Answers
The result obtained are-
smallest value = 4.largest value = 48.median = 24first quartile {Q1} = 12third quartile {Q3} = 36What is defined as the frequency table?A frequency table is merely a "t-chart" or two-column table that illustrates the numerous possible outcomes and associated frequencies demonstrated in a sample.
Part 1: Smallest value;
As the frequency table is continuous distribution with a initial value of 4.
Thus, the smallest value of the table is 4.
Part 2: largest value;
As the frequency table is continuous distribution with a final value of 48.
Thus, the largest value of the table is 48.
Part 3: Median
The median is the number in the middle of a sorted list of numbers, and it is more descriptive of the data set than that of the average.
For even number of frequencies.
median = n/2
median = 12/2 = 6
Thus, the 6th term is the median.
median = 24.
Part 4: first quartile {Q1}
When data points are organized in increasing order, the lower quartile, or the first quartile (Q1), is indeed the value at which 25% of them are found.
Thus, Q1 = 12.
Part 3: third quartile {Q3}
When arranged in increasing order, the upper quartile, as well as third quartile (Q3), has been the value at which 75% of data points are found.
Q3 = 36.
The result for the frequency distribution is obtained.
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Related Questions
y is inversely proportional to the square of x find an equation for y in terms of x
Answers
hmmm from the table, let's just pick one point since we know "y" is inversely proportional, so hmmm let's say hmm the point when x = 4 and y = 9/16
a)
[tex]\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{"y" inversely proportional to }x^2}{ {\LARGE \begin{array}{llll} y = \cfrac{k}{x^2} \end{array}}}\qquad \textit{we also know that} \begin{cases} x=4\\ y=\frac{9}{16} \end{cases} \\\\\\ \cfrac{9}{16}=\cfrac{k}{(4)^2}\implies \cfrac{9}{16}=\cfrac{k}{(16)}\implies \cfrac{9(16)}{16}=k\implies 9=k~\hfill \boxed{y=\cfrac{9}{x^2}}[/tex]
b)
when y = 16, what's "x"?
[tex]16=\cfrac{9}{x^2}\implies x^2=\cfrac{9}{16}\implies x=\pm\sqrt{\cfrac{9}{16}}\implies x=\pm \cfrac{\sqrt{9}}{\sqrt{16}}\implies \stackrel{positive~value}{x=+\cfrac{3}{4}}[/tex]
RSV has coordinates R(2,1), S(3,2), V(2,6). A translation maps point R to R' at
(-4,8). What are the coordinates for S' and V' for this translation?
Answers
Answer:
S' (- 3, 9 ) , V' (- 4, 3 )
Step-by-step explanation:
consider the coordinates of R and R'
R (2, 1 ) , R' (- 4, 8 )
2 → - 4 in the x- direction is - 6
1 → 8 in the y- direction is + 7
then the translation rule is
(x, y ) → (x - 6, y + 7 )
S (3, 2 ) → S' (3 - 6, 2 + 7 ) → S' (- 3, 9 )
V )2, 6 ) → V' (2 - 6, 6 + 7 ) → V' (- 4, 13 )
g(n)=n+3
f(n)=-n-5
Find g(3)-f(3)
Answers
Answer:
14
Step-by-step explanation:
g(3)=(3)+3
g(3)=6
f(3)=-(3)-5
f(3)=-8
6-(-8)=14
Simplify the functions, and use the distributive property.
g(3)=6 - f(3)=3+5
Continue to simplify:
g(3)=6 - f(3)=8
g(3)-f(3)=6-8
g(3)-f(3)=-2
darcy has a summer job painting houses. he is asked to paint the wooden siding on a house that is 28 feet wide and 35 feet long. the siding extends 6 feet up the side of the house. a) what is the total surface are he must paint? b) a one gallon can of the stain that darcy is using covers approximately 225 ft squared. if darcy applies 2 coats of stain, how many cabs of stain should he buy?
Answers
Darcy requires 24.14 gallons of paint to cover an area of 2716 feet².
Length of the house = 35 feet
width of the house = 28 feet
Height of the house = 6 feet
Total surface area = 2 l b + 2 b h + 2 h l
A = 2 (35) (28) + 2 (28) (6) + 2 (6) (35)
A = 1960 + 336 + 420
A = 2716 feet²
If he uses 2 coats of stain, the area he need to cover = 2 (2716) = 5432 feet²
Gallon of paint required = 5432 / 225 = 24.14 gallons.
