Find the mean of x of each distribution.
Correct answers will be mark as BRAINLIEST and get 50 points
Wrong answers will be reported
Answer:
See below ~
Step-by-step explanation:
a)
Mean = 2(11) + 3(17) + 4(24) + 5(23) + 6(18) + 7(15) / 108Mean = 22 + 51 + 96 + 115 + 108 + 105 / 108Mean = 497 / 108Mean = 4.6b)
Mean = 0(35) + 1(76) + 2(48) + 3(22) / 181Mean = 76 + 96 + 66 / 181Mean = 1.31c)
Mean = 8(7) + 9(10) + 10(3) / 20Mean = 56 + 90 + 30 / 20Mean = 176/20Mean = 8.8Answer:
a) 4.60 (2 dp)
b) 1.31 (2 dp)
c) 8.8
Step-by-step explanation:
The "Frequency" part of a frequency table is the measure of how often the data value occurs.
To calculate the mean of data presented in a frequency table, we need to multiply each data value by its given frequency, sum these, then divide by the sum of the frequency.
The formula for mean is:
[tex]\textsf{mean}=\overline{x}=\dfrac{\displaystyle \sum fx}{\displaystyle\sum f}[/tex]
Part (a)Add a row showing the values of [tex]fx[/tex]
Add a column showing the totals of [tex]f[/tex] and [tex]fx[/tex]
[tex]\large\begin{array}{| c | c | c | c | c | c | c | c |}\cline{1-8} & & & & & & & \sf Total \\\cline{1-8} x & 2 & 3 & 4 & 5 & 6 & 7 & \\\cline{1-8} \textsf{Frequency}\:f & 11 & 17 & 24 & 23 & 18 & 15 & 108\\\cline{1-8} fx & 22 & 51 & 96 & 115& 108 & 105 &497 \\\cline{1-8}\end{array}[/tex]
Now use the formula to calculate the mean:
[tex]\implies \textsf{mean}=\overline{x}=\dfrac{497}{108}=4.60\:\textsf{(2 dp)}[/tex]
Part (b)Add a column showing the values of [tex]fx[/tex]
Add a row showing the totals of [tex]f[/tex] and [tex]fx[/tex]
[tex]\large\begin{array}{| c | c | c |}\cline{1-3} x & \textsf{Frequency}\: f & fx \\\cline{1-3} 0 & 35 & 0 \\\cline{1-3} 1 & 76 & 76\\\cline{1-3} 2 & 48 & 96\\\cline{1-3} 3 & 22 & 66 \\\cline{1-3} \sf Total & 181 & 238 \\\cline{1-3}\end{array}[/tex]
Now use the formula to calculate the mean:
[tex]\implies \textsf{mean}=\overline{x}=\dfrac{238}{181}=1.31\:\textsf{(2 dp)}[/tex]
Part (c)Add a column showing the values of [tex]fx[/tex]
Add a row showing the totals of [tex]f[/tex] and [tex]fx[/tex]
[tex]\large\begin{array}{| c | c | c |}\cline{1-3} x & \textsf{Tally}\: f & fx \\\cline{1-3} 8 & 7 & 56\\\cline{1-3} 9 & 10 & 90\\\cline{1-3} 10 & 3 & 30\\\cline{1-3} \sf Total & 20 & 176\\\cline{1-3}\end{array}[/tex]
Now use the formula to calculate the mean:
[tex]\implies \textsf{mean}=\overline{x}=\dfrac{176}{20}=8.8[/tex]
volume of the house?
Answer:
Step-by-step explanation:
1.5 x 4.5 x 4.5 = 30.375
30.375 ÷ 3 = 10.125
10.125= volume of the triangle
3 x 4.5 x 4.5 = 60.75
60.75 = volume of rectangle
60.75 + 10.125 = 70.875
70.875 = total volume
1. Jessica and her family are driving to see friends who live 750 miles away. They dri for 12.5 hours before they arrive. What is their rate of change?
1. 60 miles per hour
2. 50 miles per hour
3. 75 miles per hour
4. 55 miles per hour
Answer:
60 miles per hour.
Step-by-step explanation:
speed = distance / time
= 750 / 12.5
= 60 miles per hour.
Records show that Oliver is typically 10-30 minutes late
for his shift at work. The distribution for the minutes he is
late forms a consistent pattern, which can be graphed as
the given uniform density curve.
