The approximations of the mean and the standard deviation are 233.3 and 229.82, respectively
How to determine the mean?The table of values is given as:
Savings Lower Limit Upper Limit Frequency
0-199 0 199 345
200-399 200 399 97
400-599 400 599 52
600-799 600 799 21
800-999 800 999 9
1000-1199 1000 1199 8
1200-1399 1200 1399 3
Rewrite the table to include the class midpoint and the frequency
x f
99.5 345
299.5 97
499.5 52
699.5 21
899.5 9
1099.5 8
1299.5 3
The mean is calculated as:
[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]
So, we have:
[tex]\bar x = \frac{99.5* 345 + 299.5* 97 + 499.5* 52 + 699.5 * 21 + 899.5 * 9 + 1099.5 * 8 + 1299.5 * 3}{345 + 97 + 52 + 21 + 9 + 8 +3}[/tex]
Evaluate
[tex]\bar x = 233.331775701[/tex]
Approximate
[tex]\bar x = 233.3[/tex]
Hence, the approximation of the mean is 233.3
How to determine the standard deviation?The standard deviation is calculated as:
[tex]\sigma = \sqrt{\frac{\sum f(x - \bar x)^2}{\sum f}}[/tex]
So, we have:
[tex]\sigma= \sqrt{\frac{(99.5-233.3)^2* 345 + (299.5-233.3)^2* 97 +...... + (1299.5 -233.3)^2* 3}{345 + 97 + 52 + 21 + 9 + 8 +3}[/tex]
Evaluate
[tex]\sigma = 229.82[/tex]
Hence, the approximation of the standard deviation is 229.82
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Transportation officials tell us that 60% of drivers wear seat belts while driving. Find the probability that more than 562 drivers in a sample of 900 drivers wear seat belts.
The probability that more than 562 drivers is 0.9328
What is probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given: p = 0.60
n = 900
Let X denote the number of drivers that wear a seat belt,
P(X > 562)
[tex]\mu[/tex] = n*p = 900(0.60) = 540
[tex]\sigma^{2}[/tex]= n*p*(1-p)
=900*0.60*0.40
=216
P(X >562) = Pr( Z > 1.4976)
= 0.9328
Hence, the probability that more than 562 drivers is 0.9328
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Question is the attachment
If both pipes are opened. Then the number of hours to fill up the tank fully is 100 hours.
The complete question is attached below.
What are ratio and proportion?A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.
Let t be the filling time.
Then we have
Time is inversely proportional to rate of filling tank.
1/20 – 1/25 = 1/t
0.05 - 0.04 = 1/t
0.01 = 1/t
t = 1/0.01
t = 100 hours
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What is the slope of the line (14,0), (2, -6)
Answer:
1/2 is the answers
Step-by-step explanation:
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The slope of the line is = 0.5
Given that:-one point is =(14,0)
other is =(2,-6)
Solution:-We can easily solve the question by the formula of a straight line.
The slope is = 0-(-6)/(14-2)
= 1/2
Convert:
3½ kilograms to grams
Step-by-step explanation:
3 1/2 = 3,5 kg → ? g
1 kg = 1.000 g
• Convert kg to g.
= 3,5 kg
= 3,5 × 1.000
= 3.500 grams IS THE ANSWER
Find the GCF of 12a and 18a²
Answer:
6
Step-by-step explanation:
the blue factors are all the factors 12 and 18 have in common.
find the distance around one-fifth of a circle with diameter of 14 inches
To solve this problem, you will need to know the formula to find the circumference of a circle given the diameter of a circle. After calculating the circumference, you will then divide this result by 5 to obtain the final answer needed for this problem.
Find the CircumferenceThe circumference of a circle is found using the formula C = 2πr.
[tex]C = 2\pi r[/tex]
We are given the diameter. The radius can be found using r = D/2.
[tex]\displaystyle r=\frac{D}{2}[/tex]
[tex]\displaystyle r=\frac{14}{2}[/tex]
[tex]r=7[/tex]
Plug in the radius to the formula for a circle's circumference: C = 2πr.
[tex]C = 2 \pi (7)[/tex]
Rearrange the equation to distribute the 7 into the 2π.
