Answer:
[tex]\sigma = 1.8[/tex]
Step-by-step explanation:
Given
[tex]\begin{array}{ccccccc}x & {0} & {1} & {2} & {3} & {4}& {5} \ \\ P(x) & {0.2} & {0.1} & {0.1} & {0.2} & {0.2}& {0.2} \ \end{array}[/tex]
Required
The standard deviation
First, calculate the expected value E(x)
[tex]E(x) = \sum x * P(x)[/tex]
So, we have:
[tex]E(x) = 0 * 0.2 + 1 * 0.1 + 2 * 0.1 + 3 * 0.2 + 4 * 0.2 + 5 * 0.2[/tex]
[tex]E(x) = 2.7[/tex]
Next, calculate E(x^2)
[tex]E(x^2) = \sum x^2 * P(x)[/tex]
So, we have:
[tex]E(x^2) = 0^2 * 0.2 + 1^2 * 0.1 + 2^2 * 0.1 + 3^2 * 0.2 + 4^2 * 0.2 + 5^2 * 0.2[/tex]
[tex]E(x^2) = 10.5[/tex]
The standard deviation is:
[tex]\sigma = \sqrt{E(x^2) - (E(x))^2}[/tex]
[tex]\sigma = \sqrt{10.5 - 2.7^2}[/tex]
[tex]\sigma = \sqrt{10.5 - 7.29}[/tex]
[tex]\sigma = \sqrt{3.21}[/tex]
[tex]\sigma = 1.8[/tex] --- approximated
Can you please help me with this question
Solve algebraically.
6(t-2) + 15t < 5(5 + 3t)
With work shown please!!
Step-by-step explanation:
6t-12+15t | 25+15t
21t-12 | 25+15t
21t-12 < 25+15t
hence proved..
Answer:
21t - 12 < 25 + 15t
Step-by-step explanation:
6( t - 2 ) + 15t < 5 ( 5 + 3t )
Distribute .6t - 12 + 15t < 25 + 15t
Combine like terms.21t - 12 < 25 + 15t.
Hence , Proved.
What are the solutions of the quadratic equation 49x2 = 9?
A. x = 1/9 and x = -1/9
B. x = 3/7 and x = -3/7
C. x = 3/4 and x = -3/4
D. x = 9/49 and x = -9/49
Brainliest if you explain how. got stumped on this one
Answer:
B
Step-by-step explanation:
49x^2=9
solve for x
x^2= 9/49
x=± [tex]\sqrt{9/49\\}[/tex]
which is x = ±3/7 (B)
Answer: b x=1/9 and x=-1/9
Step-by-step explanation:
Help ask anyone have any more answers for the eye level program
Answer:
1) -[tex]\sqrt{32}[/tex]
2) -[tex]\sqrt{108}[/tex]
3) -[tex]\sqrt{80}[/tex]
4) -[tex]\sqrt{112}[/tex]
5) -[tex]\sqrt{40}[/tex]
6) -[tex]\sqrt{99}[/tex]
7) -[tex]\sqrt{50}[/tex]
8) -[tex]\sqrt{150}[/tex]
Step-by-step explanation:
please mark this answer as brainlist
NEED HELP
The average amount of money spent for lunch per person in the college cafeteria is $6.75 and the standard deviation is $2.28. Suppose that 18 randomly selected lunch patrons are observed. Assume the distribution of money spent is normal, and round all answers to 4 decimal places where possible.
C. For a single randomly selected lunch patron, find the probability that this
patron's lunch cost is between $7.0039 and $7.8026.
D. For the group of 18 patrons, find the probability that the average lunch cost is between $7.0039 and $7.8026.
Answer:
C.[tex]P(7.0039<x<7.8026)=0.1334[/tex]
D.[tex]P(7.0039<\bar{x}<7.8026)\approx 0.2942[/tex]
Step-by-step explanation:
We are given that
n=18
Mean, [tex]\mu=6.75[/tex]
Standard deviation, [tex]\sigma=2.28[/tex]
c.