Oliver will get a written warning if he is more than 16
minutes late for work. What percentage of the time will
Oliver get a written warning?
30%
46.7%
70%
100%
The percentage of the time will Oliver get a written warning when he is more than 16 minutes late for his shift at work is 46.7%.
What is a density curve?The density curve is a type or way of representation of numbered distribution data over a graph. Here, the outcomes are continues. The density curve can not be below the x-axis or horizontal line of the graph.
In a density curve,
The mean of a density curve is indicated by μ (mu).The standard deviation of a density curve is indicated by Sx.Records show that Oliver is typically 10-30 minutes late for his shift at work. The distribution for the minutes he is late forms a consistent pattern, which can be graphed as the given uniform density curve.
Oliver will get a written warning if he is more than 16 minutes late for work. The time remain after the 16 minutes is,
t=30-16
t=14 min
Thus, the percentage of the time will Oliver get a written warning is,
p=(14/30)*100
p=46.7 %
Thus, the percentage of the time will Oliver get a written warning when he is more than 16 minutes late for his shift at work is 46.7%.
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Answer:
46.7%
Step-by-step explanation:
An airplane takes off from an airport. When the
airplane reaches a height of 16,500 feet (ft), the
airplane has travelled a horizontal distance of 6,000 ft,
as shown in the diagram below.
The angle of elevation is = 70° and the distance the airplane travelled in the air is = 17,557ft
Calculation of the distance travelledTo calculate the angle of elevation of the airplanetan x° = opposite/adjacent
where opposite = 16,500 feet
adjacent = 6,000 ft
tan x° = 16,500 / 6,000
tan x° = 2.75
X = arctan ( 2.75)
X = 70°
To calculate the distance the airplane travelled in the air Pythagorean Theorem is used.C² = a² + b²
C² = 16,500² + 6,000²
C² = 272250000 + 36000000
C² = 308250000
C= √308250000
C= 17,557ft
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64,000 ÷ 110
Estimate :
Quotient :
Remainder:
Answer:
640; 581 R 90; 90
Step-by-step explanation:
you can round 110 to 100
64000/100 is simply 640
then you do the real math
the quotient is 581 r 90
this means the remainder is 90
Pls help me and show work! Thank you <3
Answer: 70
Step-by-step explanation:
By the corresponding angles theorem, [tex]4x-50=2x+30 \longrightarrow x=40[/tex]
This means that [tex]2x+30=110[/tex].
Now, if we notice the linear pair, this means that [tex]y=\boxed{70}[/tex]
Two pirates were playing with golden coins. During game, the first pirate lost half of his coins to the second pirate, then the second pirate lost half of his coins to the first pirate, then again the first lost half of his coins to the second. At the end of the game, the first pirate had 21 coins, and the second had 45 coins. How many coins did the first pirate have initially?
What is the area, measured in square centimeters, of the green shape
pictured below? Do not include units in your answer.
Icm
1 cm
Answer here
Step-by-step explanation:
we can easily count this, as the diagonal lines are squares truly in half. so, 2 such cut squares are in total 1 full square.
there is one central rectangle of 4×6 squares = 24.
then in the upper left corner there is a small 2×2 square = 4.
and then we have in the bottom left 2 and the bottom right also 2 small triangles (4 in total) with each having 1 full square and 2 half-squares (2 squares in total) as area.
so, 4×2 = 8 squares.
so, the whole area is
24 + 4 + 8 = 36
When you pay with a debit or ATM card, you are not borrowing money. You are
spending your own money. When you pay with a credit card, you are always
borrowing money.
True.
False.
Does this graph show a function? Explain how you know.
5
O A. No; the graph fails the vertical line test.
B. Yes, there are no y-values that have more than one x-value.
C. Yes; the graph passes the vertical line test.
D. No; there are y-values that have more than one x-value.
Answer: A. No; the graph fails the vertical line test.
The vertical line test is a tool used to determine if we have a function. If we can draw a single straight vertical line through more than one point on the red curve, then the graph is said to have failed the vertical line test. Consequently, this leads to the relation not being a function.
For this circle graph, we can draw a vertical line through more than one point, which is why we don't have a function here.
Put another way, there are inputs (x) that produce more than one output (y), so that's why we don't have a function.