[tex]C = 7(2\pi)[/tex]
Distribute the 7.
[tex]C=14\pi[/tex]
Find One-Fifth of the DistanceTo find one-fifth of the distance (formally termed the circumference) around the circle, divide the circumference by 5.
[tex]\displaystyle \frac{14\pi}{5}[/tex]
If you are looking for a simplified answer in terms of π, this will suffice. If you need an exact answer that does not reference π, continue reading.
For a solution not in terms of π, first, multiply 14 by π.
[tex]14\times\pi = 43.98229715[/tex]
Divide this value by 5.
[tex]\displaystyle \frac{43.98229715}{5} = 8.7964594[/tex]
To make this easier to present, round to the hundredths place.
[tex]8.7964594 \approx 8.80[/tex]
The final answer, dependent on the value you are asked to provide, is:
[tex]{\boxed{\displaystyle \frac{14\pi}{5} \ \text{inches}}[/tex]
[tex]\boxed{\text{approximately} \ 8.8 \ \text{inches}}[/tex]
The perimeter of a standard-sized rectangular rug is 24 ft. The length is 2ft longer than the width. Find the dimensions.
The length and width of the rectangle are equal to: 7 ft and 5 ft, respectively
QuadrilateralsThere are different types of quadrilaterals, for example, square, rectangle, rhombus, trapezoid, and parallelogram. Each type is defined accordingly to its length of sides and angles. For example, in a rectangle, the opposite sides are equal and parallel and their interior angles are equal to 90°.
The perimeter of a geometric figure is the sum of its sides. Thus, for a rectangle, the perimeter is 2L+2W.
For this question, the length is 2ft longer than the width - L=2+W. Thus,
24=2*(2+W)+2W
24=4+2W+2W
24-4=4W
20=4W
W=5 ft
If W=5, L will be 2+5=7 ft.
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Evaluate.
-|a+bl
2-c
when a = 1, b = -2, and c = -7
Enter your answer as a simplified fraction in the box.
Answer:
-9
Step-by-step explanation:
-|1-2|2+7
-|-1|9
-9×1
-9
Sid makes a graph for estimating the y-value.He wants to compare it to the table before he turns it in. Do the table and the graph represent the same function?
Answer:
No
Step-by-step explanation:
The graph and the table do not show the same function as none of the y values on the graph correspond to the y values on the table.
THE
^
Solve: x=4+(4x-4)
O
O
O
x = 2
x = 10
x = 2 or x = 10
Ono real solution
DONE
Answer: x=0
Step-by-step explanation:
[tex]x=4+(4x-4)\\\\x=4+4x-4\\\\x=4x\\\\3x=0\\\\\boxed{x=0}[/tex]
The solution to the equation x = 4 + (x + 4) is 0.
The correct option is "one real solution".
What is an equation?Two algebraic expressions having the same value and symbol '=' in between are called an equation.
Expanding the expression on the right-hand side, we have:
x = 4 + (4x - 4)
x = 4x
Subtracting 4x from both sides, we get:
x - 4x = 0
-3x = 0
Dividing both sides by -3, we get:
x = 0
Therefore, there is one solution to the equation x = 4 + (4x - 4) as the equation simplifies to 0.
So the correct answer is 0, "one real solution".
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the funtions f(x) and g(x) are shown on the graph f(x)=x^2
what is g(x)?
Answer:
C
Step-by-step explanation:
A reflection of a graph on the x axis simply adds the opposite sign to the x^2, in this case, since f(x) = x^2 is positive, a reflection would mean that g(x) would be -x^2. As g(x) is also vertically translated down 2 units, the equation would then become g(x) = -x^2 - 2 and the correct answer would be C.
What are the coordinates of point F?
On a coordinate plane, point F is 4 units to the right and 2.5 units down.
(Negative 4, Negative 2 and one-half)
(Negative 4, 2 and one-half)
(4, negative 2 and one-half)
(4, 2 and one-half)
The coordinates of point F are 4 and negative 2.5. Option C is correct.
What is the best way to understand the Cartesian coordinate plane?A Cartesian coordinate plane is a two-dimensional plane with infinite dimensions. On an endless 2d plane, any two-dimensional figure may be drawn. A location is assigned to each point on a Cartesian plane.
