The given formula would be used to find the first quartile of a data set using the exclusive method.
What is quartile?
A quartile is a type of quantile used in statistics that divides the total number of data points into four roughly equal parts, or quarters. To compute quartiles, the data must be arranged from smallest to largest; therefore, quartiles are a type of order statistic.
The given formula is [tex]L_P = (n + 1)\frac{25}{100} \\[/tex]
This formula can also be written as,
[tex]R = (n + 1)\frac{25}{100}[/tex]
where 25 is the percentile of the data set.
So, the option (c) is correct.
The first quartile of a data set using the exclusive method.
Hence, the given formula would be used to find the first quartile of a data set using the exclusive method.
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write log7t as a base 2 logarithm. note: if you are using log you need to type it in and use the subscript button on the keyboard. there is no log button.
By using logarithm principles, log₇t in base 2 logarithm equals log₂t/log₂7.
What is logarithm?The most frequent logarithms are common logarithms with a base of 10, binary logarithms with a base of 2, and natural logarithms with a base of e 2.71828. A logarithm is the number of powers that a number must be raised to in order to acquire another number (see Section 3 of this Math Review for more about exponents). The base ten logarithm of 100, for example, is 2, because ten raised to the power of two equals 100: log 100 = 2.
Here,
logₓy=logₐy/logₐx
log₇t=log₂t/log₂7
log₇t in base 2 logarithm is log₂t/log₂7 by the help of properties of logarithm applied.
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From an angle of depression of 50 degrees, John watches his friend approach his building while standing on his rooftop. The rooftop is 16 m from the ground and John's eyelevel is about 1.8m above the rooftop. What is the distance between John's friend and the building?
The distance between John's friend and the building is 14.9 metres.
How to find the distance between the building and John's friend?From an angle of depression of 50 degrees, John watches his friend approach his building while standing on his rooftop. The rooftop is 16 m from the ground and John's eyelevel is about 1.8m above the rooftop.
Therefore, the distance of John's friend from the building can be calculated as follows:
This situation forms a right angle triangle.
Hence, using trigonometric ratios,
tan 50 = opposite / adjacent
tan 50 = 16 + 1.8 / x
tan 50° = 17.8 / x
cross multiply
x tan 50° = 17.8
x = 17.8 / tan 50
x = 17.8 / 1.19175359259
x = 14.9359734675
x = 14.9 metres
Therefore,
distance of John's friend to the building = 14.9m
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How do you solve 2/x = 7/9?
Answer:
2x=9+7
2x=16
x= 2/16
x=8
Step-by-step explanation:
For each graph below, state whether it represents function_ Graph Graph 2 Graph 3 Function? Yes No Graph 4 Yes No Graph 5 No Yes Graph Function? Yes Yes
Graphs 1,5 are functions while graphs 2,3,4,6 are not functions.
A graph represents a function if it has one and only one y value or no y value for each x. If the graph has multiple y values for any x, then it is not a graph of a function.
We can check if the following graphs are functions or not by using the vertical line test.
In the vertical line test, we draw a vertical line across the function and if that line touches two points on the graph means the graph is not a function as per the definition of the function.
Let us apply this to the following graphs -
1. Graph 1- If we draw a vertical line and drag it from left to right, we see that no two points line on the same line. So, graph 1 is a function.
2. Graph 2 - If we draw a vertical line and drag it from left to right, we see that the line crosse two points on each number. So, graph 2 is clearly not a function.
3. Graph 3 - Here too, if a vertical line is drawn and dragged from left to right, we cross two points on every number. So, graph 3 is also not a function.
4. Graph 4 - If we draw a vertical line and drag it from left to right, we see that at some places the line crosse two points on each number. So, graph 4 too, is not a function.
5. Graph 5 - If we draw a vertical line and drag it from left to right, we see that no two points line on the same line. So, graph 5 is a function.
6. Graph 6 - Here also, if a vertical line is drawn and dragged from left to right, we cross two points on point -1. So, graph 6 is also not a function.
Hence, we can conclude that - Graph 1,5 are functions while graphs 2,3,4,6 are not functions.
