The interquartile range of the data will be 0.215.
How to calculate the valueThe lower half is:
7.86, 7.87, 7.99, 8.03
The median of the lower half is:
(Q1) = (7.87 + 7.99) / 2 = 7.93
The upper half is:
8.06, 8.08, 8.09, 8.20, 8.43
The median of the upper half is:
(Q3) = (8.09 + 8.20) / 2 = 8.145
The IQR is the difference between the third and first quartiles:
IQR = Q3 - Q1 = 8.145 - 7.93 = 0.215
Lower outlier threshold: Q1 - 1.5 x IQR = 7.93 - 1.5 x 0.215 = 7.5955
Upper outlier threshold: Q3 + 1.5 x IQR = 8.145 + 1.5 x 0.215 = 8.4795
None of the data points fall outside these thresholds, so there are no outliers in this data set.
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what would the speed be if the tailwind of an airplane is 150 mph and the headwind remains at 100 mph
Answer:
To calculate the speed of the airplane, we need to subtract the speed of the headwind from the speed of the tailwind.
To calculate the speed of the airplane, we need to subtract the speed of the headwind from the speed of the tailwind. Speed of airplane = (Speed of tailwind) - (Speed of headwind)
To calculate the speed of the airplane, we need to subtract the speed of the headwind from the speed of the tailwind. Speed of airplane = (Speed of tailwind) - (Speed of headwind)Speed of airplane = (150 mph) - (100 mph)
To calculate the speed of the airplane, we need to subtract the speed of the headwind from the speed of the tailwind. Speed of airplane = (Speed of tailwind) - (Speed of headwind)Speed of airplane = (150 mph) - (100 mph)Speed of airplane = 50 mph
To calculate the speed of the airplane, we need to subtract the speed of the headwind from the speed of the tailwind. Speed of airplane = (Speed of tailwind) - (Speed of headwind)Speed of airplane = (150 mph) - (100 mph)Speed of airplane = 50 mphTherefore, the speed of the airplane would be 50 mph.
Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options. 2.3p – 10.1 = 6.4p – 4 2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2.3p – 14.1 = 6.4p – 4
The two equations that have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p include the following:
B. 2.3p – 10.1 = 6.49p – 4
C. 230p – 1010 = 650p – 400 – p
How to determine the required equations?From the information provided, we have the following equation:
2.3p – 10.1 = 6.5p – 4 – 0.01p
Next, we would simplify the given equation by collecting like terms as follows;
2.3p - 10.1 = 6.5p - 0.01p - 4 = 6.49p - 4
2.3p - 10.1 = 6.49p - 4
What is the multiplication property of equality?In Mathematics, the multiplication property of equality states that both sides of an equation will remain the same and equal, when both sides of the equations are multiplied by the same number.
By multiplying both sides of the given equation by 100, we have the following;
100 × (2.3p - 10.1) = 100 × (6.5p - 4 - 0.01p)
230p - 1010 = 650p - 400 - p
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write an equation of the line that passes through each pair of points (-8,0), (0,7)
please help, due in an hour !!
Answer:
Step-by-step explanation:
pls help very much appreciate it
if an avocado is 1$ per pound how many is it for 9 pounds?
If an avocado costs $1 per pound, the cost of 9 pounds, using multiplication, is $9.
What is multiplication?Multiplication is one of the four basic mathematical operations, including addition, subtraction, and division.
Multiplication involves the multiplicand, the multiplier, and the product.
The cost per pound of an avocado = $1
The total quantity considered = 9 pounds
Proportionately, the total cost of 9 pounds = $9 ($1 x 9)
Thus, based on multiplication operation, the total cost of 9 pounds is $9.00.
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8. A car wheel with a diameter of 18 inches spins at the rate of 10 revolutions per second. (i) What is the car's angular speed in radians per hour? (ii) What is the car’s linear speed in miles per hour?
Answer:
the car's angular speed is 72,000π radians per hour.
the car's linear speed is approximately 100.53 miles per hour.
Step-by-step explanation:
To find the car's angular speed in radians per hour, we can start by finding the angular speed in radians per second.
The formula for angular speed is:
ω = 2πf
where ω is the angular speed in radians per second, and f is the frequency or rate of rotation in revolutions per second.
In this case, the wheel is spinning at a rate of 10 revolutions per second, so:
ω = 2π(10) = 20π radians per second
To convert this to radians per hour, we can multiply by the number of seconds per hour:
20π radians per second × 3600 seconds per hour = 72,000π radians per hour
To find the car's linear speed in miles per hour, we can use the formula:
v = rω
where v is the linear speed, r is the radius of the wheel, and ω is the angular speed in radians per second.
