The variance and standard deviation for the given frequency of pupils per teacher in some states of US is
Variance= 4.62 = 4.6
Standard Deviation = 2.14 = 2.1
The frequency distribution shows the average number of pupils per teacher in some states of the United States.
Variance(σ²) is a measure of dispersion. A measure of dispersion is a quantity that is used to check the variability of data about an average value. Data can be of two types - grouped and ungrouped. When data is expressed in the form of class intervals it is known as grouped data. On the other hand, if data consists of individual data points, it is called ungrouped data. The sample and population variance can be determined for both kinds of data.
The standard deviation(σ) of a random variable, sample, statistical population, data set, or probability distribution is the square root of its variance. It is algebraically simpler, though in practice less robust, than the average absolute deviation.
That means Standard Deviation = √variance.
For the given data the sum of frequencies(ni) = 1+16+11+7+1+2= 38.
Midpoint(mi) is 12,15,18,21,24,27.
ni * mi = 12,240,198,147,24,54.
Sum of ni * mi = 675.
Mean (u) = 17.76
mi - u is -5.76,-2.76,0.24,3.24,6.24,9.24.
(mi - u)^2 is 33.17,7.61,0.057,10.49,38.93,85.37.
Sum of (mi - u)^2 = 175.62.
Variance = Sum of (mi - u)^2 / sum of frequencies
=> 175.62/38
=> 4.62 = 4.6.
Standard deviation = √variance.
=> √4.62
=> 2.14 = 2.1.
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The graph of the function f(x) = –(x + 6)(x + 2) is shown below.
On a coordinate plane, a parabola opens down. It goes through (negative 6, 0), has a vertex at (negative 4, 4), and goes through (negative 2, 0).
Which statement about the function is true?
The function is increasing for all real values of x where
x < –4.
The function is increasing for all real values of x where
–6 < x < –2.
The function is decreasing for all real values of x where
x < –6 and where x > –2.
The function is decreasing for all real values of x where
x < –4.
The correct statement about the given function is: The function is increasing for all real values of x where x < –4.
In this question, we have been given the graph of the function
f(x) = -(x + 6)(x + 2)
According to description of the graph of given function f(x), the graph of function is a parabola and on a coordinate plane, a parabola opens down.
Also, the parabola goes through (-6, 0), has a vertex at (-4, 4), and goes through (-2, 0).
We need to find to the correct statement about the function.
f(x) = -(x + 6)(x + 2)
The function is increasing until it reaches the vertex x = -4.
The function will decrease after the vertex, so after x = -4 function decreases.
increasing: -∞ < x < -4
decreasing : -4 < x < ∞
Therefore, the correct statement about the given function is: The function is increasing for all real values of x where x < –4.
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30 POINTS Graph the solution to this inequality on the number line. 1/2 x - 3 < -1 3/8
The graphing is achieved as follows:
On the graph the third sign counting from the left is used.
This is placed on the first mark of the three marks between 3 and 4. This point equivalent to 3 1/4 or 3.25
How to find the solution of the equation
Given data
the graph
and the equation 1/2 x - 3 < -1 3/8
solving for x gives
1/2 x - 3 < -1 3/8
1/2 x < 3 -11/8
x/2 < 13/8
x < 13 / 4
x < 3 1/4
On the graph the third sign counting from the left is used.
The arrow is facing left, this is to show the sign less than.
The tail has a hollow not a solid point to show that equality sign is not included.
This is placed on the first mark after point 3 as this is the point equivalent to 3 1/4 or 3.25
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8 feet
The largest possible circle is cut out of a square whose side length is 8 feet. What will be the approximate area, in square feet, of
the remaining board? (4=r2 where = 3.14)
0 5f²
O 10 ft²
O 15 ft2
○ 20 ft²
C
Answer:
50.24sqft
Step-by-step explanation:
side = 8ft
that means that the circle diameter will be 8ft
the radius will be half the diameter, so 4ft
the area of the circle is
[tex]\pi r^2 = \pi \cdot (4ft)^2 \approx 3.14 \cdot 16sqft = 50.24sqft[/tex]
Isla has $30 to spend on treats for her kindergarten class. She wants to buy her students cookies, c, and popsicles, p. Each box of cookies costs $5.50 each, and each bag of popsicles costs $3.00 each. If she must buy 3 bags of popsicles, which inequality could be used to determine the maximum number of boxes of cookies she can buy?
a
A
b
B
c
C
d
D
Answer:B
Step-by-step explanation:because she might buy more cookies but we dont know she we dont multiply it by anything but the cookies we multiply that by 3 so thats why it doesn't have p because we know how much she's getting the reason its not a is because it says greater or equal to we dont want to go over 30 we want to be equal or less than 30
hope this helps :}
Suppose you had d dollars in your bank account. You spent $14 but have at least $48 left. How much money did you have initially? Write and solve an inequality that represents this situation.
