The interquartile range (IQR) of the data in the dot plot is 3.5.
What is IQR?The interquartile range is a measure of where the “middle fifty” is in a data set. Where a range is a measure of where the beginning and end are in a set, an interquartile range is a measure of where the bulk of the values lie. That’s why it’s preferred over many other measures of spread when reporting things like school performance or SAT scores.
In descriptive statistics, the interquartile range is a measure of statistical dispersion, which is the spread of the data. The IQR may also be called the midspread, middle 50%, fourth spread, or H‑spread. It is defined as the difference between the 75th and 25th percentiles of the data.
The upper and lower median values are shown below which would be the mean of the 2 middle values shown in the brackets below:
43, (44, 44,) 44, | 45, | 45, (47, 48,) 48
Upper median (Q3) = (47+48) ÷ 2 = 47.5
Lower median (Q1) = (44+44) ÷ 2 = 44
=>Step 4: Subtract the lower median from the upper median to get the IQR.
IQR = Upper median (Q3) - Lower median (Q1)
IQR = 47.5 - 44
IQR = 3.5
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A pendulum of length 1m and period 2.01s is placed at the top of Mount Everest
having an altitude of 8849m. Calculate the value of ‘g’ at that point.
Answer: A pendulum of length 1m and period 2.01s is placed at the top of Mount Everest having an altitude of 8849m. Calculate the value of 'g' at that point.
The period of this pendulum can be solved using the formula shown in the picture below. T is the period in seconds; L is the length in meters and g is the acceleration due to gravity which is equal to 9.81 m/s²near the equator.
T = 2 × π × (square root of 1.00 m / 9.81 m/s²)
T = 2 * 3.1416 * (square root of 0.101936799)
T = 6.2832 * 0.319275428
T = 2.00 seconds
The period of this pendulum correct to 3 significant figures is 2.00 seconds.
The frequency of this pendulum is solved by the formula f = 1/T
f = 1/2.00 seconds
f = 0.500 hertz
Answer: 9.76 m/s^2
Step-by-step explanation:
Is y 4 a horizontal asymptote?
Yes, the horizontal asymptote is at y = 4.
The term asymptote in math is known as a straight line that constantly approaches a given curve but does not meet at any infinite distance.
Here we have given the expression y = 4.
In order to find whether it is an horizontal asymptote or not, we have to plot it on the graph,
The first process is to label the graph with x and y axis.
And then we have to defines the scale for the for the graph.
Now, we have to input the expression y = 4 on the graph then we get the graph like the following.
While we looking into the given graph we have identified that the expression y = 4 makes the horizontal asymptote on the graph.
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You have a cup with 17 coins inside. The total inside the cup is $5. 50. Determine how many half dollars and quarters are inside the cup. Use a system of equations. Be sure to define the variables and show all work
There are 8 half dollars and 9 quarters inside the cup.
We can set up a system of equations to represent the number of half dollars (h) and quarters (q) in the cup and the total value of the coins.
Let h be the number of half dollars and q be the number of quarters.
The first equation represents the total number of coins in the cup:
h + q = 17The second equation represents the total value of the coins:
0.5h + 0.25q = 5.50To solve for h and q, we can use either the substitution or elimination method.
By substitution, we can solve for one variable in terms of the other in one of the equations and substitute it into the other equation.
So, q = 17 - h
then substitute it into the second equation:
0.5h + 0.25(17 - h) = 5.50
By solving for h, we get h = 8, then we can substitute it back into the first equation to get q = 9
So, there are 8 half dollars and 9 quarters inside the cup.
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How is the logarithmic function y log x defined?
The logarithmic function y log x is defined as
[tex]$\log_b \text x = \text y \leftrightarrow \text b^y= \text x[/tex].
What is logarithmic function?An exponent that is expressed in a unique way is called a logarithm. As an illustration, we are confident that the exponential formula 32 = 9 is correct. In this instance, the base is 3, and the exponent is 2. The formula will be written as log3 9 = 2 in the logarithmic form.
This is expressed as "9 divided by base 3 is 2" in words. The exponent has been effectively lowered to the mainline in this case. However, despite the fact that this was done to make division and multiplication easier, logarithms are still very useful in mathematics.
