The ages of the students in a statistics class are listed below. If the 18-year-old student has a birthday and turns 19, how will it affect the mean and median ages of the class?
Ages: 14, 15, 15, 16, 16, 16, 16, 17, 17, 17, 17, 17, 18
A
Both the mean age and the median age will increase.
B
The mean age will increase, and the median age will remain the same.
C
The mean age will remain the same, and the median age will increase.
D
The mean age will remain the same, and the median age will decrease.
The mean age will increase, and the median age will remain the same.
Option B is the correct answer.
What is a mean?It is the average value of the set given.
It is calculated as:
Mean = Sum of all the values of the set given / Number of values in the set
We have,
Ages:
14, 15, 15, 16, 16, 16, 16, 17, 17, 17, 17, 17, 18
The mean of the ages.
= (14 + 15 + 15 + 16 + 16 + 16 + 16 + 17 + 17 + 17 + 17 + 17 + 18) / 13
= 211/13
= 16.23
The median of the ages.
= 16
Now,
18 becomes 19.
14, 15, 15, 16, 16, 16, 16, 17, 17, 17, 17, 17, 19.
Mean = 212/13 = 16.3
Median = 16
Thus,
The mean age is increased.
The median is the same.
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40 people attended the play. 15 were women, 10 were men, and 15 were children. what fraction were men?
Answer:
10/40 were men, or simplified the amount is 1/4 of the total is men
What is the solution to the trigonometric inequality sin(x)>1+cos(X) over the interval 0<=x<=2pi radians?
Answer:
Last choice
Step-by-step explanation:
First, convert (sinx)^2 to 1-(cosx)^2 via trigonometric identity derived from (sinx)^2 + (cosx)^2 = 1
[tex]\displaystyle \large{\sin^2x + \cos^2x=1 \longrightarrow \sin^2x=1-\cos^2x}[/tex]
Thus, the rewritten inequality is [tex]\displaystyle \large{1-\cos^2x>1+\cos x}[/tex]
Notice how the inequality has a quadratic pattern since we have (cosx)^2 and cosx in the inequality, simply arrange degrees in order.
[tex]\displaystyle \large{1-\cos^2x>1+\cos x}\\\displaystyle \large{0>1+\cos x-1+\cos^2x}\\\displaystyle \large{0>\cos x+\cos^2x}\\\displaystyle \large{\cos^2x+\cos x < 0}[/tex]
Then we factor cosx since the expression has cosx as a common factor.
[tex]\displaystyle \large{\cos x(\cos x+1)<0}[/tex]
Then we have to consider each inequalities which are cosx<0 and cosx+1<0 then merge both intervals once obtaining the solutions.
(1) [tex]\displaystyle \large{\cos x < 0}[/tex]
This inequality means that we have to find the x-value(s) that satisfy(ies) it.
Since cosx becomes negative after π/2 (Refer to unit circle, cosx becomes negative in second quadrant and this quadrant), that means it becomes negative until it reaches or < 3π/2.
Thus, [tex]\displaystyle \large{\frac{\pi}{2}<x<\frac{3\pi}{2}}[/tex] is the solution to cosx > 0.
The another way to solve inequality is to find the intersections by solving the equation then joint the interval together.
[tex]\displaystyle \large{\cos x<0 \longrightarrow \cos x=0}[/tex]
From the unit circle, cosx becomes 0 at x = π/2 and x = 3π/2 between interval [0,2π]
Therefore:
[tex]\displaystyle \large{\cos x = 0 \longrightarrow x = \frac{\pi}{2}, \frac{3\pi}{2}}\\\displaystyle \large{\boxed{\frac{\pi}{2}<x<\frac{3\pi}{2}}}[/tex]
(2) [tex]\displaystyle \large{\cos x+1<0 \longrightarrow \cos x <-1[/tex]
For this inequality, it appears that there have no solutions because cosine function is defined between [-1,1] in range hence there are no x-values in real plane that make cosx even less than -1.
Because only π satisfies cosx = -1 but not cosx < -1, we restrict π and every values.
Hence no solutions which cause a break of interval between π and π/2 < x < 3π/2
If you substitute x = π in, the inequality is false and therefore the answer is:
[tex]\displaystyle \large{\frac{\pi}{2}<x<\pi, \pi<x<\frac{3\pi}{2}}[/tex]
Answer:
D.
Step-by-step explanation:
The first two don't work, so it's between the last two.
This equation doesn't work for 180, so the answer is the last choice.
:)
find the total amount due on the simple interest loan if the principle is $3000 with a rate of 5% for 10 years
Step-by-step explanation:
hope it will help you......
How many solutions does the nonlinear system of equations graphed below
have?
O A. Two
O B. Zero
C. One
O D. Four
Answer:
d four
Step-by-step explanation:
How many solutions does the nonlinear system of equations graphed below have?
Look at the number of points where the graphs intersect each other...the points where the graphs of the functions cross each other are the solutions to the system.