It is the perpendicular distance between that point and the horizontal and vertical axes, which are commonly referred to as the x-axis and y-axis.
The location is then written as (a,b), where 'a' is the point's shortest distance from the y-axis, 'b' is the point's shortest distance from the x-axis, and 'c' is the point's shortest distance from the x-axis.
'c' is the point's shortest distance from the x-axis, and 'c' is the point's shortest distance from the x.
The coordinates of point F are 4 and negative 2.5.
Hence, the Option C is correct.
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Please answer! Will give the brainliest!
Answer: K. 3
Step-by-step explanation:
There are 30 students in total. What I did is I added everything that was in the Venn diagram and subtracted that from 30.
[tex]12+5+10=27[/tex]
[tex]30-27=3[/tex]
Therefore, there are 3 students who didn't like either English or math.
I hope this helps! Pls give brainliest!! :)
What is the simplified form of StartRoot 100 x Superscript 36 Baseline EndRoot ?
10x Superscript 18
10x Superscript 6
50x Superscript 18
50
The simplified form of the expression √(100x³⁶) will be 10x¹⁸. Then the correct option is A.
What is simplification?Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.
The expression is given below.
⇒ √(100x³⁶)
Then the simplified form of the expression will be
⇒ √[(10x¹⁸)²]
⇒ 10x¹⁸
Then the correct option is A.
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Answer:
Step-by-step explanation:
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The simplified form of √(400x¹⁰⁰) is;
D; 20x⁵⁰
We want to find the simplified form of √(400x¹⁰⁰)
Now, according to laws of indices;
√ab = √a × √b
Thus;
√(400x¹⁰⁰) = √400 × √(x¹⁰⁰)
⇒ 20√(x¹⁰⁰)
Also according to law of indices;
a⁴ = a² × a²
Thus;
x¹⁰⁰ = x⁵⁰ × x⁵⁰
Thus;
√(x¹⁰⁰) = √(x⁵⁰ × x⁵⁰)
⇒ x⁵⁰
Our final answer is;
20x⁵⁰
In 2009, there were 12,078 Burger King restaurants; in 2017, there were 16,717 Burger King restaurants. Calculate the average rate of change (slope) for the number of Burger King restaurants over this time period.
PLS HELP ME
Slope of the given data is 579.88
What is Slope?The slope of a line is defined as the change in y coordinate with respect to the change in x coordinate of that line.
Here, given data;
x₁ = 2009 y₁ = 12078 burger
x₂ = 2017 y₂ = 16717 burger
Now, Slope = (y₂ - y₁)/(x₂ - x₁)
Slope = (16717 - 12078) / (2017 - 2009)
Slope = 4639 / 8
Slope = 579.88
Thus, Slope of the given data is 579.88
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A club organises a lottery, selling tickets at 25 cents each. The club will be giving a prize of
€58
to the winner but also plans to make a profit of
€150
from the whole event. What is the least number of tickets that the club needs to sell?
Using proportions, it is found that the club needs to sell at least 832 tickets to make their desired profit.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The prize is of €58, with the event making a profit of €150, hence the amount of money they have to earn from tickets is given by:
A = 150 + 58 = €208.
The tickets are sold at €0.25, hence the number of tickets they have to sell is:
n = 208/0.25 = 208 x 4 = 832.
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What is the value of the expression
(12+x) +
4+x
when X= 4 and y=-8?
OA) 4
OB)
OC)
OD 10
Step-by-step explanation:
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The value of the expression x
4
−8x
3
+18x
2
−8x+2, when x=2+
3
, is:
Medium
Solution
verified
Verified by Toppr
Correct option is B)
Let f(x)=x
4
−8x
3
+18x
2
−8x+2
Substituting x=2+
3
, we get
f(2+
3
)=(2+
3
)
4
−8(2+
3
)
3
+18(2+
3
)
2
−8(2+
3
)+2
=(2+
3
)
2
((2+
3
)
2
+18)−8(2+
3
)((2+
3
)
2
+1)+2
=(7+4
3
)(4
3
+25)−8(2+
3
)(8+4
3
)+2
=175+48−128−96+2
=1
Hence, option B is correct.
if you put 25ml of concentration in a glass, how much water should be added
Answer:
50 ml
Step-by-step explanation:
50 ml
What is 6289 round off to the nearest 1000 (thousand)????