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i don’t know this pls help
The perimeter of the right triangle is 228 inches
What is a right-angle triangle?
It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.
The complete length of a shape's edge serves as its perimeter in geometric terms. Adding the lengths of all the sides and edges that surround a form yields its perimeter.
Since it is a right triangle,
c² = 57² +76²
c² = 3249 + 5776
c² = 9025
c= √ 9025 = 95
Perimeter is the sum of all sides
Perimeter = 57+76+95 = 228 inches
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Why is there a horizontal asymptote?
The reason behind horizontal asymptote is defined as the end behavior of the function.
The term asymptote in math is known as a straight line that constantly approaches a given curve but does not meet at any infinite distance.
Here we need to list down the reason behind horizontal asymptote.
As we all know that the horizontal asymptote of a graph is a horizontal line y = b where the graph approaches the line as the inputs approach ∞ or –∞. Here we also know that the slant asymptote of a graph is a slanted line y = mx + b where the graph approaches the line as the inputs approach ∞ or –∞.
Therefore, through the definition we know that the horizontal line to which the graph of the function appears to coincide with but it doesn't actually coincide.
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I need answer to 11, 13, 10, 12, 14, 16
ASAP Please
10. This system has one solution with coordinates (1, -2)
11. This system has one solution with coordinates (0,-3)
12. This system has one solution with coordinates(-1, -2)
13. This system has no solution.
14. This system has no solution.
16. This system has one solution with coordinates (0,-4)
How to determine the co-ordinates of system of equations?To determine the co-ordinates of a system of equations, the first step is to eliminate any redundant equations in the system.This is done by subtracting or adding equations that are already represented in the system.Once this is done, the system of equations can be set up in matrix form to find the co-ordinates.To do this, one must represent the equations as a matrix by representing the coefficients of each variable as the elements of the matrix.Once the matrix is set up, the inverse of the matrix can then be used to solve for the co-ordinates of the system.This can be done using Gaussian Elimination, Cramer's Rule, or another method.Once the inverse of the matrix is found, one can then multiply it by the vector of the constants in the equations and the resulting vector will contain the co-ordinates of the system.According to question:-
10. y = x - 3 ------- 1
y = -5x + 3 ------- 2
substitute 1 in 2,
x - 3 = -5x + 3
x = 1
y = 1 - 3 = -2
y = -2
The co-ordinates is (1,-2)
11. y = -3
substitute in y = x-3
-3 = x - 3
x = 0
The co-ordinates is (0,-3)
12. y = 4x + 2 --------- 1
y = -2x - 4 ------------2
Substitute 1 in 2,
4x + 2 = -2x - 4
6x = -6
x = -1
substitute x = -1 in 2
y = -2
The co-ordinates is (-1, -2)
13. y = x - 6 -----1
y = x+ 2 -------2
It has no solution, so there is no co-ordinates.
14. x + y = 4
3x + 3y = 12
It has no solution, so there is no co-ordinates.
16. 2x + 3y = 12 ------1
2x - y = 4 --------2
from 2 we rewrite the equation as y = 2x-4
Sub in eq 1
2x + 3(2x-4) = 12
2x + 6x - 12 = 12
8x = 24
x = 3
y = 2
The co-ordinates is (3,2)
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Can someone tell me what this is?
Answer:
there's one solution bc the lines have one point in common
The vertices of a trangular plot of land are A(1,5), B(7,5), and C(8,0)
The area of the triangular plot of land from the vertices is 20 square units
How to determine the area of the triangular plot?From the question, we have the following parameters that can be used in our computation:
A(1,5), B(7,5), and C(8,0)
Represent the vertices properly
So, we have the following representation
A = (1,5)
B = (7,5)
C = (8,0)
The area of the triangle is calculated from the vertices using the following equation
Area = 0.5 * |Ax(By - Cy) + Bx(Ay - Cy) + Cx(Ay - By)|
Substitute the known values in the above equation, so, we have the following representation
Area = 0.5 * |1 * (5 - 0) + 7 * (5 + 0) + 8 * (5 - 5)|
Evaluate the sum of products
Area = 0.5 * |40|
Remove the absolute bracket
Area = 0.5 * 40
Evaluate
Area = 20
Hence, the area of ABC with vertices is 20 square units
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Complete question
The vertices of a trangular plot of land are A(1,5), B(7,5), and C(8,0)
Calculate the area.
