4 and X = -3
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It is given that y is directly proportional to x.
1
2345
y
-4
-8
-12
-16
-20
What is the constant of variation?
When it is assumed that y is directly proportional to x, the variational constant is -4.
what is variation ?A variation is a relationship between a set of values for one variable and another set of values. direct change. If m is a nonzero constant and b = 0, the function y = mx (commonly written y = kx) that results from the equation y = mx + b is known as a direct variation. Variation Theory is a broad theory of learning that is mostly applied in mathematics teaching and pedagogy. It highlights a concept's key components by concentrating on what remains the same and what changes, which creates the possibility for meaningful connections.
given
If y and x are directly proportionate, we would write:
If we include the proportionality constant, or variation, k, we get: y = kx
Any ordered pair from the table can be used to determine the value of y when x=1. y = -4 = k (1) k = -4
When it is assumed that y is directly proportional to x, the variational constant is -4.
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what is the length of AB
Answer:
AB ≈ 5.2
Step-by-step explanation:
given ∠ CAD = ∠ BAD = Θ
then AD is an angle bisector and divides the opposite side into segments that are proportional to the other 2 sides , that is
[tex]\frac{BD}{CD}[/tex] = [tex]\frac{AB}{AC}[/tex] ( substitute values )
[tex]\frac{4.1}{4.3}[/tex] = [tex]\frac{AB}{5.5}[/tex] ( cross- multiply )
4.,3 AB = 4.1 × 5.5 = 22.55 ( divide both sides by 4.3 )
AB ≈ 5.2 ( to one decimal place )
Divide (36z^2y^6-12z^6y^6) divided by (4z^5y^2)
Therefore , the solution of the given problem of algebraic comes out to
be 9y⁴ /z³ - 3zy⁴.
What is algebraic in mathematics?Algebra is the branch of mathematics that aids in the representation of problems or situations using mathematical expressions. In algebra, we use numbers with definite or fixed values such as 2, 7, 0.068, and so on. In algebra, we use variables such as x, y, and z in addition to numbers.
Here,
Given:
=> (36z²y⁶ - 12z⁶y⁶) / 4z⁵y²
=> 9y⁴ /z³ - 3zy⁴
thus , we get the solution for the given algebraic expression.
Therefore , the solution of the given problem of algebraic comes out to
be 9y⁴ /z³ - 3zy⁴.
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Solve the following equation for z
Answer: for one what equation and two what is your profile pic god dam you go a big nose
Step-by-step explanation:
Determine the type of dilation shown and the scale factor used.
The type of dilation that is used here as well as the factor used is given as: enlargement with scale of 2.5. Option 2
What is dilation in mathematics?Reducing the object's size by dilation is a change. The items are enlarged or shrunk by dilation. An picture that retains the original shape is created by this alteration. The size of the form does differ, though.
The smaller image is resized into a bigger image from what we can see in the images that we have before us.
We would have to divide all sides of the big square with the corresponding sides of the smaller square
20 / 8 = 2.5
15 / 6 = 2.5
Hence we would see that the scale factor that is used here is 2.5. Therefore the dilation that is used is the enlargement with scale factor 2.5. Option 2 is correct
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what is 270 divided by 4.25
Answer:
1080 / 17
Step-by-step explanation:
270 divided by 4.25 = 27000 ÷ 425
= [tex]\frac{27000}{425}[/tex] = [tex]\frac{1080}{17}[/tex]
A rock climber descends 31 feet into a small canyon. Then she climbs up 5 feet. Which integer represents her final position in feet, relative to where she started?
Answer:
-15ft
Step-by-step explanation:
Answer: - 26
-31 + 5 = -26
i need the answer please
Answer:
(1.5 , -5.5)
Step-by-step explanation:
Finding the midpoint when endpoints are given:(9 , -8) ; x₁ = 9 & y₁ = -8
(-6 , -3) ; x₂= -6 & y₂ = -3
[tex]\sf \boxed{\bf Midpoint= \left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)}[/tex]
[tex]\sf = \left(\dfrac{9-6}{2},\dfrac{-8-3}{2}\right)\\\\\\=\left(\dfrac{3}{2},\dfrac{-11}{2}\right)\\\\\\=(1.5, -5.5)[/tex]
Hector is mixing fruit punch in a 40-cup punch bowl for a party. He plans to
add at least 24 cups of fruit juice to the bowl before adding ginger ale.
Identify the graph that represents the amounts of fruit juice and ginger ale he
can use, and then identify a valid solution. (The graph shows the overlapping
solution region only, not the shading for each inequality.)
The graph that represent the amounts of fruit juice and ginger ale he can use, and the valid solution is: A. valid solution (28, 8).