The radius of the wheel is half the diameter, or 9 inches. To convert this to miles, we can divide by 12 and then by 5280:
9 inches ÷ 12 inches per foot ÷ 5280 feet per mile = 0.000142045 miles
Now we can substitute the values we have found:
v = (0.000142045 miles) × (18/2 inches) × (20π radians per second)
v ≈ 100.53 miles per hour
Answer:
(i) 10 revolutions = 10(2π) = 20π radians
10 revolutions/sec =
(20π radians/sec)(3,600 sec/hr) =
72,000π radians/hr
(ii) C = 18π inches
10 revolutions × 18π inches =
180π inches
(180π in./sec)(3,600 sec/hr) =
(648,000π in./hr)(1 mi./63,360 in.)
= 225π/22 miles/hour
= about 32.13 miles/hour
You spin the spinner once. 234 What is P(not greater than 2)? Write your answer as a fraction or whole number.
What is equivalent to x^2-5x+6
Answer:
[tex]=\left(x-2\right)\left(x-3\right)\\[/tex]
Step-by-step explanation:
Given:
[tex]x^2-5x\:+6[/tex]
To find:
Equivalent to x^2-5x+6
Explanation:
[tex]x^2-5x+6\\=\left(x^2-2x\right)+\left(-3x+6\right)\\=x\left(x-2\right)-3\left(x-2\right)\\\mathrm{Factor\:out\:common\:term\:}x-2\\=\left(x-2\right)\left(x-3\right)[/tex]
Final Answer:
(x-2)(x-3)
Match each drawing on the left with its word description on the right , some of the answer choices on the right may not be used. Line segment AB , Line AB , Point AB , Ray AB , Ray BA
1) Line AB
2) Ray AB
3) Line segment AB
4)Ray BA
The first drawing is a line AB because a line passing through two different points A and B
The second drawing is ray AB because it started at A
The third drawing is a line segment AB because it is part of a straight line that is bounded by two distinct end points, and contains every point on the line that is between its endpoints
The fourth drawing is ray BA
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SOMEONE, PLEASE HELP! ASAP, WILL GIVE 30 POINTS!
Using the equations given, only equation 2 has a proportional relationship.
What is a proportional and non-proportional relationship?Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other.
The difference between proportional and non-proportional linear relationships is that, although both have constant rates of change the proportional relationship has constant output to input ratios, and the non-proportional relationship does not.
In this problem, to determine the proportional relationship, we can also check for both values of x and y.
1. y = -0.75x + 5
When x = 1
y = -0.75(1) + 5
y = 4.25
when x = 2
y = -0.75(2) + 5
y = 3.5
The relationship is not proportional since as one variable increase, the other decreases.
2. y = 4x - 1
When x = 1
y = 4(1) - 1
y = 4 - 1
y = 3
when x = 2
y = 4(2) - 1
y = 8 - 1
y = 7
This relationship is proportional since the variables increases or decreases with one another.
3. y = (3/4)x
When x = 1
y = (3/4)(1)
y = 3/4
when x = 2
y = (3/4)(2)
y = 2/3
This relationship is not proportional
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ASAP
A rectangular prism is shown in the image.
A rectangular prism with dimensions of 3 yards by 5 yards by 5 and one half yard.
What is the volume of the prism?
forty one and one fourth yd3
fifty six and one fourth yd3
eighty two and one half yd3
165 yd3
As a result, the prism's volume is given by V = lwh = 3 x 5 x 5.5 = 82.5 cubic yards. Thus, option C—eighty two and a half yards—is the correct response.
what is volume ?The quantity of room an object takes up in three dimensions is measured by its volume. It is frequently expressed in cubic units like cubic metres, cubic feet, and cubic centimetres. Mathematics formulas that are particular to the shape of the object can be used to calculate its volume, such as V = l w h for a rectangular shape or V = (4/3)r3 for a sphere.
given
V = lwh is the formula for calculating the volume of a rectangular prism, where l, w, and h stand for the prism's length, width, and height, respectively.
Here, the dimensions are 3 yards in length, 5 yards in breadth, and 5.5 yards in height.
As a result, the prism's volume is given by V = lwh = 3 x 5 x 5.5 = 82.5 cubic yards.
Thus, option C—eighty two and a half yards—is the correct response.
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Which expression is equivalent to 5^3 × 10^-2?
Answer:
[tex]5 {}^{3} \times 10 {}^{ - 2} \\ = 5 {}^{3} \times \frac{1}{10 {}^{2} } \\ = 5 {}^{3} \times \frac{1}{2 {}^{2} 5 {}^{2} } \\ = 5 \times \frac{1}{4 \\ } \\ = \frac{5}{4} [/tex]
hope it helps
College Level Trigonometry Question!