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The complete question is -
For each graph below, state whether it represents a function or not.
1. Graph 1
2. Graph 2
3. Graph 3
4. Graph 4
5. Graph 5
6. Graph 6
Samuel measured a house and it’s a lot and made a scale drawing the scale he used was 14 inches:5 feet in the drawling the porch is 56 inches wide what is width of the actual porch
the width of the actual porch will be 20 feet.
What is a rectangle?
Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A rectangle is a closed, four-sided figure in two dimensions. All of a rectangle's angles are equal to 90 degrees, and its opposite sides are equal and parallel to one another. See the shape, sides, and angles of the rectangle in the illustration below.
The scale of the Drawing was 14:5
If the width of the porch is 56 inches then what is the length of the porch
Since the scale of the drawing is 14:5 this implies that ratio of width of drawing and the original is 14:5.
Let x be the original width of porch and the width of the drawing is given as 56 inches, therefore by the given ratio we have
56:x=14:5
x = 56*5/14 = 20 feet
Hence the width of the actual porch will be 20 feet.
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the graphs of these two equations intersect in how many points? \begin{align*} x^2 y^2
The graphs of these two equations intersect in 4 points.
What is an example of a hyperbola?
A hyperbola is a collection of points in a plane whose separations from two fixed points, known as its foci (plural of focus), differ by an amount that is always the same.
Using the figure as an example, a hyperbola with foci at (-3,0) and The point at illustrates its constant distance as being 4. (-3,-2.5).
x²+y²=25
it is a circle with radius=5
x²-y²=3
it is a hyperbola.
x²-y²=3
so, they intersect in four points.
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The complete question is -
The graphs of these two equations intersect in how many points?
x^2+y^2=25
x^2-y^2=3
a simple random sample of 100 8th graders at a large suburban middle school indicated that 82% of them are involved with some type of after school activity. find the 95% confidence interval that estimates the proportion of them that are involved in an after school activity. a) [0.745, 0.895] b) [0.745, 0.695] c) [0.795, 0.800] d) [0.645, 0.845] e) [0.665, 0.895] f) none of the above
The 95% confidence interval that estimates proportion of 8th graders that are involved in an after school activity (0.745, 0.895) , the correct option is (a) .
In the question ,
it is given that ,
simple random sample of 100 8th graders is taken ,
that means ,
n = 100 ,
also given that , 82% of them are involved with some type of after school activity.
means ; p = 0.82 .
the level of significance (α) = 100 - 95 = 5% = 0.05 .
the critical value= [tex]Z_{\alpha /2}[/tex] = [tex]Z_{0.025}[/tex] = 1.959964 ......from the Z table .
the lower limit of the 99% confidence interval is = p - [tex]Z_{\alpha /2}[/tex]*SE
and the upper limit for the 99% confidence interval is= p + [tex]Z_{\alpha /2}[/tex]*SE .
the standard error is √(p(1-p)/n
= √(0.82(1 - 0.82)/100
= 0.0384
So , the lower limit is ⇒ 0.82 - 1.959964*0.0384
On simplification ,
we get ,
lower limit is = 0.7447006 ≈ 0.745 .
the upper limit is = p + [tex]Z_{\alpha /2}[/tex]*SE
= 0.82 + 1.959964*0.0384
On Simplification ,
we get ,
upper limit is = 0.8952994 ≈ 0.895 .
Therefore , the confidence interval is (0.745, 0.895) .
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Bill had 15 coins in his pocket, some quarters and the rest, dimes. If he had
$3.30 in his pocket, how many were quarters and how many were dimes?
Answer:
Step-by-step explanation:
So bill haves 12 quarters and 3 dimes
the function models the height of a ball dropped from 40 feet in the air. what was the speed of the ball when it was traveling the fastest (instantaneous rate of change)? round all answers to three decimal places.
Therefore ,the speed at height 40 feet in the air = 16*40=640 feet/sec
Function is what?A mathematical function from one set X to another gives each element of X exactly one element of the other. The sets X and Y, respectively, represent the function's domain and codomain.