Therefore, Darcy requires 24.14 gallons of paint to cover an area of 2716 feet².
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Jasmin babysits for the Smith family with 2 children. They pay her $10 an hour. She babysat 12 hours for the Smiths this week. Jasmin babysits for the Johnson family with 5 kids. They pay her $15 an hour. She babysat 6 hours for the Johnson's this weekend.
How much was she paid altogether?
Answers
The amount Jasmin was paid altogether was $210
From the question, we are to determine how much Jasmin was paid altogether
From the given information,
The Smith family pay her $10 an hour.
and
She babysat for the Smith family for 12 hours
Thus,
The amount she was paid by the Smith family is 12 × $10 = $120
Also,
The Johnson family pay her $15 an hour
and
She babysat for the Johnson family for 6 hours
Thus,
The amount she was paid by the Johnson family is 6 × $15 = $90
Therefore,
The amount she was paid altogether = $120 + $90
The amount she was paid altogether = $210
Hence, the amount Jasmin was paid altogether was $210
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How long will it take you to bike 225 miles at
a
speed of 15 miles per hour?
Am I supposed to divide
Answers
Answer:
15
Step-by-step explanation:
225/15
Find the measurement of each marked angle
Answers
Answer:
see below
Step-by-step explanation:
The interior angle of the triangle on the right is 180 - ( 9x+12)
this plus the other two sum to 180 degrees
180 - (9x+12) + 4x-3 + 6x + 3 = 180
x = 12
then the angles are 6(12) + 3 = 75 4(12) -3 = 45 and 60°
The function f(x) = x² + 4 is defined on the domain [-8, 8]. Which of the following is the correct associated range?
O [4, 68]
O [0, 4]
O [-60, 4]
O (-∞, 4]
O [-60, 68]
0 (-∞, ∞)
Answers
========================================================
Explanation:
The parabola has its lowest point when either x = -8 or x = 8
Plug either value into the function
f(x) = -x^2 + 4
f(-8) = -(-8)^2 + 4
f(-8) = -60
You should find that f(8) = -60 as well
This is the lowest output possible. Confirmation of such can be done using a graph. Look for the lowest point and only focus on the interval [tex]-8 \le \text{x} \le 8[/tex]
The highest point is at the vertex (0, 4), so the largest output is y = 4
------------
We have the lowest output y = -60 and the highest output y = 4
The possible set of outputs is the interval [tex]-60 \le \text{y} \le 4[/tex] which turns into the interval notation [-60, 4]
Check out the graph below.
What is (1 2/3) divided by (1/8)?
Answers
Answer:
13 1/3
____
Work[tex]1\:2/3 = 5/3\\1/8 = 1/8\\\\5/3 \div 1/8\\=\frac{5\cdot8}{3\cdot1}\\= \frac{40}{3}\\= 13\:1/3[/tex]
When working with mixed numbers that are being divided, you know where to start. Start by converting mixed numbers to fractions, then multiply the fractions together to divide them. Simplify your improper fraction by counting how many times it surpasses the denominator.
what is the Inverse of
Y=2x-1?
Answers
Answer:
y = [tex]\frac{x+1}{2}[/tex]
Step-by-step explanation:
y = 2x - 1
switch the x and y variables
x = 2y - 1
solve for y
x + 1 = 2y
[tex]\frac{x+1}{2}[/tex] = y
Hot tea is around 181 degrees Fahrenheit, and the room temperature is 72 degrees Fahrenheit. The rate of the hot tea cooling on a desk in the room is about 6.5% every minute. You need to determine how hot the tea will be after t minutes? Which function models this situation?
Answers
The function that models the given situation is; f(x) = 109(0.935)^(t) + 72
How to interpret function models?
We are given that;
Temperature of hot tea = 181°F
Room temperature = 72°F
Rate of the hot tea cooling on a desk in the room = 6.5% every minute
We know that an exponential function is of the form of;
y = A(r)^(x)
where;
A is the initial value.
r is the rate of increase/decrease in decimals.
Thus, our initial value is;
A = 181 - 72 = 109
The rate of increase/decrease in decimals = 1 - (6.5%) = 0.935
Since the room temperature is 72 degrees Fahrenheit, then the function is;
f(x) = 109(0.935)^(t) + 72
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..........................................................................................................................................................................