An equation that models the trigonometric graph is:
y = 4 sin 4x
How to interpret the trigonometric graph?The general form for an equation that models a wave is this:
±a (sin/cos) (2π(x - p)/T)
where:
a is the amplitude
p is the phase shift
T is the period.
The ±ve will turn into +ve if the graph tends to start from the positive direction, and then turns -ve if it the graph tends to start from the negative direction.
The (sin/cos) will definitely become sine if the graph starts at 0 before it is being shifted. Then, it becomes cosine if the graph begins at the amplitude.
In this problem, we see that the graph begins as positive, and then at the amplitude with no phase shift, we see that the ±ve becomes +ve, (sin/cos) becomes sin, and p becomes zero. Plugging in the given values in the problem, we see that a = 4 and T = π/2.
We see that this equation becomes:
y = 4sin(2πx/(π/2)).
y = 4 sin 4x
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What is the surface area of this composite solid?
The surface area of the given composite solid is calculated as: 200.24 square units.
How to Find the Surface Area of the Composite Solid?Surface area of the composite solid = surface area of rectangular prism + surface area of cylinder - 2(area of the base of the cylinder)
Surface area of rectangular prism = length * width * height = 10 * 3 * 5
= 150 square units.
Surface area of cylinder = 2πr(h + r)
height (h) = 4
Radius (r) = 2
Plug in the values:
Surface area of cylinder = 2 * 3.14 * 2(4 + 2) = 75.36 square units
Area of the base of the cylinder = πr² = 3.14 * 2²
= 12.56 square units
Thus, we have:
Surface area of the composite solid = 150 + 75.36 - 2(12.56) = 200.24 square units.
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Please help with these two equations and show work as well, thank you!
13.) The simplified polynomials that can represent the area and perimeter of the large rectangle =40x + 5x² and
12X + 16 respectively.
14.)The simplified polynomials that can represent the area and perimeter of the large rectangle =21+10x + x² and 20+4x respectively.
How to determine the simplified polynomials that can be used to represent the given shape?To determine the simplified polynomials, the formula for the area and perimeter of the rectangule should be used. That is:
Area of rectangle = length×width
where;
length = 5x
width = 8+X
Area = 5x * 8+X
= 40x + 5x²
Perimeter of rectangle = 2(length+width)
= 2(5x + 8+X)
= 10x + 16 + 2x
= 12X + 16
For question 14.)
Area of rectangle = length× width
where;
length = 7+X
width = 3+X
Area = 7+X × 3+X
= 21+7x+3x +x²
= 21+10x + x²
Perimeter = 2(length+width)
= 2(7+X+3 + X)
= 2(10+2x)
= 20+4x
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Find the probability that
event A or B takes place.
Probability that event A or B takes place is, P(A or B) = 16/21.
Here from the Venn diagram we can obtain that,
Probability of occurring event A = 2/21 + 4/21 = (2 + 4)/21 = 6/21
Probability of occurring event B = 10/21 + 4/21 = (10 + 4)/21 = 14/21
Probability of occurring event A and event B both = 4/21
So, P(A) = 6/21
P(B) = 14/21
P(A and B) = 4/21
We know that the union of events formula,
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = 6/21 + 14/21 - 4/21
P(A or B) = (6 + 14 - 4)/21
P(A or B) = 16/21
Hence the value of P(A or B) = 16/21.
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What is the equation of a parabola with a vertical axis, vertex (h, k), and directrix y = k – p, where p is a nonzero real number? How can the equation be simplified if the vertex is at the origin?
Note that equation of a parabola with a vertical axis, vertex (h, k), and directrix y = k – p, where p is a nonzero real number is (y-k)² = 4p(x-h).
How can the equation be simplified if the vertex is at the origin?The equation of a parabola with a vertical axis, vertex (h, k), and directrix y = k – p, where p is a nonzero real number, is:
(y - k)² = 4p( x - h)
If the vertex is at the origin (h = 0, k = 0 ), the equation an be simplified to....
y² = 4px
where p is still a nonzero real number.
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An oil candle globe made of hand-blown glass has a diameter of 25.8 cm. What is the volume of the globe? Use 3.14 for .
globe meaning a sphere, and since it has a diameter of 25.8, that means its radius is half that, or 12.9
[tex]\textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=12.9 \end{cases}\implies V=\cfrac{4\pi (12.9)^3}{3}\implies \stackrel{ using~\pi =3.14 }{V\approx 8987.47}[/tex]
Mrs. Garza is buying boxes of crayons for her classroom. The table below shows the
number of crayons she can buy.