[tex]P(7.0039<x<7.8026)=P(\frac{7.0039-6.75}{2.28}<\frac{x-\mu}{\sigma}<\frac{7.8026-6.75}{2.28})[/tex]
[tex]P(7.0039<x<7.8026)=P(0.11<Z<0.46)[/tex]
[tex]P(a<z<b)=P(z<b)-P(z<a)[/tex]
Using the formula
[tex]P(7.0039<x<7.8026)=P(Z<0.46)-P(Z<0.11)[/tex]
[tex]P(7.0039<x<7.8026)=0.67724-0.54380[/tex]
[tex]P(7.0039<x<7.8026)=0.1334[/tex]
D.[tex]P(7.0039<\bar{x}<7.8026)=P(\frac{7.0039-6.75}{2.28/\sqrt{18}}<\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}})<\frac{7.8026-6.75}{2.28/\sqrt{18}})[/tex]
[tex]P(7.0039<\bar{x}<7.8026)=P(0.47<Z<1.96)[/tex]
[tex]P(7.0039<\bar{x}<7.8026)=P(Z<1.96)-P(Z<0.47)[/tex]
[tex]P(7.0039<\bar{x}<7.8026)=0.97500-0.68082[/tex]
[tex]P(7.0039<\bar{x}<7.8026)=0.29418\approx 0.2942[/tex]
-9(m + 2) + 406 - 7m)
Answer:
-9(m+2)+406-7m)
=-16+388
Find the missing term in the following pattern.
1984, 992, 496, blank space, 124, 62
Answer:
248
Step-by-step explanation:
common ratio for two consecutive terms is 2/1
for eg: 1984÷992 =2
992÷ 496 = 2
124÷ 62 = 2
that means 124 ×2 = 248 Answer
14. In this picture, three straight lines intersect at a point. Form an equation in x and solve for x.
Answer:
6x = 180
x = 30
Step-by-step explanation:
Mai drives a truck for a soft drink company. Her truck is filled with 15-ounce cans and 70-ounce bottles. Let c be the number of 15-ounce cans the
truck is carrying, and let b be the number of 70-ounce bottles.
The truck must be carrying less than 4000 pounds (64,000 ounces). Using the values and variables given, write an inequality describing this.
Answer:
15c + 70b < 64,000
Step-by-step explanation:
15c will represent the amount of ounces in the truck from the 15 ounce cans.
70b will represent the amount of ounces in the truck from the 70 ounce bottles.
These need to be added together in the inequality to represent the total weight in the truck.
Then, a less than inequality sign needs to be used, since the truck has to be carrying less than 64,000 ounces.
Put this all together:
15c + 70b < 64,000
So, the inequality is 15c + 70b < 64,000
al of
10. A square field has four sprinklers that spray
in the areas represented by the circles below. If
the shaded portion represents area that is not
reached by the sprinklers, find the total area that
is not reached by the sprinklers.
Using the areas of the sqaure and of the circle, it is found that the total area that is not reached by the sprinklers is of 343.36 ft².
What is the area of a square?The area of a square of side length l is given by:
A = l²
In this problem, we have that l = 40 ft, hence:
A = (40 ft)² = 1600 ft².
What is the area of a circle?The area of a circle of radius r is given by:
[tex]A = \pi r^2[/tex]
In this problem, we have four circles of radius r = 10 ft, hence it's combined area, in square feet, is given by:
[tex]A_c = 4\pi (10)^2 = 400\pi = 1256.64 \text{ft}^2[/tex]
The area not reached by the sprinklers is the subtraction of the area of the square by the area of the circle, hence:
1600 - 1256.64 = 343.36 ft².
More can be learned about the area of a rectangle at https://brainly.com/question/10489198
14. A professor records the number of class days (x) each student misses over the course of a semester and uses a frequency distribution to display the data. What is the probability a student missed exactly 1 day
Question is incomplete, however here's an explanation to solve questions such as this
Answer and explanation:
Probability= number of favorable outcomes/total number of outcomes
The frequency distribution recorded by the professor would show number of times(frequency) each student missed a class day.