Here,
the given function is
f(t)=−8[tex]t^{2}[/tex]+25
Therefore, the speed of the ball can be calculated by using derivative of f(t)
f(t)=−8[tex]t^{2}[/tex]+25
Differentiating f(t) w.r.t t
=> d(f(t)/dt=-8*2t
=> d(f(t)/dt=-16t
Therefore the speed at height 40 feet in the air = 16*40=640 feet/sec
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2x + 4
6x - 3y = -12
Is this no solution or infinite
there
Write an equivalent expression for 6a + a + 8b + b.
A
Answer:
7a + 9b
Step-by-step explanation:
"a" is basically a shorter way of writing "1a;" and this is the same way for any singular variable. Examples would variables like "a," "b," "c," and so on. So the real equation would be 6a + 1a + 8b + 1b. If 2 numbers have the same variable then you can add them together. You solve it like this:
6a + 1a = 7a
8b + 1b = 9b
The equivalent of 6a +a + 8b + b is 7a + 9b.
How do you simplify 3/4 + (1/4−16) ?
Answer:
To add fractions, find the LCD and then combine.
3/4 + (1/4−16)= −15
Step-by-step explanation:
Determine the measure of the indicated angle 53 106 127 307
Answer: 127
Step-by-step explanation: It must add up to 180 degrees
Interior consecutive = congruent
Corresponding = 180
A certain quadratic function has x-intercepts at 2 and 3. What is the x-coordinate of its vertex?
Answer: [tex]\frac{5}{2}[/tex]
Step-by-step explanation:
The vertex is halfway between the [tex]x[/tex]-intercepts.
So, the answer is [tex]\frac{2+3}{2}=\frac{5}{2}[/tex].
NEED IT BY TODAY!! PLEASE HELP!!
The tiles that Bruce used were each of a square foot in area. The table shows the area covered by Felicia’s tiles in terms of the number of tiles used.
Number of Tiles Area Covered (sq. ft.)
9 1
18 2
27 3
Bruce and Felicia want to know whose tiles cover the most area per tile.
Q1.) Write an equation representing the area Bruce covered, y, in terms of the number of tiles he used, x.
Q2.) Write an equation representing the area Felicia covered, y, in terms of the number of tiles she used, x.
Q3.) The person whose equation has the greater unit rate is the person whose tiles cover the most area per tile. Whose equation has the greater unit rate?
Q4.) What is the slope and the y-intercept for Bruce’s equation? What is the slope and y-intercept for Felicia’s equation?
Q5.) Which line is steeper, Bruce’s or Felicia’s? Whose slope is greater? Does this match the comparison from Part C?
Answer:
Step-by-step explanation:
Q1. Since each of Bruce's tiles is one square foot in area, his equation is y=x, where y=area and x=#of tiles. The area increases by one square foot for every tile added.
Q2. If it takes 9 of Felicia's tiles to equal 1 square foot, her equation is y=(1/9)x. We can check the table to see if this equation is right. If you put 18 into this equation, you get 2, for 27 you get 3, and so forth
Q3. Bruce has the greater unit rate of 1 and has the tiles that cover the greatest area, as opposed to Felicia, whose unit rate is only 1/9, since each of her tiles covers 1/9 of a square foot
Q4. The slopes are the same as the unit rates. Bruce's is 1, Felicia's is 1/9. Both of their y intercepts are 0, because if they put down 0 tiles, there will be no area covered because the problem does not state that there were tiles placed already before Bruce and Felicia started. You can also see this by graphing their equations
Q5. Bruce's line is steeper, with a slope of 1, versus Felicia's slope, which is 1/9. This matches the comparison from part c where we discovered that Bruce had the greater unit rate
Frames-for-All sells framed pictures to hotels and other corporations across the country. Last year, the company sold a total of 720,460 pictures. This year, they sold 972,621 picyures. What is the percent of increase in yearly sales?
The percent of increase in yearly sales is 35%.
What is a percentage increase?A percentage increase means the eventual increase in the quantity in percent form. The percentage increase formula is use to compare growth in a quantity from the initial value to its final value over a period of time.
The formula for getting a percentage increase is "[(Final Value - Initial Value)/Initial Value] × 100"
Initial value = 720,460 pictures
Final value = 972,621 pictures.