Which equation will help Mrs. Garza determine the number of crayons she will get with 7 boxes?
A N=16+B
B. N-=16-B
C. N=16B
D. N=16/B
On Low Budget Airlines, the maximum weight of the luggage a passenger can bring without charge is 50 pounds. Mary Ellen has decided to weigh each item as she packs her bag. Use rounding to the nearest one pound to estimate the weight of her luggage.
The estimated weight is pounds.
Answer: 50 pounds
Step-by-step explanation:
The maximum weight of the luggage a passenger can bring without charge is 50 pounds.
Mary Ellen has decided to weigh each item as she packs her bag.
weight of Suitcase = 3.65 lbs
weight of clothing = 4.35 lbs
weight of shoes = 8.67 lbs
weight of toiletries = 11.35 lbs
weight of extras = 21.63 lbs
Now we will add the weights of each items
Total weight = 3.65 + 4.35 + 8.67 + 11.35 + 21.63 = 49.65
Rounding to the nearest to the one pound will be = 50 lbs
(Since 0.65 is greater than 0.5 so by rounding off 0.65 will become 1.)
Therefore the estimated weight is 50 pounds.
Mannys pay varies directly with the number of lawns he mows. He earns $100 for mowing 4 lawns. Find k in the equation for Mannys pay. Use P=kl
Answer:
10000
otra solución es: 10⁴
The sum of matrix A and B where B is the identity matrix with respect to addition will give the matrix.
Select one:
Matrix A
Matrix 0
Matrix B
Matrix AB
The sum of any matrix with the identity matrix of the same size, with respect to addition, will give the matrix itself. Therefore, the sum of matrix A and B, where B is the identity matrix, will give the matrix A.
So the answer is: Matrix A.Please help Thanks
there is a FRACTION symbol two variable symbols y and x
Step-by-step explanation:
The equation of the line (by inspection) is y = 1/2 x
solve the equation 3x+4/3 - 2x/x-3 =x
x = -6.
Step-by-step explanation:1. Write the equation.[tex]\sf \dfrac{3x+4}{3} -\dfrac{2x}{x-3} =x[/tex]
2. Multiply by "3" on both sides ob the equation.Applying the distributive property of multiplication on the left hand side:
[tex]\sf (3)(\dfrac{3x+4}{3} -\dfrac{2x}{x-3}) =x(3)\\ \\ \\{3x+4} -\dfrac{(3)2x}{x-3}=3x\\ \\ \\{3x+4} -\dfrac{6x}{x-3}=3x[/tex]
3. Multiply by "x-3" on both sides ob the equation.Applying the distributive property of multiplication:
[tex]\sf (x-3)({3x+4} -\dfrac{6x}{x-3})=3x(x-3)\\ \\ \\(x-3)({3x+4}) -6x=3x(x-3)\\ \\ \\(x)(3x)+(x)(4)+(-3)(3x)+(-3)(4) -[6x]=3x(x-3)\\ \\ \\[/tex]
Check the image below to see an illustration of this process.
[tex]\sf 3x^{2} +4x-9x-12 -[6x]=3x(x-3)\\ \\ \\3x^{2} +4x-9x-12 -6x=3x(x-3)\\ \\ \\3x^{2} -11x-12 =3x(x-3)[/tex]
Now simplifying on the right hand side (applying the same logic as last step).
[tex]\sf 3x^{2} -11x-12 =3x(x-3)\\ \\ \\3x^{2} -11x-12 =(3x)(x)+(3x)(-3)\\ \\ \\3x^{2} -11x-12 =3x^{2}-9x[/tex]
4. Add "9x" on both sides of the equation.[tex]\sf 3x^{2} -11x-12+9x =3x^{2}-9x+9x\\ \\ \\3x^{2} -2x-12 =3x^{2}[/tex]
5. Subtract "3x²" from both sides.[tex]\sf 3x^{2} -2x-12-3x^{2} =3x^{2}-3x^{2}\\ \\ \\-2x-12 =0[/tex]
6. Add "12" on both sides.[tex]\sf -2x-12+12=0+12\\ \\ \\-2x=12[/tex]
7. Divide by "-2" ob both sides.[tex]\sf \dfrac{-2x}{-2} =\dfrac{12}{-2} \\ \\ \\x =-6[/tex]
8. Verify the answer.If "x= -6" is the correct answer, substituting "x" by "-6" on the original equation should return the same value on both sides of the equal (=) symbol. Let's test!
[tex]\sf \dfrac{3(-6)+4}{3} -\dfrac{2(-6)}{(-6)-3} =(-6)\\ \\-6=-6[/tex]
That's correct!
x = -6 is the corect answer.