Upon looking, you should see 4 points where the graphs intersect, so there are 4 solutions to the non-linear system of equations.
hello need help question below
eric scored 5 more than twice the points that josh did they scored 134 points together what is erics score
Answer:
I believe it'd 69.5
Step-by-step explanation:
if u use the equation 2x+5=134, you get 64.5 for Josh and 69.5 for eric
2 1/2 divided by 5/2
[tex]\dfrac{2 \tfrac 12 }{\tfrac 52}\\\\\\\\= \dfrac{\left(\tfrac 5 2\right)}{\left(\tfrac 52 \right) }\\\\\\\\=1[/tex]
5/50 divided by 15/30 solve it out for me please
Answer:
1/5
Step-by-step explanation:
First and foremost, I want to simplify these fractions, just to make everything a lot easier when I actually get to dividing. 5/50 can be divided by 5/5 to get 1/10, and 15/30 can be divided by 15/15 to get 1/2. So, now we're dividing 1/10 by 1/2.
To divide fractions, we can multiply the first fraction (in this case, 1/10) by the reciprocal of the second fraction (in this case, 1/2). The reciprocal of 1/2 is 2, so we can multiply 1/10 by 2 to find our answer. 1/10 × 2 = 2/10, or 1/5, so this is our final answer.
Hopefully that's helpful! If you have any further questions, let me know. :)
The quotient of given fractions is 1/5.
Given that, 5/50 divided by 15/30.
What are fractions?In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.
Now, 5/50 ÷ 15/30
Keep the first fraction 5/50 same change the division symbol and reciprocate the fraction 15/10
That is, 5/50 × 30/15
= 1/10 × 2/1
= 2/10
= 1/5
Therefore, the quotient of given fractions is 1/5.
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need help math problem give you 5 stars and a good rating if you do this
Answer:
Add 9.6 then divide by 3.2
NO NEED FOR LINKS NEED HELP RIGHT NOW
Answer:
1a.2
2a. 9
3a. 6000
1b. 9000
2b. 3000
3b. 9
Step-by-step explanation:
Hope you could get an idea from here.
Doubt clarification - use comment section.
PLZ answer correctly! Brainliest!
Answer:
[tex]A=\left(-1\dfrac{5}{5}\right)=(-2)\\\\B=\left(-\dfrac{4}{5}\right)\\\\C=\left(\dfrac{3}{5}\right)[/tex]
Step-by-step explanation:
Look at the picture.
[tex]\dfrac{2}{10}=\dfrac{1}{5}[/tex]
a^3/2a^0 simplify pls i need help
Answer:
a^3/2
Step-by-step explanation:
a^3/2a^0
We already know that any value to the zeroth power is 1, so we can start off by rewriting the equation as
a^3/2(1)
We also know that any value multiplied by 1 would result in itself. In this case, 2(1) is 2
Thus, our simplified expression is
a^3/2
You are designing a new, larger coral reef habitat that will stun visitors with its size and vibrant colors. The tank requires special glass to protect this delicate environment. The glass costs $25,000 + a 10% engineering fee + a 5% shipping fee. The shipping fee is calculated on the cost of the glass plus engineering charges. What is the total cost of the glass, including fees?
Answer:
$28,875
Step-by-step explanation:
First, we would have to find 10% of $25,000
10% of $25,000 = $2,500
Now, we have to add the 2 values together
$25,000 + $2,500 = $27,500
Now, we can find the shipping fee, since it includes the engineering fee
5% of $27,500 = $1,375
Now, we can add the shipping fee to find the total
$27,500 + $1,375 = $28,875
Is the sum of 3/5 and v13 a rational or Irrational number
Answer:
The sum of 3/5 and Square root of 13 is irrational. Since square root of 13 is irrational. And when you add it gives u irrational.
Circle A has a circumference of 9 cm. Circle B has a radius of 5 cm.
Which circle has the larger circumference?
About how many centimeters larger is it?
Answer:
B has a bigger circumference.
It is larger by 69.5 cm
Step-by-step explanation:
B: 3.14×5²=78.5
A: 9
Pre college need helppp
Answer:
check online for more information
the sum of three consecutive odd integers is 129. find the integers
Answer:
[tex]\huge\boxed{\sf 41,\ 43, \ 45}[/tex]
Step-by-step explanation:
Let the three consecutive integers be x, x + 2 and x + 4
So, the given condition is:
x + x + 2 + x + 4 = 129
3x + 6 = 129
Subtract 6 to both sides
3x = 129 - 6
3x = 123
Divide 3 to both sides
x = 123/3
x = 41
So, the integers are:
x = 41
x + 2 = 41 + 2 = 43
x + 4 = 41 + 4 = 45
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH18072cosAcosB =
• cos(A + B) + cos(A - B)
• sin(A - B) + tan(A + B)
Answer:
2cosAcosB = cos( A + B ) + cos( A - B )
please help i only have a few minutes left!!
Answer:
VI
Step-by-step explanation:
The letter "A" is a vowel and a capital letter, so this should be categorized in group VI, where the vowel circle and the capital letter circle overlap.
Answer:
F
Step-by-step explanation:
It is a capital letter and a vowel
What is the range of tanx?