The percentage increase:
= [(972,621 - 720,460] / 720,460} * 100
= 0.35 * 100
= 35%
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Select all triangle congruence theorems that can be used to prove the two triangles congruent.
AAS
ASA
AAA
SSS
SSA
HL
SAS
Only three of them are correct
Answer:
SAS, ASA, and AAS
Step-by-step explanation:
SSA, AAA are NOT Theorems. SSS requires three sides and HL requires the triangles to be a right triangle (90 degrees).
Also, the two triangles forms Vertical angles.
Which of the following is not the test of congruence of two triangles ? ASA test ,
AAS test, SSA test , SAS test.
Answer:
Answer Option C: SSA test
Find the slope of the line through each pair of points.
1) (8, 12), (11,-17)
3) (-1, -8), (-20, 19)
5) (2,16), (8, 20)
7) (11,-6), (8,5)
2) (2.-11). (15, 11)
Date
4) (5, -18), (-15, -16)
6) (9, 10), (-12,-4)
8) (11, 8), (-6, 3)
The slope of the line that passes through each pair of points are:
1. -29/3
3. -27/19
5. 2/3
7. -11/3
2. 22/13
4. 1/5
6. 2/3
8. 5/17
How to Find the Slope of the Line?The slope of a line that joins two points can be found by using the formula below:
Slope (m) = change in y / change in x
1. Slope (m) of the line that goes through (8, 12) and (11, -17):
Slope (m) = (-17 - 12) / (11 - 8) = -29/3
3. Slope (m) of the line that goes through (-1, -8) and (-20, 19):
Slope (m) = (19 - (-8)) / (-20 - (-1)) = 27/-19
m = -27/19
5. Slope (m) of the line that goes through (2,16) and (8, 20):
Slope (m) = (20 - 16) / (8 - 2) = 4/6
m = 2/3
7. Slope (m) of the line that goes through (11,-6) and (8,5):
Slope (m) = (-6 - 5) / (11 - 8) = -11/3
2. Slope (m) of the line that goes through (2.-11) and (15, 11):
Slope (m) = (-11 - 11) / (2 - 15) = -22/-13
m = 22/13
4. Slope (m) of the line that goes through (5, -18) and (-15, -16):
Slope (m) = (-16 - (-18)) / (-15 - 5) = 2/10
m = 1/5
6. Slope (m) of the line that goes through (9, 10) and (-12,-4):
Slope (m) = (-4 - 10) / (-12 - 9) = -14/-21
m = 2/3
8. Slope (m) of the line that goes through (11, 8) and (-6, 3):
Slope (m) = (8 - 3) / (11 - (-6)) = 5/17
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please help memeemeemee
Answer:
6
Step-by-step explanation:
it is a8=a1 +(n-1)x d
41=-1+ 7xd
42/7=d
d=6
Answer: 6
Step-by-step explanation:
[tex]a_1=-1\ \ \ \ \ \ \ \ a_8=41\ \ \ \ \ \ \ \ d=?\\\\\boxed{a_n=a_1+d(n-1)}\\\\Hence,\\\\a_8=-1+d(8-1)\\\\41=-1+7d\\\\41+1=-1+7d+1\\\\42=7d\\\\[/tex]
Divide both parts of the equation by 7:
6=d
Thus, d=6
A cylinder fitted with a movable piston contains ideal gas at 27 degrees C, pressure 0.50*10^5 Pa, and volume 1.25 m. What will be the final temperature if the gas is compressed to 0.80 m^3 and the pressure rises to 0.82*10^5 Pa?