The inequality that represents this situation is d - 14 >= 48 and the solution is d >= 62
How to write and solve an inequality that represents this situation.The given parameters are:
Initial amount = d
Spent = 14
Amount left = at least 48
The above means that
d - 14 = at least 48
at least 48 means greater than or equal to 48
So, we have
d - 14 >= 48
Add 14 to both sides
d >= 62
Hence, the inequality that represents this situation is d - 14 >= 48 and the solution is d >= 62
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How to spell 737 in number form
Answer:
737 or seven hundred thirty-seven
Step-by-step explanation:
Simplify 2x + x
Show your work
Answer:
Step-by-step explanation:
=2x+1x
=(2+1)x
=3x
Find the weighted mean. Round your answer to one decimal place.
Deliveries Per Week
Frequency
2
4
6
8
Weighted mean =
Question Help:
5
4
2
7
deliveries per week
I
Enter an integer or decimal number [more..]
Merrage instructor
The weighted mean as 5.22 for the data given for deliveries per week and the frequency of the deliveries.
We are given the data:
Deliveries Per Week (X) Frequency (Y) X Y
2 5 10
4 4 16
6 2 12
8 7 56
Sum 18 94
We need to find the mean.
Mean = Sum of observations / Number of observations.
Mean = 94 / 18
Mean = 5.22
Therefore, we get that, the weighted mean as 5.22 for the data given for deliveries per week and the frequency of the deliveries.
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what is 17 + 1? And 16 divided by 2?
17+1=18 and 16÷2=8
It's pretty self explanatory? I mean you could just look at it, and know the answer.
Answer:
the answer is : 18 and 8
what is the equivalent fraction of -3.2
Answer:
- 3 and 1/5
Step-by-step explanation:
Answer: - 16 / 5
Step-by-step explanation:
EASY Question 20 POINTS
Answer:
2 option
Step-by-step explanation:
im right
Answer:
No.2
Step-by-step explanation:
$
5.79 for 4 quarts
dollars per quart
quarts per dollar.
Answer:
1.45 dollars per quart.
0.69 quarts per dollar.
Explanation:
To find dollars per quart,
5.79 ÷ 4 = 1.4475
Round to the nearest hundredth; 1.4475 -> 1.45
-
To find quarts per dollar,
4 ÷ 5.79 = 0.6908462867
Round to the nearest hundredth; 0.6908462867 -> 0.69
Dividing was all you needed!
Find the AREA of the triangle formed by the x-axis, the y-axis and
the line y = 2x + 4
Remember that the area of a triangle is: A = (base) (height)
Hint: Sketch the graph using x- and y-intercepts.
square units
Area =
the x-axis, the y-axis and
the line y = 2x + 4
Remember that the area of a triangle is: A = (base) (height)
Hint: Sketch the graph using x- and y-intercepts.
square units
Ar
I’m really not understanding what the next step is or what I did wrong. if anyone could help that would be appreciated:)
The vehicle will get speed of approximately 15 mph and -210 mph.
What is speed?Science's most important concept is measurement. Many measurable quantities are measured in fundamental or base units. One such measurable quantity is speed, which is defined as the ratio of an object's distance travelled to the time required to travel that distance. Let us learn about speed in depth during this session.
The ratio of distance to time taken to cover a distance is used to calculate speed. Because it only has one direction and no magnitude, speed is a scalar quantity.
Given the equation for gas mileage = 0.02x² + 3.9x - 43 where x means speed
We have been asked to find x if gas mileage = 20 that is
0.02x² + 3.9x - 43 = 20
Lets simplify
⇒ 0.02x² + 3.9x - 43 = 20
⇒ x² /50 + 39x/10 - 63 = 0
⇒ x²/ 50 + 195x/50 - 3150 = 0
⇒ 1/50 (x + 195x - 3150 ) = 0
⇒ 1/50 (x + 210x - 15 x - 3150 ) = 0
⇒ 1/50 (x (x+210) −15 (x+210)) = 0
⇒ 1/50 (x−15)(x+210) = 0
⇒ (x−15)(x+210) = 0 × 50
⇒ (x − 15)(x + 210) = 0
⇒ x = 15, x = -210
So, try using 15 mph and -210 mph, that might work.
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In Exercises 6-10, use the diagram.
6. Find the perimeter of AABC.
7. Find the perimeter of quadrilateral
ACDE.