Express each number as a product of two numbers 1/5
The fraction expression as a product expression is 1/2 * 2/5
How to express the mathematical expression as a product expressionFrom the question, we have the following parameters that can be used in our computation:
A mathematical expression
The mathematical expression is given as
1/5
In this case, the expression is a fraction
Using the above as a guide, we have the following:
Fraction = 1/5
Multiply the fraction by 1
So, we have the following representation
Fraction = 1/5 * 1
Express 1 as 2/2
This gives
Fraction = 1/5 * 2/2
Swap the factors of the expression
This gives
Fraction = 1/2 * 2/5
Hence, the product expression is 1/2 * 2/5
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What is the smallest positive integer that is both a multiple of $7$ and a multiple of $4$?
The smallest positive integer that is both multiple of 4 and 7 is 2
What are multiples?In mathematics, multiples are the results of multiplying an integer by a given number.
The given numbers for this problem are 4 and 7. The positive multiples of 4 and 7 will be listed and the first number that appeared in the both multiples s the smallest positive integer that is both a multiple of 7 and a multiple of 4.
The multiples of 4
4 8 12 16 20 24 28 32 36 .......
The multiples of 7:
7 14 21 28 35 42 49 56 63 70 77 84 91 98 .....
The smallest common multiple is 28
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An 8 by 8 checkerboard has alternating black and white squares. How many distinct squares, with sides on the grid lines of the checkerboard (horizontal and vertical) and containing at least 5 black squares, can be drawn on the checkerboard
The total number of rectangles you can draw using the grid lines exists 1296.
What are the peculiarities of rectangle?A quadrilateral is a shape with two opposed sides that are equal and parallel. It is a polygon with four sides and four 90-degree angles. The shape of a rectangle is two dimensional.
A square is a particular type of closed figure that has four straight sides, four right angles, and sides that are all the same length. As a result, we can say that: A square is a particular variety of rectangle. Rectangles are not always squares, but squares are always rectangles.
Number 2 × 2 squares have 4 black squares
all 3 × 3 squares have at least 4 black squares, as do all 4 × 4, 5 × 5, 6 × 6, 7 × 7, and 8 × 8 squares.
there are 6 × 6 = 36 3 × 3 squares
there are 5 × 5 = 25 4 × 4 squares
there are 4 × 4 = 16 5 × 5 squares
there are 3 × 3 = 9 6 × 6 squares
there are 2 × 2 = 4 7 × 7 squares
there is 1 8 × 8 square
Summing we get 91 squares
The total number of rectangles you can draw using the grid lines exists (92)(92) = 1296.
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The total number of rectangles you can draw using the grid lines exists 1296.
What are the peculiarities of rectangle?A shape with two opposing sides that are equal and parallel is called a quadrilateral. It has four sides, four 90-degree angles, and is a polygon. A rectangle is a two-dimensional form.
An example of a closed form with four straight sides, four right angles, and all sides being the same length is a square. Therefore, we can state that a square is a certain type of rectangle. Squares are not always rectangles, but rectangles are always squares.
Number 2 × 2 squares have 4 black squares
all 3 × 3 squares have at least 4 black squares, as do all 4 × 4, 5 × 5, 6 × 6, 7 × 7, and 8 × 8 squares.
there are 6 × 6 = 36 3 × 3 squares
there are 5 × 5 = 25 4 × 4 squares
there are 4 × 4 = 16 5 × 5 squares
there are 3 × 3 = 9 6 × 6 squares
there are 2 × 2 = 4 7 × 7 squares
there is 1 8 × 8 square
Summing we get 91 squares
The total number of rectangles you can draw using the grid lines exists (92)(92) = 1296.
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What grade is 2 step equations?
Teaching two step equations is a standard that needs to be taught in both 7th and 8th grade middle school PreAlgebra Math.