Help with math problems
Answer:
Step-by-step explanation:
15.) [tex]\sqrt{12}[/tex]
[tex]\sqrt{4}[/tex] * [tex]\sqrt{3}[/tex]
Answer: 2[tex]\sqrt{3}[/tex]
17.) Distribute 3[tex]\sqrt{3}[/tex] into both sides of the parentheses
3[tex]\sqrt{3}[/tex] * 4 = 12[tex]\sqrt{3}[/tex]
3[tex]\sqrt{3}[/tex] * -3[tex]\sqrt{5}[/tex] = -9[tex]\sqrt{15}[/tex]
Answer: 12[tex]\sqrt{3}[/tex] - 9[tex]\sqrt{15}[/tex]
19.) Distribute 4[tex]\sqrt{15}[/tex] into both sides of the parentheses
4[tex]\sqrt{90}[/tex] + 4[tex]\sqrt{75}[/tex]
4*[tex]\sqrt{9}[/tex]*[tex]\sqrt{10}[/tex] + 4*[tex]\sqrt{25}[/tex]*[tex]\sqrt{3}[/tex]
4*3*[tex]\sqrt{10}[/tex] + 4*5*[tex]\sqrt{3}[/tex]
12[tex]\sqrt{10}[/tex] + 20[tex]\sqrt{3}[/tex]
21.) Distribute [tex]\sqrt{15}[/tex] into both sides of the parentheses
2[tex]\sqrt{150}[/tex] - 4[tex]\sqrt{90}[/tex]
2*[tex]\sqrt{25}[/tex]*[tex]\sqrt{6}[/tex] - 4*[tex]\sqrt{9}[/tex]*[tex]\sqrt{10}[/tex]
2*5*[tex]\sqrt{6}[/tex] - 4*3*[tex]\sqrt{10}[/tex]
10[tex]\sqrt{6}[/tex] - 12[tex]\sqrt{10}[/tex]
Please help me who knows how to do this
What is the answer to (x^2)+(2x)-(5)=0
The solution to the given quadratic equation is [tex]=-1\pm \sqrt{6}[/tex]
What is a quadratic equation?A quadratic equation is an equation whose highest power is raised to the power of 2. Mathematically it is written in the form ax² + bx + c. There are many ways in which we can solve a quadratic equation such as:
FactoringQuadratic formulaCompleting the square methodFrom the given information, we have:
x² + 2x - 5 = 0
Using the quadratic formula method;
[tex]=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
here;
a = 1b = 2c = -5[tex]=\dfrac{-2\pm \sqrt{2^2-4(1)(-5)}}{2(1)}[/tex]
[tex]=\dfrac{-2\pm \sqrt{4+20}}{2}[/tex]
[tex]=\dfrac{-2\pm \sqrt{24}}{2}[/tex]
[tex]=\dfrac{-2\pm 2\sqrt{6}}{2}[/tex]
[tex]=-1\pm \sqrt{6}[/tex]
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Polynomial Functions
a) Yes, the function is in standard form.
Degree = 2
Exponent = 2
Constant term = -1
b) No, the function is not in standard form.
And it doesn't have the degree, exponent and constant term.
Firstly, let's consider the function f(x) = x(x-1). To determine if it is a polynomial function, we need to check if all of its terms have non-negative integer exponents. In this case, we see that f(x) can be written as x² - x, which has only two terms, and each term has a non-negative integer exponent. Therefore, f(x) is a polynomial function.
In this case, the degree of f(x) is 2 because the highest exponent of x is 2.
In this case, the leading term of f(x) is x², and its leading coefficient is 1.
Finally, the constant term is the term that does not have the variable in it. Here, the constant term of f(x) is -1.
Next, let's consider the function f(x) = 3 - 1/2 x. We can see that f(x) is not a polynomial function because it has a term with a negative exponent.
Polynomial functions must have non-negative integer exponents on all terms.
Therefore, the answer to the first question is 'no.'
Since f(x) is not a polynomial function, it does not have a degree, leading term, or constant term.
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solve for x, neg x over 4 = 12 A 48 or B -3 or C 3 or D -48?
The solution for x is -48, the answer is D) -48.
What is Algebraic expression ?
An algebraic expression is a mathematical phrase that contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. It represents a value that can change based on the values assigned to the variables.
Starting with:
x:4 = 12
Multiplying both sides by -1 gives:
(-x÷4) = -12
Simplifying the left side:
x÷4 = -12
Multiplying both sides by 4 gives:
x = -48
Therefore, the solution for x is -48, the answer is D) -48.
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