Statements I, II, and III are partially correct, but statement II needs to be corrected to indicate that stem plots are better for small to moderate-sized datasets.
We might choose to display data with a stem plot rather than a boxplot because:
Reveals the shape of the distribution.
Is better for small to moderate-sized datasets.
Displays the actual data.
A stem plot is a type of graph that shows the distribution of data by grouping the observations into stems and leaves.
It allows for the display of the actual data values, which is not possible in a boxplot.
Additionally, stem plots are particularly useful for small to moderate-sized datasets as they provide a detailed view of the distribution, allowing for the identification of patterns such as skewness, multimodality, and outliers.
On the other hand, boxplots are better for large datasets as they provide a more concise summary of the distribution, including information about the median, quartiles, and outliers, while still conveying information about the spread and shape of the distribution.
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Please solve number 7 I do not understand it at all. Please and thank you so much.
The equation of the largest circle is given as follows:
x² + y² = 9².
What is the equation of a circle?The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle, while the diameter of the circle is the distance between two points on the circumference of the circle that pass through the center. Hence, the diameter’s length is twice the radius length.
The largest circle will have the largest radius, while the coefficients of x and y should be both of 1, hence the equation is given as follows:
x² + y² = 9².
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A man starts from his home and drives 169 km to the east and then 192 km to the west. How far is he from home finally and in which direction
The man is 23 km west of his home after driving 169 km to the east and 192 km to the west.
To determine how far the man is from his home after driving 169 km to the east and 192 km to the west, we can think of his movements as a displacement vector.
The vector representing the man's movement to the east has a magnitude of 169 km and is directed towards the east. Similarly, the vector representing his movement to the west has a magnitude of 192 km and is directed towards the west.
Since these two vectors are in opposite directions, we can subtract them to find the net displacement vector.
Net displacement = 169 km east - 192 km west
= -23 km west
The negative sign indicates that the net displacement vector is directed towards the west, which means that the man is 23 km west of his home.
To determine the distance between the man and his home, we can use the Pythagorean theorem. Since the man moved only in the east-west direction, the distance between him and his home is the absolute value of the net displacement, which is 23 km.
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Angles X and Y are supplementary. Angle X measures 115. 75° and angle Y measures (m − 8)°. Find m∠Y
The measure of angle Y is m - 8 = 72.25 - 8 = 64.25 degrees.
What is the supplementary angle?
Two angles are said to be supplementary if their sum is equal to 180 degrees. In other words, if angle A and angle B are supplementary, then:
A + B = 180.
Since angles X and Y are supplementary, their measures add up to 180 degrees. So we have:
X + Y = 180
Substituting the given values, we get:
115.75 + (m - 8) = 180
Simplifying, we get:
m - 8 = 180 - 115.75
m - 8 = 64.25
Adding 8 to both sides, we get:
m = 72.25
Therefore, the measure of angle Y is m - 8 = 72.25 - 8 = 64.25 degrees.
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select all the values that are solutions to x < -4
Any value of x that is less than -4 is a solution to the inequality x < -4.
Selecting the values that are solutions to x < -4Any value of x that is less than -4 is a solution to the inequality x < -4.
Some examples of such values are:
x = -5
x = -10
x = -100
In fact, any value that is to the left of -4 on the number line is a solution to the inequality x < -4. On a number line, we represent this inequality by shading everything to the left of -4.
To understand this visually, imagine a number line with -4 as the reference point.
All the values to the left of -4 will be negative, and all the values to the right of -4 will be positive.
So, the inequality x < -4 means that x can be any value to the left of -4 on the number line.
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Can you guys help me with this
Answer:
C
Step-by-step explanation:
Recall the point-slope form of a linear equation:
[tex]y-y_{1}=m(x-x_{1} )[/tex]
Where y1 and x1 are points from the ordered pair (x1, y1),
and m represents the slope of the line.
We are given that the point (-5, 7) belongs to the graph. Here, the x-coordinate is -5, and the y-coordinate is 7.
Let's plug in these values, were x1=-5, and y1=7:
[tex]y-y_{1}=m(x-x_{1} )=\\y-7=m(x-(-5))=\\y-7=m(x+5)[/tex]
We are also given that the slope is -4/3.
In other words, m=-4/3. Let's plug this value in:
[tex]y-7=m(x+5)=\\y-7=-\frac{4}{3}(x+5)[/tex]
Thus, the answer is C.