There were 38 balloons at the beginning of a party. By the end of the party, c of them had popped. Using c, write an expression for the number balloons that were left.
Answer:
[tex]37 - c = x[/tex]
Step-by-step explanation:
We'll use c to represent the amount taken away (subtracted) and x to represent the amount left (the answer).
We begin with 37 balloon, and take away c amount to make x.
37 - c = x
NO LINKS!! Please help me with this translation: 2 units right and 5 units up
Answer:
g(x) = 5|(x - 2) - 2| - 2
Step-by-step explanation:
To shift 5 units right :
⇒ f(x) = 5|(x - 2) - 2| - 7
⇒ Applied rule : a units right → f(x) = (x - a)
To shift 5 units up :
⇒ g(x) = 5|(x - 2) - 2| - 7 + 5
⇒ g(x) = 5|(x - 2) - 2| - 2
Answer:
[tex]g(x)=5|x-4|-2[/tex]
Step-by-step explanation:
Translations
For [tex]a > 0[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]
Parent function:
[tex]f(x)=5|x-2|-7[/tex]
Translate 2 units right:
[tex]\begin{aligned}\implies f(x-2)& =5|x-2-2|-7\\ & =5|x-4|-7 \end{aligned}[/tex]
Then translate 5 units up:
[tex]\begin{aligned}\implies f(x-2)+5& =5|x-4|-7+5\\ & =5|x-4|-2 \end{aligned}[/tex]
Therefore:
[tex]\implies g(x)=5|x-4|-2[/tex]
Suppose a butterfly can fly 68 feet in 5 seconds. A dragonfly can fly 34 feet in 3 seconds. Which can fly faster and by how much?
Will give brainly
Answer:
butterfly1 second in 68 ft, or 2 4/15 ft/sStep-by-step explanation:
Speed is the ratio of distance to time. Speeds can be compared by comparing the times for the same distance, or by comparing the distances for the same time. A faster speed means more distance is covered in less time.
__
Here, we observe that 68 feet is a multiple of 34 feet, so it is easiest to compare the speeds of the insects by comparing their times for the same distance.
butterfly: 68 ft in 5 seconds
dragonfly: 2×34 ft in 2×3 seconds, or 68 ft in 6 seconds
The butterfly covers the same distance in less time, so it can fly faster.
__
Since our comparison of speeds is made using travel times, we can say the answer to "how much faster" is "1 second less over a distance of 68 feet."
_____
Additional comment
You may be expected to figure the speeds in units of feet per second. You do that by dividing feet by seconds.
butterfly: 68 ft/(5 s) = 13.6 ft/s
dragonfly: 34 ft/(3 s) = 11 1/3 ft/s
The difference in speeds is ...
(13 3/5) -(11 1/3) = 2 4/15 . . . ft/s
The butterfly's speed is 2 4/15 ft/s faster than the dragonfly's speed.
__
You see time comparisons in human foot races, often with differences measured in milliseconds. Almost never are speeds compared in terms of feet (or meters) per second.
Solve using the quadratic formula
x^2 - 8x - 84 = 0
Show all work
Answer:
x²-8x-84
Using quadratic Formular -b±√b²-4ac/2a
--8±/8²-4×1×-84 /2×1
8±/64+336/2
8±/400/2
8±20/2
8+20/2, 8-20/2
28/2, -12/2
14,-6
An ice cream truck began its daily route with 84 gallons of ice cream. The truck driver sold 74% of the ice cream. How many gallons of ice cream were sold?
gallons of ice cream were sold
nearest gallon)
Answer:
We need to find 74% of 84 (that's the amount that was sold// If you would have been asked for the amount left, it would be (100%-74%), but here it's easier since it's already given to us)
Now, let's write the percentage as a fraction
74/100 of 84
**Trick, for percentages, anytime you see a "of" replace it with a multiplication symbol
74/100 x 84
Now, it's just a simple multiplication
(74x84)/100
*You can use a calculator and find your answer
It would give you 62.16 and you will need to round it to a whole number, so 62 gallons
*If you can't use a calculator, simplify the fraction as much as you can and try to approximate
Step-by-step explanation:
~62
Please solve with explanation (high points)
By concepts of trigonometry and of perpendicularity, the angles AKL and AKC from respective right triangles have measures of 90° and 32.3°, respectively.