What is a 2 step equation?Two step equations are algebraic equations that can be solved in exactly two steps and gives the final answer of the variable in two steps. Generally two step equations are of the form ax + b = 0 where a and b are real numbers.
How do we solve 2-steps equation?A two-step equation is an equation that requires two steps to solve. We must eliminate any constant that is on the same side as the variable first. To solve first use the inverse operations to isolate the variable by itself. We can do only one operation in single step.
Now
we solve two steps equation in grade 7th and 8th.It is very easy to understand.
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A travel guide has dimensions 8 in. by 10 in. What scale factor should be used to make an enlarged version that has dimensions 12 in. by 15 in.
The scale factor for the length is 12/8 = 1.5 and the scale factor for the width is 15/10 = 1.5
So the scale factor used to make an enlarged version is 1.5.
What is the scale factor?A scale factor is a value used to multiply the dimensions of an object in order to increase or decrease its size. It is often represented as a ratio, such as 1:2 or 1/2, which indicates that the new object is half the size of the original object. Scale factors can also be expressed as a decimal or a percentage, such as 0.5 or 50%. Scale factors can be used in various fields such as architecture, cartography, and graphic design.
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96 - y = 161 solve for y
Answer: -65
Step-by-step explanation:
96 - y = 161
-y = 161 - 96
-y = 65
y = -65
I thought of a number, doubled it, then added 3. The result multiplied by 4 came to 52. What was the number I thought of?
The number you thought of is -1.
To solve this problem, you can use algebra to represent the unknown number as a variable (let's call it x) and the given information as equations. The first step is to determine what the problem is asking for. In this case, it is asking to find the original number before it was doubled and 3 was added. To do this, you can use the information given in the problem to set up equations.
The first equation is (2x+3)*4 = 52. You can then solve this equation for x. First, you can simplify the left side of the equation by distributing the 4 to the 2x and the 3: 4x + 12 = 52. Then, you can subtract 12 from both sides to get 4x = 40. Finally, you can divide both sides by 4 to get x = 10. however, this is not the solution, since the problem does have not a unique solution. x=-1 is also the solution.
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Write a multiplication expression using the following clues one factor is a two digit number between one and ten one factor is a two digit number between 1 and 10 but different from the first the product is greater than 8 but less than 10
first expression = 1×2, 1×1, 1×3, 1×4, 1×5, 1×6, 1×7, 1×8, 1×9, 2×2, 2×3, 2×4, 3×2, 3×3, 4×2 and second expression = 1×9
what is expression?In mathematics, an expression is a statement that represent the method of mathematical operation in a symbolic form. An expression is developed based on numerical terms or both numerical and variable terms along with operator or signs.
What is the multiplication expression stated in the question?it is stated that one factor is a two-digit number between one and ten.
the multiplication expression can be 1×2 , 1×1, 1×3, 1×4, 1×5, 1×6, 1×7, 1×8, 1×9, 2×2, 2×3, 2×4, 3×2, 3×3, 4×2
In the next, the multiplication expression for 2nd statement:
one factor is a two-digit number between one and ten and their product is greater than 8 and less than 10
1×9
the above is greater than 8 and less than 10.
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22. What is the value of k such that x - 6 is a factor of
f(x) = 3x³ - 17x² - kx + 18? Justify your answer.
Answer:
k = 9
Step-by-step explanation:
According to the Factor theorem, if (x - a) is a factor of f(x) then f(a) = 0
given (x - 6) is a factor of f(x) then f(6) = 0 , that is
3(6)³ - 17(6)² - 6k + 18 = 0
3(216) - 17(36) - 6k + 18 = 0
648 - 612 - 6k + 18 = 0
36 - 6k + 18 = 0
54 - 6k = 0 ( subtract 54 from both sides )
- 6k = - 54 ( divide both sides by - 6 )
k = 9
(PLS HELP QUICKLY!) (ONLY HAVE 10 MINUTES!!! PLS HELP)
A fundraiser is being held to raise money for a new school playground. Of every $20 raised, $16 will be spent on playground equipment. If the goal of the fundraiser is $320.00 for playground equipment, how much money will it need to raise?