Answer:
C
Step-by-step explanation:
The point-slope form of the equation of a line passing through the point (x1, y1)with a slope of m is given by:
y - y1 = m(x - x1)
To find the equation of the line passing through the point (-5, 7)with a slope of -4/3, we substitute m = -4/3, x1 = -5, and y1 = 7 into the point-slope form equation:
y - 7 = (-4/3)(x - (-5))
Simplifying this equation, we get the final result in slope-intercept form:
y = (-4/3)x + (17/3)
Therefore, the equation of the line in a point-slope form that passes through (-5,7) and has a slope of -4/3 is y + 7 = -4/3 (x + 5)
If h(x)=â«x3â12+t2ââââââât for xâ¥0, then hâ²(x)=
Therefore, according to the given information, h ²(x) = (x^3 - 12 + t^2)^3 - 12 + t^2.
The function h(x) is defined as x³ minus 12 plus t squared, where x is greater than or equal to 0, and t is some constant. To find h²(x), we need to first calculate the result of applying h(x) to itself, which we can write as h(h(x)). After some calculations, we arrive at h(h(x)) equals x⁹ minus 36 times x to the power of 6 multiplied by t squared, plus 324 times x to the power of 3 multiplied by t to the power of 4, minus 12 times x cubed, plus 145 times t squared, minus 35 times t to the power of 4. Therefore, h²(x) is equal to the same expression we obtained for h(h(x)).
To find h²(x), we need to first find h(h(x)).
h(x) = x^3 - 12 + t^2
h(h(x)) = (h(x))^3 - 12 + t^2
Substituting h(x) into the above equation, we get:
h(h(x)) = (x^3 - 12 + t^2)^3 - 12 + t^2
Therefore, h²(x) = (x^3 - 12 + t^2)^3 - 12 + t^2.
Therefore, according to the given information, h ²(x) = (x^3 - 12 + t^2)^3 - 12 + t^2.
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URGENT - Will also give brainliest to simple answer
Find the length of the arc that outlines the sector
Answer:
4 or ≈ 12.6
Step-by-step explanation:
L = r * θ
r = 12
θ = 60 = (/3) when converted to radians by multiplying (/180)
then multiply
(/3)*12 = 4 or ≈ 12.6
what is the congruent segment of pr
Answer:
In geometry, congruent segments are segments that have the same length. If you can provide me with more context, such as what "p" and "r" represent in this scenario, I can give you a more detailed response.
Step-by-step explanation:
A pizza with a diameter of 18 inches is cut into 10 equal slices. To the nearest square inch , what is the area of each slice of pizza
If a pizza with an 18-inch diameter is divided into 10 equal pieces, then each slice will have a surface area of roughly 25.45 square inches.
What is diameter?Diameter is defined as a straight line across the middle of a body or figure, particularly a circle or sphere. Pizza diameter is the length of a straight line that touches two locations on the edge of a pizza pie and passes through its center.
Each sector of the pizza, which is divided into 12 equal sections, has an arc measurement of 360/10= 36 degrees.
As = (360÷Ф) ×X r² where x is the measure of the intercepted wave, yields the area of a sector.
We know that x=36 and
d=18→r=9 in. Thus, r is the radius and A is the area of each intersecting arc of a sector.
A=1/10×81π
then each slice will have a surface area of roughly 25.45 square inches.
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A candle is in the shape of a cylinder. The candle has a diameter of 3. 5 inches and a height of h inches. Which equation can be used to find V, the volume of this candle in cubic inches?
The volume of the candle is,⇒ V = 31.4 in³.What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.Given that;A candle in the shape of a cylinder has the dimensions shown, in inches.And, Diameter of candle = 5 in.Height of candle = 8 in.We know that;Volume of cylinder = πr²hHence, We get;The volume of the candle is,⇒ V = 3.14 × (5/2)² × 8⇒ V = 3.14 × 10⇒ V = 31.4 in³.Thus, The volume of the candle is,⇒ V = 31.4 in³.
Find the value of x. If a segment looks like a tangent, it is a tangent.
Using laws of the outside angle theorem, we can find the value of the arc x to be = 130°.
Define outside angle theorem?The measure of an exterior angle is equal to the sum of the measures of the two distant interior angles of the triangle, according to the external angle theorem. According to the exterior angle inequality theorem, any triangle's outside angle has a measure bigger than either of its opposing interior angles.
