The mean and the standard deviation are 16.15 and 12.03, respectively
How to determine the mean and the standard deviation?The table of values is given as:
Work hours Frequency
0 - <10 45
10 - <20 33
20 - <30 20
30 - <40 7
40 - <50 8
Start by rewriting the table using the midpoint of each class
x f
5 45
15 33
25 20
35 7
45 8
The mean is then calculated as:
[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]
This gives
[tex]\bar x = \frac{5 * 45 + 15 * 33 + 25 * 20 35 * 7 + 45 * 8}{45 + 33 + 20 + 7 + 8}[/tex]
Evaluate the sum and the products
[tex]\bar x = \frac{1825}{113}[/tex]
Divide
[tex]\bar x = 16.15[/tex]
The standard deviation is:
[tex]\sigma =\sqrt{\frac{\sum f(x - \bar x)^2}{\sum f}}[/tex]
This gives
[tex]\sigma= \sqrt{\frac{45 * (5 - 16.15)^2 + 33 * (15 - 16.15)^2 + 20 * (25 - 16.15)^2 + 7 * (35 - 16.15)^2 + 8 * (45 - 16.15)^2 }{45 + 33 + 20 + 7 + 8}}[/tex]
Evaluate the sum and the products
[tex]\sigma= \sqrt{\frac{16350.4425}{113}}[/tex]
Divide
[tex]\sigma= \sqrt{144.694181416}[/tex]
Take the square root
[tex]\sigma= 12.03[/tex]
Hence, the mean and the standard deviation are 16.15 and 12.03, respectively
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5, 3.1.24
f(x) = 3x² + 5; find f(x + 3) - [f(x) + 3]
Given that [tex]f(x) = 3x^2 + 5[/tex], we have
[tex]f(x + 3) = 3 (x + 3)^2 + 5 \\\\= 3 (x^2 + 6x + 9) + 5 \\\\= 3x^2 + 18x + 32[/tex]
so that
[tex]f(x+3) - (f(x) + 3) = (3x^2 + 18x + 32) - (3x^2 + 8) \\\\= \boxed{18x + 24}[/tex]
EAsy math challenge! Click me!
Answer:
the answer is 64
Step-by-step explanation:
now atleast mark me brainliest answer
5m³ into cm³
Show the answer step by step
Answer: So you want to convert 5 cubic meters into cubic centimeters? If you're in a rush and just need the answer, the calculator below is all you need. The answer is 5000000 cubic centimeters.
Step-by-step explanation:
What is the inverse of p>q
Inequalities help us to compare two unequal expressions. The inverse of p>q is p<q.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.
It is mostly denoted by the symbol <, >, ≤, and ≥.
Given the inequality that p is greater than q, therefore, the inverse of it will be p smaller than q. Thus, The inverse of p>q is p<q.
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A bag of 20 marbles consists of 5 blue marbles, 4 red marbles and 9 yellow marbles. You draw a marble out of the bag, put it back then draw out another marble. Calculate the probability you will draw a blue marble on your first draw and then draw a blue marble on your second draw? Write your answer a percentage to the nearest hundredth.
The probability you will draw a blue marble on your first draw and then draw a blue marble on your second draw is 0.063.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
Total marbles = 20
Number of blue marbles = 5
P(blue) = 5/20
P(blue∩blue) = P(blue)×P(blue)
= (5/20)(5/20)
= 25/400
= 1/16
= 0.0625 ≈ 0.063
Thus, the probability you will draw a blue marble on your first draw and then draw a blue marble on your second draw is 0.063.
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Find the area of the shaded portion of the
figure. All angles are right angles.
Dimensions are in inches.
3
8
5
======================================================
Explanation:
The white rectangle is 3 by 6 with area of 3*6 = 18 square inches.
The larger rectangle is 8 by 5 with area of 8*5 = 40 square inches.
The difference of these will get us the shaded area:
40 - 18 = 22 square inches
what is it asap please
for what value of k will the relation not be a function
R={(k-8.3+2.4k,-5),(3/4k,4)}
Step-by-step explanation:
hope you can understand
The velocity of a car over five hours is given by v(t)=60ln(t+1),0≤t≤5 in kilometers per hour. What is the total distance traveled from t=0 to t=5? Round your answer to the nearest whole number and do not include units.
Step-by-step explanation:
as the velocity is not constant over time, we actually have to integrate v(t) over the interval 0<=t<=5 to get the distance.
v(t) = 60×ln(t + 1)
V(t) = 60 × integral(ln(t + 1)) between 0 and 5.
integral(ln(t + 1)) = (t + 1)ln(t + 1) - t + C
V(t) = 60 × ((t + 1)ln(t + 1) - t + C)
the distance traveled between t = 0 and t = 5 is then
60 × ((5 + 1)ln(5 + 1) - 5 + C) - 60 × ((0 + 1)ln(0 + 1) - 0 + C) =
= 60×(6ln(6) - 5 + C) - 60×(1ln(1) + C) =
= 60×(5.750556815... + C) - 60×C =
= 60×5.750556815... = 345.0334089... ≈ 345 km
what is the general term for sequence -6;3;15;30?