8. Find the area of AABC.
9. Find the area of quadrilateral
ACDE.
10. Find the area of pentagon ABCDF.
B(-1,5) Y
A(-4, 3)
2
F(-4,-3)
-2-
N
E(-2,-3)
C(2, 3)
2 4 X
D(4,-3)
Answer: 5
Step-by-step explanation:
The temperature readings for 20 days at 4 AM at a local ski resort were recorded as follows: 24° −10° 9° 18° 23° 27° 8° 17° 3° 7° −2° −6° 2° −9° −8° 21° 25° 15° 10° 29° What was the average of the recorded temperatures for these 20 days? Do not round your answer.
Based on the temperature readings, the average recorded temperature in the 20 days was 10.15°
What was the average temperature?The average temperature can be found by adding all the temperatures and then dividing by the number of temperatures taken which is 20.
The average is therefore:
= 24° + (−10°) + 9° + 18° + 23° + 27° + 8° + 17° + 3° + 7° + ( −2°) + (−6°) + 2° + (−9°) + (−8°) + 21° + 25° + 15° + 10° + 29°) / 20
= 203 / 20
= 10.15°
In conclusion, the average temperature was 10.15°.
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The student activities office has four students who work part-time on a work-study program. Three of the students work
17 hours per week, 19 hours per week, and 16 hours per week. The office policy is that the average number of hours
students work per week in the student activities office is less than 17.5 hours. What is the restriction for the number of
hours that the fourth student can work?
Answer:
less than 18 hours
Step-by-step explanation:
You want the restriction on the fourth value such that the average of it and 17, 19, and 16 will be less than 17.5.
Average valueThe average of a set of numbers is their sum, divided by the number of numbers. The average of the four students' hours will be ...
(17 +19 +16 +h)/4 < 17.5 . . . . . . restriction on average hours
SolutionMultiplying by 4 gives ...
52 +h < 70
h < 18 . . . . . . . . subtract 52
The fourth student can work less than 18 hours.
three answers !
please help me i need to finish this today :((
Answer:
Your answer should be 90 degrees for angle one. For angle two, 58 and angle three 32.
Step-by-step explanation:
This is because they are supplementary angles! I hope this helps. Xx
Answer: ∠1 = 90°
Step-by-step explanation:
∠1 = ∠4
∠2 = ∠5
∠3 = ∠6
reason = vertically opposite angle
∠1 = 90°
∠2 = 58°
∠3 = 32°
checking :
total angles = 360°
360° = ∠1 + ∠2 + ∠3 + ∠4 + ∠5 + ∠6
360° = 90° + 58° + 32° + 90° + 58° + 32°
360° = 360°
What's the correct answer?
Answer- D = (equal sign)
Explanation-
When you see two straight lines in math | | with number inside, regardless if the number inside is positive or negative, the outcome will be positive. This is called the absolute value. After we solve our absolute value however, there is a negative on the outside, which means that 61 will become negative again. Our equation is now -61 _____ -61. Your correct choice will be the equal sign, since -61 is equal to -61.
HOPE THIS HELPS GOOD LUCK!
I need help with #55.
Answer:change
Step-by-step explanation:
1 change them
2 switch sides
3 move the colors
WILL MARK BRANLIEST !!!!
For each line, determine whether the slope is positive, negative, zero, or undefined.
Answer: 1st is positive 2nd is negative 3rd and 4th are undefined or 0
Step-by-step explanation:
Answer:
1.positive
2.undefine
3.positive
4.negative
fill in the blanks to find x line ab is a straight line(Please show your work)
Statement Reason
1. m<AOB = 180 degrees Angle on a straight line
2. m<AOE + m<EOF + m<FOB = m<AOB supplementary angles
3. x + 2x + 34° + 20° = 180 degrees Substitution
4. x = 42 degrees Algebra
How to solve for the missing angle xx + 2x + 34° + 20° = 180 degrees - supplementary angles
3x + 54 = 180
3x = 180 - 54
3x = 126
x = 126 / 3
x = 42 degrees
What is angle on a straight line?
This refers to angle formed by a straight line which is equal to 180 degrees.
What are supplementary angles?
This refers to angles whose sum is equal to 180 degrees. Sum of angles on a point on a straight line is equal to 180 degrees
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27. You are driving on the interstate with your cruise control on at a constant speed of 64 miles per hour.
Use the number lines below to determine how long it will take to drive to the next rest sop that is 16
miles away (see textbook, page 20). Explain the thinking you used to determine your answer.
The car will take 15 minutes to drive to the next stop which is 16 miles away.