Here in the question,
As per the outside angle theorem,
50° = 180° - x°
Adding x° on both sides:
⇒ 50° + x° = 180°
Now subtracting 50° from both sides:
⇒ x° = 180° - 50°
⇒ x° = 130°
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a lot is in the shape of a right triangle. the shorter leg measures 150 m. the hypotenuse is 50 m longer than the length of the longer leg. how long is the longer leg?
Answer:
Starting with the 3-4-5 right triangle, multiply all lengths by 50, obtaining 150, 200, and 250. So the length of the longer leg is 200 meters.
using complete sentences, explain which function has the greatest y-intercept.
Answer:
Step-by-step explanation:
To determine which function has the greatest y-intercept, we need to look at the constant term, which represents the y-intercept, of each function. The function with the largest constant term will have the greatest y-intercept.
For example, consider the following three functions:
1. f(x) = 2x + 5
2. g(x) = 3x - 7
3. h(x) = -4x + 10
The constant term for each function is 5, -7, and 10 respectively. Therefore, h(x) has the greatest y-intercept of 10, since its constant term is larger than those of f(x) and g(x).
11. You have a bank account in which
your balance increases annually at a rate of 7.25%. If your initial
investment was $250, write an
equation that represents your
balance after x years.
Initial Value (a):
Rate (r):
Time (x):
Equation:
The equation that represents your balance after x years is: [tex]250 * (1.0725)^x[/tex]
what is interest ?
To calculate simple interest, multiply the principal by the rate of interest rates, the duration, and several other variables. The marketing formula is simple returns = capital + interests + hours.
Initial Value (a): $250
Rate (r): 7.25% per year (or 0.0725 as a decimal)
Time (x): x years
The formula for calculating the balance after x years is:
[tex]Balance = a * (1 + r)^x[/tex]
Plugging in the values, we get:
[tex]Balance = 250 * (1 + 0.0725)^x[/tex]
So the equation that represents your balance after x years is:
[tex]Balance = 250 * (1.0725)^x[/tex]
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The
perimeter of a rectangle is 75
ft and the length is 27 ft. What is
the area of the rectangle?
Given right triangle ABC with altitude BD drawn to hypotenuse AC. If BD = 3 and DC = 9, what is the length of AC?
Given right triangle ABC with altitude BD drawn to hypotenuse AC. If BD = 3 and DC = 9, the length of AC is: 4 units.
How to find the length?In a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse into two segments. Let's call the length of the hypotenuse AC as x, and the length of the segment containing point B as y. Then, the length of the other segment containing point C is x - y.
Using similar triangles, we can set up the following proportion:
BD/DC = y/(x - y)
Substituting the given values, we get:
3/9 = y/(x - y)
Simplifying this equation, we get:
x - y = 3y/9
x = 4y/3
We also know from the Pythagorean theorem that:
AC^2 = AB^2 + BC^2
Since triangle ABC is a right triangle, we have:
AB^2 + BC^2 = x^2
Substituting x = 4y/3, we get:
AB^2 + BC^2 = (4y/3)^2
But we also know that:
AB/BC = 3/4
So we can set up another proportion:
AB/BC = y/(x - y)
Substituting x = 4y/3, we get:
AB/BC = y/(4y/3 - y)
Simplifying this equation, we get:
AB/BC = y/((4/3)y - y)
AB/BC = y/((1/3)y)
AB/BC = 3
So we have:
AB = 3BC
Substituting this into AB^2 + BC^2 = (4y/3)^2, we get:
(3BC)^2 + BC^2 = (4y/3)^2
10BC^2 = 16y^2/9
But we also know that:
BC^2 + y^2 = x^2
Substituting x = 4y/3, we get:
BC^2 + y^2 = (4y/3)^2
5BC^2 = 7y^2/9
Combining this with 10BC^2 = 16y^2/9, we get:
15BC^2 = 21y^2/9
BC^2 = (7/3)y^2/3
Substituting this into BC^2 + y^2 = (4y/3)^2, we get:
(7/3)y^2/3 + y^2 = 16y^2/9
7y^2/9 + 9y^2/9 = 16y^2/9
16y^2/9 = 16y^2/9
So this equation is true for any value of y. Therefore, the length of AC is:
AC = x = 4y/3
Substituting y = BD = 3, we get:
AC = 4(3)/3 = 4
Therefore, the length of AC is 4 units.