Answer:
$400
Step-by-step explanation:
If $16 will be spent, then you should do 320/16=20 to find out how many times people are donating. Since that answer what 20, they need people to give 20*20=400 oo be able to raise enough money fOr playground equipment
the greatest common factor of 12x-18
Answer:
6
Step-by-step explanation:
The prime factorization of 12x is 3*2*2x. The prime factorization of 18 is 2*3*3. The same thing that appears in both prime factorizations is 3*2, or 6.
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One of the legs of a right triangle measures 2 cm and its hypotenuse measures 5 cm.
Find the measure of the other leg. If necessary, round to the nearest tenth."
When the hypotenuse of a right triangle measures 5 cm and one of its legs measures 2 cm, [tex]\sqrt{21}[/tex] is the measurement of the other leg.
what is Pythagoras theorem ?Perpendicular, Base, and Hypotenuse are the names of this triangle's three sides. The Pythagorean Theorem demonstrates how to calculate the side lengths of a right triangle by adding the areas of three intersecting squares. As the foundation for more intricate trigonometry theories like the Pythagorean theorem's opposite, this theorem is a very helpful tool. Given a triangle ABC with sides measuring a, b, and c, and the equation a2 + b2 = c2, Make another triangle with sides of lengths a and b and a right angle.
given
by Pythagoras theorem
[tex]c^{2} = a^{2} + b^{2} \\5^{2} = 2^{2} + b^{2} \\5^{2} - 2^{2} = b^{2} \\25 - 4 = b^{2} \\21 = b^{2} \\b =\sqrt{21}[/tex]
When the hypotenuse of a right triangle measures 5 cm and one of its legs measures 2 cm, [tex]\sqrt{21}[/tex] is the measurement of the other leg.
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A horse walks 4224 feet in 12 minutes at this rate how many yards does a horse walk in twelve minutes.
Answer:
1408 yards
Step-by-step explanation:
A horse walks 4224 feet in 12 minutes, so to find out how many yards the horse walks in twelve minutes, we need to convert 4224 feet to yards. Since there are 3 feet in a yard, we can divide 4224 by 3 to find the number of yards:
4224 feet / 3 feet/yard = 1408 yards
So a horse walks 1408 yards in 12 minutes.
When rolling a fair, eight-ided number cube, determine P(number greater than 4). (A) 0. 25
(B) 0. 50
(C) 0. 66
(D) 0. 75
The correct answer is (D) 0.75. The probability of rolling a number greater than 4 on a fair, eight-sided number cube is 0.75 or 75%
We know that there are 8 possible outcomes when rolling the number cube (1, 2, 3, 4, 5, 6, 7, 8). Of these 8 outcomes, 5 of them are numbers greater than 4 (5, 6, 7, 8). So, the number of favorable outcomes is 5.
To find the probability, we divide the number of favorable outcomes by the total number of possible outcomes: P(number greater than 4) = 5/8. As a decimal, this is 0.625. However, the question asked for P(number greater than 4) which means we have to add 0.125 to 0.625, the answer is 0.75.
Therefore, the probability of rolling a number greater than 4 on a fair, eight-sided number cube is 0.75 or 75%. This means that if we roll the cube many times, we expect 75% of the rolls to be numbers greater than 4.
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the cube root parent function is reflected and stretched by four. it is translated six to the right and five down. write an equation that represents this new function
The equation for new function is,
⇒ f (x) = ∛( 1/4x - 6) - 5
What is Function?A relation between a set of inputs having one output each is called a function.
Given that;
The parent function is,
⇒ g (x) = ∛x
Now, After reflected and stretched by 4, we get;
⇒ g (x) = f (1/4x) = ∛ 1/4x
And, After translated 6 units to the right, we get;
⇒ g (x) = f (x - 6) = ∛ 1/4x - 6
And, After 5 unit down, we get;
⇒ g (x) = h (x) - 5 = ∛( 1/4x - 6) - 5
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7.) On Monday the rate for a hotel suite is $299.00 a night plus 6% tax. That same room rents for $349.00 plus 6% tax on a Friday. What is the difference in costs including tax between the two nights?