Answers
Answer:
0.012÷2=12 thousandths ÷ 2
Halla tres enteros pares consecutivos tales que 6 veces el primer entero sea 26 más que la suma del segundo y tercer enteros.
Answers
The consecutive even integers are 8, 10 and 12.
How to calculate the value?Let the integers be x, x + 2, and x + 4.
Therefore, the equation will be:
6(x) = x + 2 + x + 4 + 26
6x = 2x + 32
Collect like term
6x - 2x = 32
4x = 32
Divide
x = 32/4.
x = 8
The numbers are 8, 10 and 12.
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A school has 1000 students. of these, 3/4 are boys. how many of the students are boys? how many of the students are girls?
Answers
Answer:
750 students are boys, 250 are girls.
Step-by-step explanation:
1/4 of 1000 is 250.
250 + 250 + 250 = 750 boys.
if 3/4 are boys, then 1/4 (the rest of the school population) are girls.
150 students are girls.
-2(7-x) + 4= -4
what’s “x” equal
Answers
Answer: x=3
Step-by-step explanation:
-2(7-x) + 4= -4
-14 + 2x + 4= -4
2x - 10= -4
2x = 6
x=3
Find a vector function r(t), that represents the curve of intersection of the two surfaces. the cylinder x2 y2=36 and the surface z=4xy
Answers
Given:
[tex]\begin{aligned}&x^2+y^2=16 \\&z=x y\end{aligned}[/tex]
Express 16 as [tex]4^{2}[/tex]: [tex]x^2+y^2=16[/tex]
[tex]x^2+y^2=4^2\\x^2+y^2=4^2 \times 1[/tex]
Trignometry,
[tex]\cos ^2(t)+\sin ^2(t)=1[/tex]
Now, substitute [tex]\cos ^2(t)+\sin ^2(t)[/tex] for 1:
[tex]\begin{aligned}&x^2+y^2=4^2 \times 1 \\&x^2+y^2=4^2 \times\left[\cos ^2(t)+\sin ^2(t)\right]\end{aligned}\\x^2+y^2=4^2 \times \cos ^2(t)+4^2 \times \sin ^2(t)[/tex]
Law of indicates:
[tex]\begin{aligned}&x^2+y^2=[4 \times \cos (t)]^2+[4 \times \sin (t)]^2 \\&x^2+y^2=[4 \cos (t)]^2+[4 \sin (t)]^2\end{aligned}\\x^2=[4 \cos (t)]^2 \text { and } y^2=[4 \sin (t)]^2[/tex]
Taking positive square roots as follows:
[tex]x=4 \cos (t), y=4 \sin (t)[/tex]
Recall that, z = xy.
Now, we have:
[tex]\begin{aligned}&z=4 \cos (t) \times 4 \sin (t) \\&z=16 \cos (t) \cdot \sin (t)\end{aligned}[/tex]
Now, substitute the values:
[tex]r(t)=x_t i+y_t j+z_t k[/tex]
So, the vector r(t) is: [tex]r(t)=(4 \cos (t)) i+(4 \sin (t)) i+(16 \cos (t) \cdot \sin (t)) i[/tex]
Therefore, the vector function r(t) is written as: [tex]r(t)=x_t i+y_t j+z_t k[/tex]
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Kenzie runs at an average speed of 6.25mi/h. The length of her typical run is within one mile of 6 miles long.
Write an absolute value equation to represent the situation. Find the shortest or longest amount of time for Kenzie’s run. Round to the nearest minute.
Answers
Answer: 13512
100332
Step-by-step explanation:
The shortest time for her run is approximately 36 minutes and the longest time is approximately 67 minutes.
To represent Kenzie's situation, we can use an absolute value equation. Let x represent the length of her run in miles.
The equation would then be |x - 6| ≤ 1, which means the distance between x and 6 is less than or equal to 1.
To find the shortest or longest amount of time for Kenzie's run, we need to consider the speed.
The time can be found by dividing the distance by the speed, so the minimum time would be (6 - 1)/6.25 hours,
which is approximately 0.6 hours or 36 minutes.
The maximum time would be (6 + 1)/6.25 hours,
which is approximately 1.12 hours or 67 minutes.
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Each figure shows a triangle with one of its angle bisectors.