The final temperature is calculated to be 41.8 degrees Celcius if the gas is compressed to 0.80 m^3 and the pressure rises to 0.82*10^5 Pa
The final temperature can be calculated by using the combined gas law as follows;
[tex]\frac{P_{1}V_{1} }{T_{1} } = \frac{P_{2}V_{2} }{T_{2} }[/tex]
Here [tex]P_{1}[/tex] and [tex]P_{2}[/tex] represent the initial and final pressure respectively,
[tex]V_{1}[/tex] and [tex]V_{2}[/tex] represent the initial and final volume respectively
[tex]T_{1}[/tex] and [tex]T_{2}[/tex] represent the initial and final temperature respectively
Converting [tex]T_{1}[/tex] to kelvin as follows;
[tex]T_{1}[/tex] = 27 degrees Celcius = 27 + 273 = 300 K
Now the final temperature can be determined by substituting the values in this equation of the combined gas law as follows;
(0.50×10^5)(1.25) / 300 = (0.82×10^5)(0.80) / [tex]T_{2}[/tex]
208.333333333 = (0.82×10^5)(0.80) / [tex]T_{2}[/tex]
208.333333333 ([tex]T_{2}[/tex]) = (0.82×10^5)(0.80)
[tex]T_{2}[/tex] = (0.82×10^5)(0.80) ÷ 208.333333333
[tex]T_{2}[/tex] = 314.8 K
Converting K to degree Celcius as follows;
[tex]T_{2}[/tex] = 314.8 - 273 = 41.8 degree Celcius
Hence 41.8 degrees Celcius is calculated to be the final temperature.
Although a part of your question is incorrect, you might be referring to this question:
A cylinder fitted with a movable piston contains ideal gas at 27 degrees C, pressure 0.50*10^5 Pa, and volume 1.25 m^3. What will be the final temperature if the gas is compressed to 0.80 m^3 and the pressure rises to 0.82*10^5 Pa?
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What is the solution set of [xl x>-5}u [xl x<5}?
all numbers except-5 and 5
The numbers between-5 and 5
The empty set
All real numbers
The solution set express the numbers between -5 and 5.
What is set in mathematics?It is a mathematical model contains various elements such as numbers, variables, sign and so on arranged in a sequence order. Different set represents different expression.
what is solution set?The elements of a set that satisfy certain given conditions.
in the question, the set represent the numbers which are > -5 and < 5.
hence, the set indicate the numbers between -5 and 5
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Which of the following is the discriminant of the quadratic equation: ax- bx +c= 0, where a,b,c are real number and a 0? A. b2
B. Vb2 - 4ac
C. b2 - 4ac
D. -b + Vb2 - 4ac
The required discriminant of the quadratic equation ax-bx+c= 0 is D = b² - 4c.
What is discriminant?In mathematics, the discriminant of a polynomial is a quantity that depends on the coefficients and allows some root properties to be inferred without having to compute them.
It is essentially a polynomial function of the coefficients of the initial polynomial.
So, we have the quadratic equation:
ax- bx +c= 0
We know that the discriminant formula is as follows:
Discriminate = b² - 4c
Now, get the discriminant:
D = b² - 4c
Therefore, the required discriminant of the quadratic equation ax-bx+c= 0 is D = b² - 4c.
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if f(x) = , what is f(7.6)? 3 3.5 3.8 4
The solution of the given greatest integer function is found as 3.5.
Explain the term greatest integer function?The largest integer function is one that yields an integer that is closest to the specified real value. Additionally known as the step function. The closest integer is used to round off the input using the biggest integer function.We have to compute;
f(x) = 1/2[x]
Given what we have; f(7.6).
Enter x = 7.6 in the function provided;
f(7.6) = 1/2[7.6]
As ,the value (7.6) --> 7.0 (greatest integer function)
f(7.6) = 7/2
f(7.6) = 7/2
f(7.6) = 3.5
Thus, the solution of the given greatest integer function is found as 3.5.
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The correct question is-
If f(x) = 1/2[x], what is f(7.6)?
3
3.5
3.8
4
a pharmaceutical company receives large shipments of ibuprofen tablets and uses an acceptance sampling plan. this plan randomly selects and tests 31 tablets, then accepts the whole batch if there is at most one that doesn't meet the required specifications. what is the probability that this whole shipment will be accepted if a particular shipment of thousands of ibuprofen tablets actually has a 8% rate of defects?
The probability that the shipment is accepted is 0.278685
The following problem is a problem of the binomial distribution. Here,
n = 31
p = probability of pills being a defect = 0.08
We need to find the probability that the batch is affected.