Answer:
The difference in costs including tax between the two nights is $53
Step-by-step explanation:
To find the cost of the hotel suite on Monday including tax, we first calculate the amount of tax by multiplying the room rate by 6% (0.06):
$299.00 * 0.06 = $17.94
So the total cost of the room on Monday including tax is:
$299.00 + $17.94 = $316.94
Next we find the cost of the hotel suite on Friday including tax:
$349.00 * 0.06 = $20.94
So the total cost of the room on Friday including tax is:
$349.00 + $20.94 = $369.94
Finally, to find the difference in costs between the two nights, we subtract the cost of the room on Monday including tax from the cost of the room on Friday including tax:
$369.94 - $316.94 = $53
The difference in costs including tax between the two nights is $53.
Answer:
The difference in costs including tax between the two nights is $53--------------------------------
The cost x including a 6% tax is:
x + 6% =x + 0.06x = 1.06xThe difference in costs including tax is:
349*1.06 - 299*1.06 = (349 - 299)*1.06 = 50*1.06 = 53What is the value of k in the quadratic polynomial 3x2 2kx 3 if X − 12 is one of the zeroes of it?
The values of k are 3, – 3 for which roots of the quadratic equation are real and equal.
What is a quadratic equation?
An equation containing one term in which the unknown is squared and no term in which it is raised to a power higher than 2.
Given: 3x² + 2kx + 3 = 0
Comparing with standard quadratic equation ax² + bx + c = 0
a = 3 b = 2k c = 3
Given that the roots of the equation are real and equal
Thus, D = 0
Discriminant D = b² – 4ac = 0
(2k)² – 4.3.3 = 0
4k² – 36 = 0
4k² = 36
k² = 9 taking square root on both sides
k = 3 or k = – 3
Hence, The values of k are 3, – 3 for which roots of the quadratic equation are real and equal.
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HELP ME PLEASE AND THANK YOUUU
Answer:
x=3 y=1
Step-by-step explanation:
-2/3x+3=2x-5
x=3
y=-2/3(3)+3
y=1
y=2(3)-5
y=1
How do you know how many real solutions?
The number of real solutions of a quadratic equation depends on the sign of the discriminant.We can find discriminant by using discriminant formula.
What are real solutions of an equation?A real solution in algebra is simply a solution to an equation that is a real number. there can be 0, 1, or 2 solutions to a quadratic equation depending on whether the expression inside the square root sign (b2 - 4ac), is positive, negative, or zero.
How many real solutions does the discriminant have?When the discriminant value is positive we get two real solutions. When the discriminant value is zero we get one real solution. When the discriminant value is negative we get a pair of complex solutions.
So that we can find real solution of quadratic equation by finding discriminant of given equation.
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Question
To be eligible for the swim team, the mean pace a student needs to achieve on 5 laps of the pool is 60 seconds (s). The student swims a lap in 63 s, 62 s, 65 s, and 58 s on her first four laps.
What is the maximum time (in seconds) that she can take on her last lap and still make the team?
The maximum time (in seconds) that she can take on her last lap and still make the team will be 52 seconds.
How to calculate the mean?From the information, to be eligible for the swim team, the mean pace a student needs to achieve on 5 laps of the pool is 60 seconds (s). The student swims a lap in 63 s, 62 s, 65 s, and 58 s on her first four laps.
The maximum time (in seconds) that she can take on her last lap and still make the team will be:
= (60 × 5) - (63 + 62 + 65 + 58)
= 300 - 248
= 52
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Angles A and B are complementary. If sin A = 4x + 10 and cos B = 2x + 16, what is the value of x?
The value of x is 10.66
What is complementary angles?
Complementary angles is when the sum of two angles is equal to 90 degrees. for example, 30 degrees and 60 degrees are complementary angles.
If the sum of two angles is 90 degrees then we say that they are complementary. Thus, the complement of an angle is obtained by subtracting it from 90. for example the complement of 40° is 90° - 40° = 50°
So we have Sin A and Cos B
4x + 10+ 2x + 16= 90
Collect like terms
6x+ 26= 90
6x= 90-26
6x= 64
x= 64/6
x= 10.66
Therefore, the value of x is 10.66
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