Can someone help me
Answers
6- C ( 38°)
Some Math i can’t helppp
Answers
Annually The amount after 10 years = $ 7247.295
quarterly compound after 10 years = $7393.5
Continuously interest =$7,419
Given:
P = the principal amount
r = rate of interest
t = time in years
n = number of times the amount is compounding.
Principal = $4500
time= 10 year
Rate = 5%
To find: The amount after 10 years.
The principal amount is, P = $4500
The rate of interest is, r = 5% =5/100 = 0.05.
The time in years is, t = 10.
Using the quarterly compound interest formula:
A = P (1 + r / 4)4 t
A= 4500(1+.05/4)40
A= 4500(4.05/4)40
A= 4500(1.643)
Answer: The amount after 10 years = $7393.5
Using the Annually compound interest formula:
A = P (1 + r / 100) t
A= 4500(1+5/100)10
A= 4500(105/100)10
Answer: The amount after 10 years = $ 7247.295
Using the Continuously compound interest formula:
e stands for Napier’s number, which is approximately 2.7183
[tex]A=Pex^{rt} \\A=4500(e)^{.5} \\A= 4500(2.71)^{.5}[/tex]
A= $2,919
Answer: The amount after 10 years = $4500+$2,919=$7,419
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Point D is 1n of the way from C(−2.5, 1.25) to E(5, 15). What are the coordinates of D if n = 5?
Answers
Answer:
Coordinates of D are (-1, 4)
Step-by-step explanation:
I have assumed that what you wrote as 1n is actually 1/n otherwise the question does not make sense
1/n with n = 5 ==> that D is 1/5th of the distance from C on the CD line segment
Point D is 1/5th of the way from C to D
I will represent the (x, y) coordinates of points C, D and E as
[tex](x_C, y_C), (x_D, y_D) , (x_E, y_E)[/tex] respectively
Then the x-distance from C to E = [tex]x_E - x_C[/tex] and the y-distance from C to E will be [tex]y_E - y_C[/tex]
[tex]\text{1/5th of }[/tex] [tex]x_E - x_C = \dfrac{x_E - x_C}{5}[/tex] but this is relative to the location of [tex]x_C[/tex].
So we have to add this to [tex]x_C[/tex] to get the absolute x-coordinate of D
So
[tex]\displaystyle \large x_{D}=x_{C}+\dfrac{x_{E}-x_{C}}{5}[/tex]
and similarly
[tex]{\displaystyle y_{D}=y_{C}+\dfrac{y_{E}-y_{C}}{5}}[/tex]
Putting in the values for these coordinates we get
[tex]x_{D}=-2.5+\dfrac{5-(-2.5)}{5} \\\\= -2.5 + \dfrac{5 + 2.5}{5}\\\\\= -2.5 + \dfrac{7.5}{5}\\\\= - 2.5 + 1.5\\\\= -1.0[/tex]
[tex]y_{D}=1.25+\dfrac{15-1.25)}{5} \\\\= 1.25+ \dfrac{15 - 1.25}{5}\\\\\ = 1.25+ \dfrac{13.75}{5}\\\\= 1.25+ 2.75\\\\= 4.0[/tex]
So the coordinates of D are:
[tex]\boxed{D(-1, 4)}[/tex]
The graph shows the point D is indeed 1/5th of the distance from C to D
CD is a line of length 12 cm
E is a point on the line segment CD.
CE: CD = 1:2
Mark point E on the line with a cross.
Answers
Answer:
E would be 6 spaces or the middle of points C and D.
Step-by-step explanation:
Please see picture.
Which expression represents the product of n and
25?
A. 25n
C. 25 + n
B. 25-n
D. 25 ÷ n
Answers
Answer:
25n
Step-by-step explanation:
product of n and 25
Product means multiply
25n
Line l passes through point (6,0) and line p is the graph of 2x-3y=4. If l is perpendicular to line p, what is the equation of l.
Answers
Equation of line p:
[tex]{\sf{2x - 3y = 4}}[/tex]
[tex]{\sf{y = \frac{2x}{3} - \frac{4}{3}}}[/tex]
Slope of line p (m):
[tex]{\sf{\frac{2}{3}}} [/tex]
Since, l is perpendicular to line p, the product of slopes of line l & p should be -1. We assume slope of line l be m2
Hence,
[tex]{\sf{m \times m2 = - 1}}[/tex]
[tex]{\sf{ \frac{2}{3} \times m2 = - 1}}[/tex]
[tex]{\sf{m2 = \frac{ - 3}{2}}}[/tex]
Since, line l passes through points (6, 0).