This means we need to find
P(X≤1)
PMF of Binomial is given by
P(X = x) = ⁿCₓ pˣ (1-p)ⁿ⁻ˣ
= P(X = 0) + P(X = 1)
= ³¹C₀ 0.08⁰ 0.92³¹ + ³¹C₁ 0.08 X 0.92³⁰
= 0.92³⁰(0.92 + 31X0.08)
= 0.92³⁰ X 3.4
=0.278685
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3√-120
….
Help me!Exam tomorrow!
Answer:
6[tex]\sqrt{30}[/tex]i
Step-by-step explanation:
120 = 2x2x2x3x5 I can pull out a set of 's
3x2 = 6
6[tex]\sqrt{2x3x5}[/tex]
6[tex]\sqrt{30}[/tex]
[tex]\sqrt{-1}[/tex] = i
Please solve for X AND USE THE PROBLEM ANSWER BOTH QUESTIONS
Answer:
x= -2
y= 0
Step-by-step explanation:
isolate y in second equation
-3x=6-y
+y. +y
-3x+y=6
+3x. +3x
y=3x+6
now we know y is the same as 3x+6 we can put it into the first equation where y is
-4x+2(3x+6)=8
-4x+6x+12=8
2x+12=8
-12. -12
2x= -4
/2. /2
x= -2
now fill in x to find y
-3(-2)=6-y
6=6-y
-6. -6
0= -y
/-1. /-1
0 =y
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Twenty-Five Decreased By One Fifth Of A Number Is Eighteen. Find The Number.
The equation of the given condition is written as 25 - (1/5)x = 18. And the solution of the equation will be 35.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The act of converting a specified statement into an expression or equation is known as a sentence-to-equation transformation.
Twenty-Five Decreased By One-Fifth Of A Number Is Eighteen.
Let the number be 'x'. Then the equation is given as,
25 - (1/5)x = 18
Simplify the equation, then the value of the variable 'x' is calculated as,
25 - (1/5)x = 18
(1/5)x = 25 - 18
(1/5)x = 7
x = 7 (5)
x = 35
The equation of the given condition is written as 25 - (1/5)x = 18. And the solution of the equation will be 35.
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find the relative maxima and relative minima, if any, of the function. (if an answer does not exist, enter dne.) g(x)
The relative maxima and minima of the function g(x) are at the point (-4, 22) at the local maxima and at point (4,-124) at the local minima.
Given:
Function g(x) = x^3 - 48x + 4
Take the derivative and set it equal to zero
3x^2 - 48 = 0
x^2 = 48/3 = 16
x = sqr16 = ±4
At x=+4, y = (4)^3 -48(4) + 4 = 64 -192+4 = -124
Point (4,-124) is a local or relative minimum
At x-4 y=(-4)^3 -48(-4)+4 = -64 + 192 + 4 = 122
The point (-4, 22) is a local or relative maximum
Refer to this complete question:
Find the relative maxima and minima, if any, of the function. (If an answer does not exist, enter DNE.) f(x) = x3 − 48x + 4 relative maximum (x, y) = relative minimum (x, y) =?
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A small business earns a profit of $6500 in January and $17,500 in May. What is the rate of change in profit for this time period. Explain how you got it.
The rate of change in the profit for the five months earned by the given small business is $2750.
How to calculate the rate of change?The rate of change explains the relationship between two quantities.
Consider two quantities such profit and time in a small business.
Then, the rate of change in the profit is calculated by the ratio of change in the profit for the particular period to the time. I.e.,
rate of change in the profit = (change in the profit)/time
or
r = (p2 - p1)/(t2 - t1)
Where p1 is the profit gained at time t1 and p2 is the profit gained at time t2.
Calculation:Given that, a small business earns a profit of $6500 in January (the first month of the year) and $17,500 in May (the fifth month of the year).
So, here p1 = $6500; p2 = $17,500; t1 = 1; and t2 = 5
Then, the rate of change in the profit for this period is
r = (17,500 - 6500)/(5 - 1)
= 11000/4
= 2750
Therefore, the rate of change in the profit for the five months is $2750.
Learn more about the rate of change at the following link:
https://brainly.com/question/24313700
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