How to write and solve the system of inequalities graphically?In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of cups of fruit juice and number of hours clearing tables respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of cups of fruit juice.Let the variable y represent the number of cups of ginger ale.Since Hector is mixing fruit punch in a 40-cup punch bowl for a party, an inequality which models this situation is given by:
x + y ≤ 40.
Additionally, Hector plans to add at least 24 cups of fruit juice to the bowl before adding ginger ale:
x ≥ 24.
Based on the graph (see attachment), we can logically deduce that a valid solution to the given system of inequalities is the overlapping solution region, which is given by the ordered pair (28, 8).
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The sum of the measures of five exterior angles of a hexagon is 257°
. What is the measure of the sixth exterior angle?
What is the solution for X?
By virtue of the properties of congruency of sides of opposite sides, the solution of x is 5 as 4/x-3 = x-7/35.
what is solution ?a number or values that, when used as a substitution for one or more variables in an equation, make the equation true. For instance, the answers to the equation x2 = 4 are 2 and -2. a method or technique for solving a problem. an explanation of a solution. specifically: a collection of variable values that satisfy an equation. A number that can be entered as the variable's replacement in an equation serves as the solution. 6+5=11 is correct according to the formula 3(2)+5=11. The answer is therefore 2,
given
AB / CD = EF/GH
4/x-3 = x-7/ 35
x = 5
so By virtue of the properties of congruency of sides of opposite sides, the solution of x is 5 as 4/x-3 = x-7/35.
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The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 7 to 5 If there were 4255 no votes, what was the total number of votes?
The total number of votes is given as 10212
How to solve for the number of votesThe total number of votes that would be in the city is given as 7400.
How to find the total number of votes
The ratio of votes is in terms of yes to no
This is 7 : 5
Given that the number of no votes is 4255, we can use this number in order to find the yes votes.
7 + 5 = 12
there were 4255 no votes.
we would have:
(5 / 12 )x= 4255
5x = 12 * 4255
5x = 51060
x = 10212
The total number of votes is given as 10212
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Planes X and Y and points C, D, E, and F are shown.
Vertical plane X intersects horizontal plane Y. Point D is on the left half of plane Y. Point F is on the bottom half of plane X. Point E is on the right half of plane Y. Point C is above and to the right of the planes.
Which statement is true about the points and planes?
The line that can be drawn through points C and D is contained in plane Y.
The line that can be drawn through points D and E is contained in plane Y.
The only point that can lie in plane X is point F.
The only points that can lie in plane Y are points D and E.
The correct option is (B) The line that can be drawn through points D and E is contained in plane Y.
What are planes and points?A point is a location in space. It has neither shape nor size. A line is a connected set of points that extends infinitely in two directions. A plane can be defined by three noncollinear points, two parallel lines, or two intersecting lines.
The planes X and Y and points C, D, E and F are shown in the given figure.
We are to select the TRUE statement about the points and the planes.
We know that, if two points lie in a plane, then the line drawn through the points will contain in the same plane.
The points C lies outside the plane Y and the point D lies on the plane Y, so the line drawn through the points C and D will not contain in plane Y.
So, option (A) is NOT correct.
The points D and E, both lie in the plane Y, so the line drawn through the points D and E will also contain in plane Y.
So, option (B) is CORRECT.
Since the plane X contain infinitely many points, so F is not the only point that can lie in plane X.
So, option (C) is NOT correct.
Similarly, there are infinitely many points in the plane Y, so the points D and E are not the only points that can lie in plane Y.
So, option (D) is NOT correct.
Thus, the correct option is, The line that can be drawn through points D and E is contained in plane Y.
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Write the standard equation of the circle given a center (-14,7) and a radius of 2
Answers-
A. (x-14)^2 + (y+7)^2 =1
B. (x+14)^2 + (y-7)^2 =8
C. (x-14)^2 + (y+7)^2 =4
D. (x+14)^2 + (y-7)^2 =4
The standard equation of the circle given a center (-14,7) and a radius of 2 is (x+14)^2 + (y-7)^2 =4.
What is standard equation?The standard equation of a line is y = mx + b, where m is the slope of the line and b is the y-intercept. This equation can be used to graph any line, provided the values of m and b are known. It can also be used to calculate the slope and y-intercept of any given line.
This equation describes a circle that has a center at the point (-14,7) and a radius of 2 units.
The equation (x+14)^2 + (y-7)^2 =4 can be used to determine the coordinates of points on the circle, as well as the length of its circumference.
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How do you solve a factor by step by step?
Therefore , the solution of the given problem of factor comes out to be
the factor can be solved by listed below steps.
What is a factor?A factor seems to be a variable that is multiplied by another to produce a result. A multiplication puzzle has a product as its answer. Consider an arithmetic problem as the process of multiplying the factors to obtain the product. For instance, the factors of 8 are 2 and 4: A number may have only two components or many other factors.