Answer:
[tex] \frac{3}{2} n {}^{2} + \frac{9}{2} n - 12[/tex]
Step-by-step explanation:
This sequence is a quadratic sequence meaning that we should find the difference and the constant second difference.
The difference between the 4 terms is in the sequence:
9;12;15
The constant second difference is 3.
Use your method of finding the general term:
2a=3 3a+b=9 a+b+c=-6
a=3/2 3(3/2)+b=9 3/2+9/2+c=-6
b=9/2 c=-12
Standard form for quadratic sequence:
[tex] {an}^{2} + bn + c[/tex]
Therefore your general term is the one stated above in the answer.
Hope that helps!
Please help !!! I will give 20 points to correct answer !!!!
Answer:
the answer above the image
Answer:
a=-4/3, 14/3
Step-by-step explanation:
absolute value only makes the answer become positive whether the value inside is negative or positive.
so -3a+5=9 or -3a+5=-9 all works
-3a+5=9
-3a=4
a=-4/3
If -3a+5=-9
-3a=-14
a=14/3
Discriminat step by step of x^2+4x+5=0
Answer:
-4
Step-by-step explanation:
x^2+4x+5=0
a=1,b=4^1 C=5
4^2-4×1×5
-4
Let's say that the turkey sat on the counter for an additional hour (beyond the 390 minutes) and its temperature cooled to 80 degrees. Write that value in function notation
The value of the temperature in function notation is gotten as; f(x) = 91 - 11x
How to write a function Notation?Let us first find the relationship between temperature and how long the turkey sits out.
The temperature after the normal 390 minutes is equal to approximately 6.5 hours.
Let us create a ratio and solve for x, which represents the temperature change during that extra hour after the "normal time sitting out".
Thus;
(7.5/6.5) = (80/80+ x)
Solving for x gives x = -10.7.
This means that for every extra hour it sits out, the turkey cools approximately 11°. When we add that to 80°, we have 91° which is the expected temperature after 390 minutes (6.5 hours) of sitting out.
Thus, the motion as a function of time is;
f(x) = 91 - 11x
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The vehicle preference of police officers and firefighters is given in the table.
Police Officers Firefighters
Cars 12
Trucks 9
SUVS 15
3
4
2
Based on the information in the table, which of the following is an example of independent events.
An example of independent events is P(Police Officers and choose cars).
Which pair of events are called independent events?When one event's occurrence or non-occurrence doesn't affect the occurrence or non-occurrence of another event, then such events are called independent events.
Symbolically, we have:
Two events A and B are said to be independent if we have:
P(A ∩ B) = P(A)P(B)
Police Officers Firefighters
Cars 12 3
Trucks 9 4
SUVs 15 2
Let P(A) = Firefighters choose cars
P(B) = Firefighters choose Trucks
P(A ∩ B) = Police Officers choose cars
Thus,
P(A ∩ B) = P(A)P(B)
12 = (4) ( 3)
Hence, an example of independent events is P(Police Officers and choose cars).
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is y=6x-3 a function
Yes it is
Step-by-step explanation:
it is a linear function as it is written in the standard form Y=MX+C
Determine the equation of the line with slope m=2/3, passing through the point (0,4)
Answer:
y = 2/3x + 4
Step-by-step explanation:
The slope-intercept form is y=mx+b. m (the slope) is equal to 2/3, so you can substitute that number in for m. B is the y value of the y-intercept. The y-intercept is (0,4) as given in the problem, so the value of b is 4. You can substitute that value into the equation as well.
Boxes of tins are delivered to a shop. There are 37 boxes. Each box contains 25 tins. How many tins are there?
Answer:
Step-by-step explanation:
it equal 925 tins in total when you multiply 37 times 25. Hope that helps
Samantha is 9 years younger than her brother Maurice. In 10
years, Maurice will be 1.5 times older than his sister. Find their
present ages.
Step-by-step explanation:
hope you can understand
Answer:
Samantha is 8 years and Maurice is 17 years
Step-by-step explanation:
First represent Samantha's brother's age with a variable, x.
Secondly, find Samantha's age. since shes 9 years younger, then it will be her brother's age which is x minus 9
Thirdly, in ten years, they will all age hence 10 will be added to all their ages.
Fourthly, once 10 has been added to their after 10 years, rhen we realise Maurice age will be 1.5 timess Samantha's age... Then you solve the resulting equation.
why is smallest possible angle of a 36-gon 5 degrees instead of 4.72222222222?
The smallest interior angle of the given regular polygon with 36 sides is; 170°
How to find the sum of interior angles of a polygon?The formula for calculating the sum of interior angles of a regular polygon is; S = (n − 2) × 180°
where n is number of sides of the polygon
We are told that number of sides of ploygon is 36. Thus;
S = (36 - 2) × 180°
S = 6120°
Thus;
Smallest possible angle of polygon = 6120/36 = 170°
Sum of external angles of a regular polygon is;
S = 360/n
S = 360/36
S = 10°
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The function y=(x-4)2+3 is a transformation of the function y=x2. How is the functions vertex affected by the transformation?