How to find angles by trigonometric relationships
As planes ABCD and BCLK are perpendicular to each other, the triangles AKL and AKC are right angled. The required angles can be found by using the following trigonometric relationships:
[tex]\angle AKL = 90^{\circ}[/tex] (As line segments AK and KL are perpendicular to each other)
[tex]\angle AKC = \tan^{-1} \left(\frac{AC}{KC} \right) = \tan^{-1} \left(\frac{\sqrt{2}\cdot a}{\sqrt{5} \cdot a} \right) = \tan^{-1} \sqrt{\frac{2}{5} }[/tex] (as line segments AC and KC are perpendicular to each other)
[tex]\angle AKC \approx 32.312^{\circ}[/tex]
By concepts of trigonometry and of perpendicularity, the angles AKL and AKC from respective right triangles have measures of 90° and 32.3°, respectively.
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Interest rate. Multiple choice
Answer:
A. 9.9%
Step-by-step explanation:
[tex] {e}^{14r} = 4[/tex]
[tex] ln(4) = 14r[/tex]
[tex]r = \frac{ ln(4) }{14} = .099 = 9.9\%[/tex]
Which is correct???????
Answer:
Bias compare results implement treatments
Step-by-step explanation:
Pls help me and show work! Thank you <3
Answer: 6
Step-by-step explanation:
If the lines are parallel, then this means that by the corresponding angles theorem, the two angles marked in the image are congruent.
If we consider the right triangle, then by the exterior angle theorem, [tex]4x+90=11x-8 \longrightarrow x=14[/tex].
So, if [tex]x=14[/tex], then the indicated angle measures [tex]56^{\circ}[/tex], and since vertical angles are congruent, [tex]9y+2=56 \longrightarrow \boxed{y=6}[/tex]
Does anyone know the answer? Please and Thank you!
Answer:
By multiplying both side with the inverse of the coefficient of x
Step-by-step explanation:
coefficient of x = -6/4
inverse of coeefficient =-4/6.
multiply both sides.
x = 12(-4/6) = -8
2(6n+8)
Explain please
Answer:
12n + 16
Step-by-step explanation:
2 (6n + 8)
= (2*6n) + (2*8) [distributive property]
= 12n + 16
Hope it helps ⚜
Answer:
12n + 16
Step-by-step explanation:
Distributive Property
a(b + c) = ab + acDistributing the terms
2(6n + 8)2(6n) + 2(8)12n + 16What is the measure of the unknown angle?
Image of a full circle divided into two angles. One angle is fifty degrees and the other is unknown
Group of answer choices
300°
The measure of the unknown angle in the full circle is calculated as: 310 degrees.
What is the Measure of a Full Circle?The angle measure of a full circle equals 360 degrees.
The full circle given is divided into two angles, of which 50 degrees is a measure of one of the angles.
The unknown angle = 360 - 50 = 310 degrees.
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The measure of angle w is 130 degrees. What is the measure of angle b? You can use the equations you just wrote to help. W=y. C+b=90. Y+c=180
Answer:
b = 40
Step-by-step explanation:
Solve system of equations.
1) w = y
2) c + b = 90
3) y + c = 180
Since we want to solve for b, second equation would be a good starting point.
c + b = 90
b = 90 - c
But what is c?
Let's make c the subject in 3rd equation.
y + c = 180
c = 180 - y
Insert c back in second equation.
b = 90 - c
b = 90 - (180 - y)
b = 90 - 180 + y
b = -90 + y
All we need now is y. Notice that in the first equation w equals y and w is 130°, which means y is also 130°. Substitute again.
b = -90 + y
b = -90 + w
b = -90 + 130
b = 40
---
This is how it looks like if you solve it in one go (same procedure as above but in one place).
c + b = 90
b = 90 - c
b = 90 - (180 - y)
b = -90 + y
b = -90 + w
b = -90 + 130
b = 40
Write the equation for the line in slope-intercept form.
Answer:
y = -3x - 3
Step-by-step explanation:
The line intercepts the y-axis at -3, and moves down 3 on the y for moving to the right 1 along the x-axis
Find a formula for the nth term in this
arithmetic sequence:
a₁ = -7, a2 = -1, a3 = 5, a4 = 11,
-7+(n-1)6
-7 is the starting term
n is the term that you are looking for
6 is the common difference
The formula for the nth term in the arithmetic sequence is:
a(n) = 6n - 13
What is an arithmetic sequence?It is a sequence where the difference between each consecutive term is the same.