Here,
There are four main steps in the Solve via Factoring process:
1) Use addition or subtraction to transfer all terms around one part of the equation, typically the left.
2) Completely factor the equation.
3) Solve by setting each element to zero.
4) Identify each of the Step 3 answers as a solutions to the initial problem.
Therefore , the solution of the given problem of factor comes out to be
the factor can be solved by listed above steps.
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Sofia earned a score of 460 on Exam A that had a mean of 400 and a standard
deviation of 20. She is about to take Exam B that has a mean of 100 and a
standard deviation of 25. How well must Sofia score on Exam B in order to do
equivalently well as she did on Exam A? Assume that scores on each exam are
normally distributed.
X2 = 175 Sofia needed a certain grade on Exam B to perform at the same level as she did on Exam A.
What is standard deviation ?Data are said to be more closely grouped around the mean when the standard deviation is low and more dispersed when the standard deviation is high. The dispersion of the data around the mean value is measured by the standard deviation. It might be helpful when comparing data sets that may have the same mean but a different range. The means of the two numbers 15, 15, 15, 14, 16, and 2, 7, 14, 22, 30 are the same, for instance. The second, though, is unmistakably wider.
given
X1
u1 = 400 u2 = 100
20 25
X2
Z1 score = Z2 score
X1 - u1 / 20 = X2 - u2 / 25
460 - 400 / 20 = X2 -100 / 25
3 = X2 - 100 /25
X2 = 175 score on exam b
X2 = 175 Sofia needed a certain grade on Exam B to perform at the same level as she did on Exam A.
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What is the table of 4?
The multiplication table for 4's underlying pattern: To begin with, let your child know that 4 is an even number. Therefore, no matter what number you multiply by 4 .
what is sequence ?A list of items in a sequence is one that is ordered (or events).The number of elements in an ordered sequence determines its length (potentially infinite). Arithmetic sequences, geometric sequences, quadratic sequences, and special sequences are the four primary types of sequences that you need to be familiar with. Number sequences are collections of numbers connected by some kind of rule. If you understand the rule, you can determine the numbers that will come after that in the sequence. Each number differs from the other in this case by 6. In this case, the rule for this sequence is to add 6 each time.
given
The multiplication table for 4's underlying pattern: To begin with, let your child know that 4 is an even number.
Therefore, no matter what number you multiply by 4, the result will always have either 0, 2, 4, 6 or 8 at the end.
With the aid of this method, kids will be able to distinguish multiples of 4, which will make learning the table of four much simpler.
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In the coordinate plane point a has coordinates of A (-5,8). Which is further from a point B or point C given that they have coordinates of B(1,0) and C(-10,16)
The point that is further from point A is point B
How to find length of lineThe length of line in an ordered pair is calculated using the formula
d = √{(x₂ - x₁)² + (y₂ - y₁)²}
where
d = distance between the points
x₂ and x₁ = points in x coordinates
y₂ and y₁ = points in y coordinates
distance between points A (-5, 8) and B(1, 0) is calculated as follows
d = √{(x₂ - x₁)² + (y₂ - y₁)²}
d =√{(-5 - 1)² + (8 - 0)²}
d =√{36 + 64}
d = √100
d = 10 units
distance between points A (-5, 8) and C(-10, 16) is calculated as follows
d = √{(x₂ - x₁)² + (y₂ - y₁)²}
d =√{(-5 + 10)² + (8 - 16)²}
d =√{25 + 64}
d = √89
d = 9.43 units
comparing both points shows that point B shows further away
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work out 4 1/2×1 2/5 give your answer in its simplest form
What scale factor was used in the dilation?
The scale factor used in the dilation of the triangle ABC is 3.
What is the dilation of a triangle?Dilation is a method for generating analogous figures decreasing or increasing their dimensions by some scaling factors.
By dividing distances by the scale factor, each point is stretched outward from the central point D if the scaling factor is more than 1 or inwards if the scale factor is less than 1.
Considering the triangle ABC:
The length of the side AB is 2 units
Compared with triangle DEF, the length of the similar side DE is 6 units
The scaling factor = length of side DE /length of the side AB
The scaling factor = 6 / 2
The scaling factor = 3
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For $2.75 you can buy 20 small bags of jelly beans. How much is 1 bag of jelly beans?
Answer:
The answer is $ 0.13
Pls mark me as brainliest
subtract 11 hrs from 6 hrs 51 min
Answer:
(A) -5 hr 51 mins (B) 7:51 am/pm
Step-by-step explanation:
(A):
6 hr 51 mins
-
11 hr 0 mins
___________
-5 hr 51 mins
(B):
6 hr 51 mins - 11 hr 0 mins = 18 hr 51 mins - 11 hr 0 mins = 7 hr 51 mins am/pm or 7:51 am/pm.
Hope this helps!
P.S. Feel free to suggest any edits.