It is shifted 4 units right and 3 units up.
Tim has 9 pencils in his book bag. Jaime has 3 more pencils than Tim. Which of the following equations would describe n, the number of pencils that Jaime has in her book bag?
The functions f(x) = x2 – 2 and g(x) = –x2 + 5 are shown on the graph.
The graph shows f of x equals x squared minus 2, which is an upward opening parabola with a vertex at 0 comma negative 2 and a point at negative 1 comma negative 1 and a point at 1 comma negative 1. The graph also shows g of x, which is a downward opening parabola with a vertex at 0 comma 5 and a point at negative 1 comma 4 and a point at 1 comma 4.
Explain how to modify the graphs of f(x) and g(x) to graph the solution set to the following system of inequalities. How can the solution set be identified?
y > x2 – 2
y ≥ –x2 + 5
We will need to shade the region above f(x) and the region below the function g(x)…
How to transform the graph into the solution set?We have:
f(x) = x² - 1
g(x) = -x² + 4
Both of these are already graphed, and we want to transform it into:
y > f(x)
y ≤ g(x)
The first inequality means that we need to graph f(x) with a dashed line, because f(x) is not part of the solution, and then we shade all the region above f(x)…
For the other inequality, we use a solid line (because the points on the line are solutions) and then we shade the part below the curve…
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The graph of a function is shown on the coordinate plane below.
Between which two values of x is the function nonlinear and increasing?
A -5 and -3
B -3 and 1
C 1 and 4
D 4 and 6
The answer to this question is choice B
the product of a quarter of 3 more than a number a and 2 times a number b
Answer:
[tex] \frac{1}{4} (3a + 2b)[/tex]
The expression from the given condition is 1/4(3a+4b).
We have given that,
The product of a quarter of 3 more than a number a and 2 times a number b.
What is the quarter?
The quarter means divided into four equal or corresponding parts.
Therefore we get the expression from the given condition is
1/4(3a+4b).
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A consultant needs to make at least $600 this week. She earns $120 for each
new written piece and $60 for each review. Which of the following inequalities
represents the possible combinations of reviews and new written pieces that
she must complete?
OA. 120x+60 y ≤ 600
OB. 120x+60y < 600
O C. 120x+60y 2 600
OD. 120x+60y > 600
SUBMIT
algebra 2 help needed image below urgent !!!
Answer:
Domain = x ≥ 0
Range = y ≥ 20
Step-by-step explanation:
The equation in slope-intercept form would look like this:
y = 4x + 20
The slope is $4 because that is the money that can be made depending on the week. Because he received a random $20 at the beginning, this is just an additional income.
---------------------------------------------------------------------------
In this scenario, the domain (x-values) represent the number of weeks. The range (y-values) represent the total money made.
So the domain is asking, what is the lowest/highest amount of weeks he can save for? We know the number of weeks cannot be negative because he can't save for negative weeks. However, he could save for zero weeks. He can be saving for theoretically infinite weeks. Therefore, the domain is x ≥ 0.
The range is asking, how much money can he save? Since he starts out with a baseline of $20, this is the lowest amount of money he can have. If he were to save for an infinite amount of weeks, he could make an infinite amount of money. Therefore the range is y ≥ 20.
A survey of 600 randomly selected high school students determined that 290 play organized sports. what is the probability that a randomly selected high school student plays sports
Answer:
29/60
Step-by-step explanation:
probability of playing is 290/600 which when simplified is29/60
It takes 70 pounds of seed to completely plant an 8-acre field. How many acres can be planted per pound of seed?
No. of pounds of seed it takes to plant an 8-acre field = 70 pounds.
No. of acres can be planted per pound of seed = 70/8
= 8.75.
thus, 8.75 acres can be planted per pound of seed.
Need help with this geometric question
Answer: QN=19
Step-by-step explanation:
Diagonals of an isosceles trapezoid are congruent, so NQ=PM.
By the segment addition postulate, NQ=QR+RN=3x+7.
So,
[tex]6x-5=3x+7\\\\3x-5=7\\3x=12\\\\x=4[/tex]
So, [tex]QN=3(4)+7=\boxed{19}[/tex]
Isabella is making a scrapbook each page of the scrapbook is a square with a length of 11 in if each page holds three pictures that each have an area of 15 in squared what is the remaining area on each page and square inches that can be used for decoration
The remaining area of the page will be 80 square inches.
The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the square in a two-dimensional plane is called the area of the square.
The area of the remaining part will be calculated as;-
Area of the square page will be = 11 x 11 = 121 square inches.
Area of three pictures will be = 15 x 3 = 45 square inches.
So the remaining area will be = 121 - 45 = 80 square inches.
Therefore the remaining area of the page will be 80 square inches.
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