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Find the area of an equilateral triangle with a perimeter of 45 inches.
The area of the equilateral triangle is approximately 58.78 square inches.
An equilateral triangle has all sides equal, so we can divide the perimeter by 3 :
45 inches ÷ 3 = 15 inches
Therefore, each side of the equilateral triangle measures 15 inches.
Area = (√3 / 4) x (side length)²
After putting the values,
Area = (√3 / 4) x 15 x 15 square inches
Area = (√3 / 4) x 225 square inches
Area = 58.78 square inches
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Find the value of X.
Answer:
92.5°
Step-by-step explanation:
You want the angle where chords cross, given that they intercept arcs of 55° and 130°.
Chord angleThe angle x° is the average of the measures of the intercepted arcs:
x° = (55° +130°)/2
x° = 92.5°
Convert the following decimals to percents.
1.37 =_%
Answer:
137%
Step-by-step explanation:
1.37 x 100 = 137%
Question 4
Davey is setting up a retirement account, planning to invest $5,000 per year. Assume the account earns 9.35%. He will keep these deposits up for the first 20 years, and then stop making deposits, leaving the account open for another 20 years. Based on these assumptions, how much will he have in the account at the end of 40 years?
Hence, after 40 years, Davey will have $1,476,289.64 in his retirement account as n = the number of cycles.
what is unitary method ?A problem-solving strategy known as the unitary technique is determining the worth of one unit of such a quantity and utilising that value to determine the value of an other number of units related to that quantity. For issues where the price of one unit is given and the value of some other quantity is needed, it is a proportionality strategy. The unitary method's fundamental principle is to establish a ratio between two numbers, where one of the numbers is represented in the form of one unit while the other quantity is defined in terms of a greater number of units.
given
If Davey doesn't add any more money to his retirement account for the next 20 years, it will increase to:
[tex]FV = P * (1 + r)^n[/tex]
where FV is the lump sum's future value
P is the lump sum's present value, which in this example is $214,111.26.
R is the annual interest rate, which in this case is 9.35%.
n = the number of cycles (in this case, 20 years)
The following equation can be used to determine Davey's retirement account's potential value after 40 years:
[tex]FV = 214,111.26 * (1 + 0.0935)^20 = $1,476,289.64[/tex]
Hence, after 40 years, Davey will have $1,476,289.64 in his retirement account as n = the number of cycles.
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john has a new house. the lot that the house stands on is a rectangle that is 125' long and 77' deep. the house sits near the center of the lot and is 40' wide, 36' deep and two stories high. john needs to plant his new lawn with grass seed. each box of seed covers 500 square feet of ground. how many boxes of seed does he need to purchase?
If john has a new house. the lot that the house stands on is a rectangle that is 125' long and 77' deep, John will need to purchase up to 19 boxes of grass seed.
First, we need to calculate the total area of the lot. The area of a rectangle is given by its length multiplied by its width, so:
Area of lot = 125 ft * 77 ft = 9625 square feet
Next, we need to determine the area of the portion of the lot that is not covered by the house. Since the house is located near the center of the lot, we can find the area of the rectangle that represents the space around the house and subtract it from the total area of the lot:
Area around house = (125 ft - 40 ft - 40 ft)/2 * (77 ft - 36 ft - 36 ft)/2 = 22.5 ft * 16.5 ft = 371.25 square feet
Area to be planted = 9625 square feet - 371.25 square feet = 9253.75 square feet
Now we can calculate the number of boxes of grass seed needed by dividing the area to be planted by the coverage of each box:
Number of boxes = 9253.75 square feet / 500 square feet per box = 18.51 boxes
Since you can't purchase a fraction of a box, John will need to round up to 19 boxes of grass seed.
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Write a porportion that you can use to convert 60 inches to centimeters
Answer:
152.4 centimeters.
Step-by-step explanation:
1 inch = 2.54 centimeters
60 inches = x centimeters
Where x is the number of centimeters equivalent to 60 inches.
To solve for x, we can set up a proportion:
1 inch / 2.54 centimeters = 60 inches / x centimeters
Cross-multiplying, we get:
1 inch * x centimeters = 2.54 centimeters * 60 inches
Simplifying, we get:
x = (2.54 cm/in) * (60 in)
x = 152.4 cm
Therefore, 60 inches is equivalent to 152.4 centimeters.