Answer:
6230 will be answer I think
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Answer:
Well, it's to the nearest thousand, and we know that 6289 is 6 thousand 2 hundred and 89. So, you look at the number next to the thousand which is the hundreds, and as we can see that is 2. Therefore it will be 6000, as 6289 cannot be rounded to 7000 since 2 doesn't exceed 5.
So, the answer is 6000
(I don't mind being marked brainliest for this I'd just like to help someone. :)
|4x + 7| − 4 = 20
Can anyone help me with this
Answer:
x = -31/4 or x = 17/4
Step-by-step explanation:
|4x + 7| − 4 = 20
⇔ |4x + 7| − 4 + 4 = 20 + 4
⇔ |4x + 7| = 24
⇔ 4x + 7 = 24 or 4x + 7 = -24
⇔ 4x = 24 - 7 or 4x = -24 - 7
⇔ 4x = 17 or 4x = -31
⇔ x = 17/4 or x = -31/4
Answer:
x = [tex]\frac{17}{4}[/tex] (17/4 = 4.25)
or x = [tex]-\frac{31}{4}[/tex] (-31/4 = -7.75)
Step-by-step explanation:
| | is notation for absolute value
absolute value - the distance that a number is from 0
> essentially, you can think of absolute value as the "positive version" of whatever is inside of the | |
if we have | x | = 20, we could really have (without the | | ) two versions of x
either | x | = 20 ; or | -x | = 20 {because a negative x inside of the | | has the same value as positive x}
we set this up as two equations:
x = 20 or -x = 20
^ {multiply by -1}
x = 20 or x = -20
now, let's plug our understanding into the equation
|4x + 7| - 4 = 20
first, we should simplify our equation to:
|4x + 7| - 4 = 20
+ 4 + 4
|4x + 7| = 24
now, let's separate this absolute value equation into two separate equations:
4x + 7 = 24:
- 7 - 7 {subtract 7 from both sides to isolate x}
4x = 17
÷4 ÷4 {divide both sides by 4 to get 1x}
x= [tex]\frac{17}{4}[/tex]
or,
4x + 7 = -24:
- 7 -7 {subtract 7 from both sides to isolate x}
4x = -31
÷4 ÷4 {divide both sides by 4 to get 1x}
x = [tex]-\frac{31}{4}[/tex]
so, we know that
x = [tex]\frac{17}{4}[/tex] (17/4 = 4.25)
or x = [tex]-\frac{31}{4}[/tex] (-31/4 = -7.75)
hope this helps!!
Question 4(Multiple Choice Worth 4 points)
Which of the following is a rational number?
√1. √2. √3, √5
O√1
O √2
O√3
√√5
Answer:
1
Step-by-step explanation:
The square root of 1 is 1 so it is a rational number while others are irrational
Graph the equation by plotting three points. If all three are correct, the line will appear. -3y=2x-7 ....... 20 POINTS
First lets simplify to slope intercept (y=mx+b)
y=[tex](2x-7)/-3[/tex]
y=-2/3x+7/3
Point 1: (0,7/3) as when x is 0, y=7/3.
Point 2: lets plug x in as 3 to cross cancel.
[tex]\frac{-2}{3} *\frac{3}{1} = \frac{-2}{1}[/tex]
So (3,-2).
Lets do point 3: plug in -3.
[tex]\frac{-2}{3} *\frac{-3}{1} = \frac{2}{1} = 2[/tex]
So (-3,2).
Your three points are (0,2.33 repeat) or (0,7/3), (3,-2) and (-3,2)
Hopefully this helps you out, heart if it was helpful and please do not hesitate to ask any questions. I have also attached an image of the line
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A boardwalk game of chance costs $1 to play. You have a 25% chance of winning $1 back, a 20% chance of winning $2
(your $1 back, plus an additional $1), and a 10% chance to win $5 (a gain of $4). What is the expected value of playing
the game if you lose your bet 45% of the time?