We apply,
[tex]{\sf{(y - y1) = m2(x - x1)}}[/tex]
[tex]{\sf{y - 0 = \frac{ - 3}{2}(x - 6)}} [/tex]
[tex]{\sf{2y - 0 = - 3x + 18}}[/tex]
[tex]{\sf{3x + 2y - 18 = 0}}[/tex]
The equation of line l:
[tex]{\sf{\red{\boxed{\sf{3x+2y-18=0}}}}}[/tex]
Write the decimal equivalent for each rational number. Use a bar over any repeating digits 3/11
Answers
Answer:
see below
Step-by-step explanation:
1/11=0.0909....
3/11=0.090909...*3 or 0.27272727...
order these following rational numbers from least to greatest:
3.4 -0.01 1/4 12% -26.1
Answers
Answer:
3.4, 1/4, 12%, -0.01, -26.1
Step-by-step explanation:
The simplest way to do these type of problems is to convert all of the numbers into either a fraction, decimal, or a percentage. In my opinion, it is easier to use a percentage here.
12% is already a percentage
-0.01 = -1%
1/4 = 25%
3.4 = 340%
-26.1 = -2610%
Now that the rational numbers are all in the same unit, it is easier to sort them. In the end, we get this list (from greatest to least):
3.4, 1/4, 12%, -0.01, -26.1
FINAL ANSWER: 3.4, 1/4, 12%, -0.01, -26.1
someone help please!!!!
Answers
Answer:
x = -2
TU = 4
UB = 2
Step-by-step explanation:
you can add x^2 with 4x+10 and equate it to 6:
x^2 + 4x + 10 = 6
x^2 + 4x + 4
then u can use the roots formula : x = (-b ± √ (b2 - 4ac) )/2a
so it'll be x = {-4±[√16 - 4(4)]}/2
x= -2
then u can substitute it and find TU and UB
TU= (-2)^2 = 4
UB= 4(-2)+10 = 2
The lengths of the four sides of a
quadrilateral (in inches) are consecutive integers. If
the perimeter is 110 inches, find the value of the longest of the four side lengths.
Answers
The value of the longest of the four side length is 29 inches, if the lengths of the four sides of a quadrilateral (in inches) are consecutive integers.
According to the given question.
The lengths of the four sides of a quadrilateral (in inches) are consecutive integers.
So, let the length of the quadrilateral be x, (x + 1), (x + 2), and (x + 3).
Also, it is given that the perimeter of the quadrilateral is 110 inches.
⇒ x + x+1 + x + 2 + x + 3 = 110
⇒ 4x + 6= 110
⇒ 4x = 110 -6
⇒ 4x = 104
⇒ x = 104/4
⇒ x = 26 inches
Thereofore, the length of the sides of the quadrilaterals is given by
x = 26 inches
x + 1 = 26 + 1 = 27 inches
x + 2 = 26 + 2 = 28 inches
x + 3 = 26 + 3 = 29 inches
Hence, the value of the longest of the four side length is 29 inches, if the lengths of the four sides of a quadrilateral (in inches) are consecutive integers.
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An explanation needed, thx
The points (-4,2) and (4,2) are two vertices of a square. State all other order pairs that could be the other two vertices of the square.
Answers
Solve the simultaneous equation
-4x+3y=1
6x-y=2
Answers
Let's change the equation,
→ 6x - y = 2
→ y = 6x - 2
Then the value of x will be,
→ -4x + 3y = 1
→ -4x + 3(6x - 2) = 1
→ -4x + 18x - 6 = 1
→ 14x = 1 + 6
→ x = 7/14
→ [ x = 1/2 ]
Hence, the value of x is 1/2 (or) 0.5.
Now the value of y will be,
→ y = 6x - 2
→ y = 6(1/2) - 2
→ y = 3 - 2
→ [ y = 1 ]
Hence, the value of y is 1.
Find the perimeter of a rectangle with a length of 9 yards and a width of 6 yards.
Answers
Answer:
30 yards
Step-by-step explanation:
9+9+6+6=30yards