As per the question statement, we are supposed to find the time taken by the car to drive to the next stop which is 16 miles away if it is driving on the interstate with cruise control on at a constant speed of 64 miles per hour.
Before solving the question, we need to know the concept of relation between time, distance and speed, which states that
[tex]speed=\frac{distance}{time}[/tex]
In the question [tex]speed = 64 mph\\distance = 16 miles\\time taken = t[/tex]
Substituting values in the formula above,
[tex]64=\frac{16}{t} \\t=\frac{16}{64} \\t=0.25 hours =0.25 *60\\t=15 minutes[/tex]
Hence the time taken by car to drive to the next stop which is 16 miles away is 15 minutes or [tex]\frac{1}{4}[/tex] hours.
Cruise control: An electrical device called cruise control makes it possible to lock the accelerator of a moving car at a particular pace.To learn more about speed and distances, click on the link given below:
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What is the 19th term of the sequence:
gn=gn−1⋅(−12) if g17=162
the sixth term is ______
This is an arithmetic sequence
The nth term of an arithmetic sequence is Tn = a + (n-1)d
a is the first term.
n is the number of terms
d is the common difference
Given that 19th term of the sequence is:
gn=gn−1⋅(−12) if g17=162
Suppose a=12
Then,
The 17th term g17=a+(n-1)d
= 12+(17-1)d
'n' means number of terms
12+(17-1)d=162 because g17=162
12+16d=162
16d=162-12
Subtract the values,
We can write,
16d=150
d=150/16
Divide the values,
We can write,
d=25
To get the sixth term g6
g6=12+(6-1)d
=12+5d
Replace with d value in above equation,
Then, g6=12+5(25)
g6=12+125
g6=137
So, the sixth term is g6=137.
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What is the midpoint of the segment?
(-6, 5) and (-6, 8)
Greetings from Brasil...
The expression that allows calculating the midpoint is:
M = [(X₁ + X₂)/2 ; (Y₁ + Y₂)/2]
X₁ = - 6
X₂ = - 6
Y₁ = 5
Y₂ = 8
then
M = [(- 6 + (- 6))/2 ; (5 + 8)/2]
M = [(- 12)/2 ; 13/2]
M = (- 6; 13/2)Answer:
(−6,6 1/2)
Step-by-step explanation:
Calculate the midpoint, using the midpoint formula:
In decimal form, it would be (-6,6.5).
Brian had a collection of 25 toy cars. Each month his grandpa buys him a new one. Identify the slope.
y=mx+b
y=1x+25--> equation
m=slope
b=y-intercept
slope is 1
pls answer if wrong reported
Answer: 48
I hope this helps!
QUESTION IN IMAGE, WILL GIVE BRAINLIEST AND LOTS OF POINTS
Answer:
Option 1
Step-by-step explanation:
(3)(-17.25) = -51.75, he withdrew $51.75.
3 because he withdrew a total of 3 times.
-17.25 because he was taking out money.
Answer:(3)(-17.25)= -51.75
Step-by-step explanation:
The new dolphin tank at the city aquarium is in the shape of a rectangular prism. It is 25 yd long by 14yd wide by 5yd deep. To make the tank livable for the dolphins, the aquarium workers treat the water using bags of salt. The amount of water a bag of salt can treat is known in cubic feet.
The amount of water a bag of salt can treat is 47, 250 cubic feet
How to determine the volumeThe formula for volume of a rectangle is expressed as;
Volume = length × width × height
From the information given, we have the following parameters;
Length = 25 yardsWidth = 14 yardsHeight = 5 yardsSubstitute the values into the formula
Volume = 25 × 14 × 5
Find the product
Volume = 1750 cubic yards
Covertoing cubic yard to cubic feet
I cubic yard = 27 cubic foot
1750 yards = x
x = 27 × 1750
x = 47, 250 cubic feet
Thus, the amount of water a bag of salt can treat is 47, 250 cubic feet
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The average annual cost of living in State A, State B, and State C are displayed in the
table below.
Average Annual
Cost of Living
$44,400 =A
$62,000 = B
$55,600 = C
Suppose you were offered a job in State B that pays $117,200.
How much is this equivalent to in State A? Round your answer to the nearest whole
dollar.
The equivalent income in City A given the average annual cost of living in City A and city B is $163,658.
What is the equivalent income?The first step is to determine the ratio of the average cost of living in State A and State B. Ratio is used to show the relationship that exists between two or more values.
Cost of Living in City B / Cost of Living in City A
$62,000 / $44,400 = 1.39640
Multiply the ratio gotten in the previous step by the offered salary in State B : 1.39640 x $117,200 = $163,658
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