A. -$1.00
B. -$0.25
C.-$0.15
D. $0.15
Answer:
the answer is c
Step-by-step explanation:
A school is arranging a field trip to the zoo. The school spends 737.38 dollars on passes for 44
students and 2 teachers. The school also spends 393.36 dollars on lunch for just the students.
How much money was spent on a pass and lunch for each student?
Step-by-step explanation:
since there is no other information, we have to assume that the prices for student passes and teacher passes are the same.
therefore, the pass price per person is
$737.38 / (44 + 2) = $737.38 / 46 = $16.03
and the lunch costs per student are
$393.36 / 44 = $8.94
altogether,
$16.03 + $8.94 = $24.97
was spent for each student.
Which of the following equations would correspond to a conic section formed when a plane intersects a cone parallel to the base?
x2 + y2 = 32
x squared over 2 squared plus y squared over 3 squared equals 1
x2 = 8y
x squared over 2 squared minus y squared over 3 squared equals 1
The equation of the circle, ellipse, and hyperbola will be x² + y² = 3², x² + y² / 3² = 1, and x² / 2² - y² / 3² = 1, respectively.
What is the conic section?The curve that is derived from the section of the cone is known as conic section.
The following equations are given below.
x² + y² = 3², this is the equation of the circle.
x² + y² / 3² = 1, this is the equation of the ellipse.
x² / 2² - y² / 3² = 1, this is the equation of the hyperbola.
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Amy and Laura recorded the average gas mileage (MPG) of their vehicles each week for four weeks. What can be concluded about the relationships shown in the graph and table?
Amy and Laura recorded the same gas mileage each week.
Both Amy and Laura increased their gas mileage in the first two weeks.
Amy had greater gas mileage than Laura.
Laura had a constant gas mileage in the first four weeks of data.
Who runs fastest?
When do Andy and Berta cross paths?
Who is closest to the 1.5 mile mark after 6 minutes?
Both Amy and Laura increased their gas mileage in the first two weeks.
Option B is the correct answer.
The missing graph is attached with the answer.
What is a Graph ?A graph is a statistical way of showing data , it is used to show relation between the points.
A graph is useful in understanding the nature of a function.
From the data given in the question
The statements that can be concluded is , Option B
Both Amy and Laura increased their gas mileage in the first two weeks.
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List all the factors of 66 from least to greatest.
The factors of 66 are 1, 2, 3, 6, 11, 22, 33, and 66. Out of these factors, the greatest factor of 66. The next highest factor other than 66 is 33. A number which is three more than 33 is 33 + 3 = 36.
10% of an amount is 6.2 . Wirk out the original account
Answer:
the original amount was 62
Step-by-step explanation:
You can use the part over whole formula like this:
[tex]\frac{part}{whole} = ( \frac{6.2}{?} * \frac{10}{100})\\ ? = 62[/tex]
why?
because we know that 10% = 10/100, we can easily find out the answer by cross multiplying
? * 10 (let's use x, instead of ?)
=10x
6.2 * 100
= 620
Now we have an equation that looks like this: 10x = 620
By using the inverse operation tool (dividing each side by 10 to isolate x) we have:
x (or ?) = 62
If a 103 pound man can have 1292 mg of a medicine in a day, how much can a 102 pound woman have? (round answer to one decimal place) She can have mg
Answer:
1279.5mg
Step-by-step explanation:
103 pound man takes -1292mg of medicines
102 pound woman will take -xmg of medicine
cross multiply
102x1292=103x
131784=103x
x=131784/103
x=1279.5mg
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Women will have 1279.5mg of medicine in a day.
How much can a 102-pound woman have?103-pound man takes -1292mg of medicines.
102-pound woman will take x mg of the medicine.
By cross multiply
102x1292=103x
131784=103x
x=131784/103
x=1279.5mg
What is an example of a word problem?Word problems normally include mathematical modeling questions, where records and information approximately a positive machine is given and a student is needed to expand a model. For example, Jane had $5.00, then spent $2.00. How much does she have now?
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If x = 3, then 3x – 4 = 5. x = 3 law of detatchment
Answer:
3x-4=5
Step-by-step explanation:
it is correct