We have,
We are given the first four terms of an arithmetic sequence:
a₁ = -7, a₂ = -1, a₃ = 5, a₄ = 11
To find the formula for the nth term, we need to find the common difference (d) first.
We can do this by subtracting any two consecutive terms:
d = a₂ - a₁ = (-1) - (-7) = 6
Now we can use the formula for the nth term of an arithmetic sequence:
a(n) = a₁ + (n - 1)d
Substituting the values we found:
a(n) = (-7) + (n - 1)(6)
Simplifying:
a(n) = -7 + 6n - 6
a(n) = 6n - 13
Therefore,
The formula for the nth term in the arithmetic sequence is:
a(n) = 6n - 13
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Will give brainliest!! One x-intercept of y = x2 – 6x + c is 3.
How you can find the value of c?
What is the value of c?
What is true about the x-intercepts of this function?
Answer:
9.
Step-by-step explanation:
1) the condition 'One x-intercept of y = x2 – 6x + c is 3' means, that x=3 and y=0;
2) it is possible to substitute the values x=3 and y=0 into the given equation and to calculate 'c':
0=9-18+c; ⇒ c=9.
A rectangle has a length of k cm (where k is an integer) and width of k +3cm. the perimeter of this rectangle is less than 24cm.
form and solve an inequality and find the largest possible value of k.
Answer:
So our unknown width is X and the unknown length is X + 3. We know the perimeter is 2 times the length plus 2 times the width so let's set up that equation:
2 X + 2 (X+3) = 24
Now solve for X
2 X + 2 X + 6 = 24
4 X + 6 = 24
4 X = 18
X = 4.5 - this is the width
X + 3 = 4.5 + 3 = 7.5 - this is the length
Step-by-step explanation:
Prove the identity 2csc2x=csc^2xtanz
Step-by-step explanation:
Consider the LHS, after the 5th step, consider the RHS
[tex]2 \csc(2x) = \csc {}^{2} (x) \tan(x) [/tex]
[tex]2 \frac{1}{ \sin(2x) } = \csc {}^{2} (x) \tan(x) [/tex]
[tex]2 \times \frac{1}{2 \sin(x) \cos(x) } = \csc {}^{2} (x) \tan(x) [/tex]
[tex] \frac{1}{ \sin(x) \cos(x) } = \csc {}^{2} (x) \tan(x) [/tex]
[tex] \csc(x) \sec(x) = \csc {}^{2} (x) \tan(x) [/tex]
Consider the RHS
[tex] \csc(x) \sec(x) =( 1 + \cot {}^{2} (x) ( \tan(x)) [/tex]
[tex] \csc(x) \sec(x) = \tan(x) + \cot(x) [/tex]
[tex] \csc(x) \sec(x) = \frac{ \sin(x) }{ \cos(x) } + \frac{ \cos(x) }{ \sin(x) } [/tex]
[tex] \csc(x) \sec(x) = \frac{1}{ \sin(x) \cos(x) } [/tex]
[tex] \csc(x) \sec(x) = \csc(x) \sec(x) [/tex]
Consider the function g, domain R, defined by f(x)=2x^2+4x-1.
What is the codomain of the g function?
A: ]-∞,-3]
B: [-1,+∞[
C: [-3,+∞[
D: ]-∞,-1]
So, the answer to this question is option C, but I don't know why. Can anyone explain it to me?
Answer:
see explanation
Step-by-step explanation:
the codomain are the values of f(x) from the y- coordinate of the vertex upwards.
given a quadratic in standard form
y = ax² + bx + c ( a ≠ 0 )
then the x- coordinate of the vertex is
[tex]x_{V}[/tex] = - [tex]\frac{b}{2a}[/tex]
f(x) = 2x² + 4x - 1 ← is in standard form
with a = 2 and b = 4 , then
[tex]x_{V}[/tex] = - [tex]\frac{4}{4}[/tex] = - 1
substitute x = - 1 into f(x) for y- coordinate of vertex
f(- 1) = 2(- 1)² + 4(- 1) - 1 = 2 - 4 - 1 = - 3
vertex = (- 1, - 3 )
since the coefficient of the x² term > 0 then the graph opens up U
then codomain is [ - 3, ∞ )