1. all real numbers
2. -1 ≤ y ≤ 1
3. y > 0
all real numbers except the 90 and 270 because of cosx
Find the equation of a line whose slope is 6 and passing through (3 , 3 ).
Answer:
y=6x-15
Step-by-step explanation:
y-y1=m(x-x1)
y-3=6(x-3)
y-3=6x-18
y=6x-18+3
y=6x-15
which expression is equal to 4-6
-1-1 or 2-4 or 3-5 or 6-8 or 7-9 or 8-10
2/5 x 7/9 = ( fractions )
Answer:
32/45 is your required answer
Answer:
your answer will be 14/45
Step-by-step explanation:
2/5 × 7/9
= 2 × 7
5 × 9
= 14/45
Pls help plz thank you
Answer:
14, 31, 62
Step-by-step explanation:
11 + 3 = 14
14*2 = 28
28 + 3 = 31
31*2=62
: West Gorham High School is to be located at the population center of gravity of three communities: Westbrook, population 16,000; Scarborough, population 22,000; and Gorham, population 36,500. Westbrook is located at 43.6769˚N, 70.3717˚W; Scarborough is located at 43.5781˚N, 70.3222˚W; and Gorham is located at 43.6795˚N, 70.4447˚W.
a. Where should West Gorham High School be located?
b. If only two pieces of adequate land are available for sale: Baker’s Field at 43.6784˚N, 70.3827˚W; or L onesome Acres at 43.5119˚N, 70.3856˚W, using rectilinear distances, which is closer to the site located in part (a)?
Answer:
(a) 43.6490°N, 70.3928°W
(b) Baker's Field
Step-by-step explanation:
The locations are all within a 7-mile square, so we will make the assumption of a flat Earth with parallel longitude lines. Then the "central" location will be the weighted average of the latitude and longitude coordinates.
(a)Total population is 16000 +22000 +36500 = 74,500. For purposes of the arithmetic, we will subtract 43 from latitude and 70 from longitude, then multiply each fraction by 10. Similarly, we will divide each population by 1000.
The weighted average location is found from ...
(16/74.5)(6.769, 3.717) +(22/74.5)(5.781, 3.222) +(36.5/74.5)(6.795, 4.447)
= (1.4537, 0.7983) +(1.7071, 0.9515) +(3.3291, 2.1787) = (6.490, 3.928)
The center of gravity is about 43.6490°N, 70.3928°W.
__
(b)The coordinate differences from the center of gravity are (in (°lat, °long)) ...
Baker's Field: (0.0294, -0.0101)
Lonesome Acres: (-0.1371, -.0072)
Clearly, Baker's field is closer to the site of part (a).
_____
Additional comment
Distance calculations could be refined further by considering that a degree of longitude at this latitude represents about 0.72 times the distance of a degree of latitude. In this problem, the location of Lonesome Acres has a latitude difference that is several times any of the other coordinate differences, so it is clearly much farther away from the desired location.
The calculations done here are a sort of first-level approximation. The least-significant digits in the coordinates represent a distance of less than 50 feet. If you really want accuracy to that level, then the (approximately) spherical shape of the Earth needs to be accounted for. As a second-level approximation, some reference point needs to be identified, and coordinates in miles (or feet) need to be expressed in relation to that reference. The best accuracy would be obtained using spherical trigonometry to identify the distances.
We expect any school that is constructed to be somewhat larger than 50 feet in any direction, so accuracy to the 4th decimal place in these locations is probably not required--except to satisfy some answer-checker.
which one is great 10% or 1.0- which on is greater 30% or 1/3- which one is greater 0.9 or 95%- which one is greater 80% or 5/8
Answer:
see exp
Step-by-step explanation:
1.0, 1/3, 95%, 80%
Write the missing volues to make these equivalent fractions correct.
2/3 = 4/ = /12
Answer:
2/3 = 4/6 = 8/12
Step-by-step explanation:
Tara stayed at the Merry Mountain campgrounds last weekend. She paid a rental
fee to use a kayak for 4 days. She also paid $18 for a guided waterfall tour. Tara
paid $94 in all. What was the rental cost of each day Tara used the kayak?
Answer:
she will pay $19 for each day
Step-by-step explanation:
94-18=76
76÷4=19
The rental cost of each day Tara used the kayak is $19 if Tara stayed at the Merry Mountain campgrounds last weekend. She paid a rental fee to use a kayak for 4 days.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
Tara stayed at the Merry Mountain campgrounds last weekend. She paid a rental fee to use a kayak for 4 days.
Let x be the rental cost of each day Tara used the kayak.
4x + 18 = 94
4x = 94 - 18
4x = 76
x = 76/4
x = $19
Thus, the rental cost of each day Tara used the kayak is $19 if Tara stayed at the Merry Mountain campgrounds last weekend. She paid a rental fee to use a kayak for 4 days.
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What is a 15% tip on a meal that costs $38.40?
Answer:
its $5.76
Step-by-step explanation:
because $38.40 / 15 is $5.76