Probabilities always lie between _ and _ when in decimal form.
Answer:
0 and 1
Step-by-step explanation:
hope this helps ;)
The graph shows f(x). The absolute value function g(x) is described in the table.
The graph shows a v-shaped graph, labeled f of x, with a vertex at 0 comma 1, a point at negative 1 comma 2, and a point at 1 comma 2.
x g(x)
−4 0
−2 −2
0 −4
2 −2
4 0
If g(x) = f(x) + k, what is the value of k?
k = −5
k = −4
k = 4
k = 5
The value of k given the absolute value functions is (a) k = -5
Given that
graph = f(x)
table = g(x)
Since the vertex of the function f(x) is at (0,1), we have f(0) = 1.
Also, from the given table, we have g(0) = -4.
Therefore, if g(x) = f(x) + k, we must have g(0) = f(0) + k = 1 + k.
But we also know that g(0) = -4. Thus, we have:
1 + k = -4
Solving for k, we get:
k = -5
Therefore, the value of k is -5.
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How can I find the length of AB
To find line segment AB, you'd have to use the principle of proportions. Thus, Line AB is 10.5.
What is the explanation for the above response?To derive line segment AB,
6/4 = AB/7
To solve for AB, we can cross-multiply and simplify:
6/4 = AB/7
Multiply both sides by 7:
(6/4) * 7 = AB
Simplify:
10.5 = AB
Therefore, AB is equal to 10.5.
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Can someone help me find the area of this shaded shape?
Write an inequality to compare -21 and -13 which temperature is warmer?
Answer:
[tex]-13 > -21[/tex]
-13 is the warmer temperature.
Step-by-step explanation:
When comparing negative numbers, the number closer to zero on the number line is greater.
(OR, the negative number that, if it was positive, would be less).
In this case, that number is -13.
We now know that -13 is greater than -21, so we can write this inequality:
[tex]-13 > -21[/tex]
In regards to temperature, greater numbers usually mean hotter temperature, so -13 is the warmer temperature.
sketch three solutions, with initial values y(0) > 0, y(0) = 0, and y(0) < 0.
To sketch three solutions with initial values y(0) > 0, y(0) = 0, and y(0) < 0, we'll need to use a differential equation or system of differential equations. So, to sketch three solutions with initial values y(0) > 0, y(0) = 0, and y(0) < 0, we would first draw a slope or direction field for our differential equation. Then, we would start at the point (0, y(0)) and follow the direction of the slope or arrow to sketch the solution for each initial value.
To sketch three solutions with the given initial values, follow these steps:
1. Determine the differential equation you're working with. For example, let's consider the equation y'(t) = y(t). This is just an example, and the process will be similar for other differential equations.
2. Solve the differential equation to obtain a general solution. In our example, the general solution is y(t) = C * e^t, where C is an arbitrary constant.
3. Apply the initial values to find specific solutions:
a. For y(0) > 0, choose a positive value for C, such as C = 1. The specific solution is y(t) = e^t.
b. For y(0) = 0, choose C = 0. The specific solution is y(t) = 0.
c. For y(0) < 0, choose a negative value for C, such as C = -1. The specific solution is y(t) = -e^t.
4. Sketch the three solutions on the same graph:
a. For y(t) = e^t, draw a curve that starts at (0,1) and increases exponentially as t increases.
b. For y(t) = 0, draw a horizontal line at y = 0.
c. For y(t) = -e^t, draw a curve that starts at (0,-1) and decreases exponentially (toward 0) as t increases.
These three curves represent the solutions with the specified initial values. Note that this process assumes you have a specific differential equation in mind. If you have a different equation, just follow the same steps to find and sketch the solutions.
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If you know a ratio, the inverse trig function gives you an...
Answer: angle
Step-by-step explanation:
The distance, y, in miles, that Taryn is from home after x hours of driving
is represented by y = 60 - 45x. Which two statements accurately
describe Taryn's distance from home?
(A) She started 45 miles from home
(B) Here, distance from home decreases by 60 miles per hour.
(C) Her distance from decreased by 45 miles per hour
(D) She started 60 miles from her home.
Answer:
(C) and (D) are correct.