We are required to fund the probability that a student would miss class
Probability = number of times the student missed class/ total number of classes missed by all students
Example, if student missed class 20 times in a semester and all students in total missed class 200 times
Probability that the student would miss class=20/200= 1/10
Can the range of a function be written like this {6,7,8,10} instead of like this [tex]6\leq x\leq 10[/tex]?
Answer:
No unless x is being used to define only elements of an integer set.
Step-by-step explanation:
No, not in general unless x is defined as a integer or a subset of the integers like the naturals, whole numbers....
Usually 6<=x<=10 means all real numbers between 6 and 10, inclusive. This means example that 6.6 or 2pi are in this set with infinitely other numbers that I can't name.
{6,7,8,9,10} just means the set containing the numbers 6,7,8,9,10 and that's only those 5 numbers.
The movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer
Which sentence correctly compares the two numbers 5.395 and 5.385?
05.395 < 5.385
05.385 > 5.395
o 5.395 = 5.385
5.385 < 5.395
h
Submit
Pass
Don't know answer
Answer:
5.385 < 5.395
Step-by-step explanation:
Compare digits one by one starting form the left.
5.395 and 5.385
The 5s in the ones place are equal.
5.395 and 5.385
The 3s in the tenths place are equal.
5.395 and 5.385
The 9 in the hundredths place is greater than the 8 in the hundredths place, so the number with the 9 is grater than the number with the 8.
That makes the number with the 8 less than the number with the 9.
Answer: 5.385 < 5.395
Classify the following polynomials. Combine any
like terms first.
x^2+3x + 2x - 2x^2
X^3+ 4x - 4x - 4x^2
X^3+2x - X^3- 2x^2+ 3
First simplify all polynomials and rewrite them in descending exponent order.
1. [tex]-x^2+2x[/tex]
2. [tex]x^3-4x^2[/tex]
3. [tex]-2x^2+2x+3[/tex]
Now observe the terms with highest exponents in each expression, in particularly focus on their exponent value,
[tex]-x^2[/tex] with value of 2
[tex]x^3[/tex] with value of 3
[tex]-2x^2[/tex] with value of 2
The value is also known as order of polynomial and it is a way to classify polynomials.
Every order creates a family of polynomials determined by the order (which is always greater than -1)
A polynomial such as (1) and (3) have an orders of 2, which is often called quadratic order and thus the polynomials (1), (3) are classified in the same family of quadratic polynomials, these are polynomials with order of 2.
Polynomial (2) however has an order of 3, which is called cubic order. This polynomial (2) is classified in the family of cubic polynomials.
There are of course many other families, in fact, infinitely many of them because you have order 0, 1, 2, 3, and so on there are precisely [tex]\aleph_0+1[/tex] read as "aleph 0 + 1" (the number of natural numbers + 1 (because 0 is not a natural number)) of polynomial families.
The first few have these fancy names, for example:
order 0 => constant polynomial
order 1 => linear polynomial
order 2 => quadratic polynomial
order 3 => cubic polynomial
order 4 => quartic polynomial
and so on.
Hope this helps!
Thirty-six percent of customers who purchased products from an e-commerce site had orders exceeding 110. If 17% of customers have orders exceeding 110 and also pay with the e-commerce site's sponsored credit card, determine the probability that a customer whose order exceeds 110 will pay with the sponsored credit card.
Answer:
The right solution is "0.5".
Step-by-step explanation:
According to the question,
P(pay with the sponsored credit card | order exceeds $110)
= [tex]\frac{P(Pay \ with \ the \ sponsored \ credit\ card\ and\ order\ exceeds\ 110)}{P(order \ exceeds \ 110)}[/tex]
= [tex]\frac{P(A \ and \ B)}{P(A)}[/tex]
By putting the values, we get
= [tex]\frac{0.17}{0.34}[/tex]
= [tex]0.5[/tex]
Thus, the above is the right solution.
Solve (x - 5)2 = 3.
Answer:
x = 5±√3
Step-by-step explanation:
Equation: (x-5)² = 3
Step 1: Take the square root of both side of the equation
√(x-5)² = ±√3
x-5 = ±√3
Step 2: add 5 to both side of the equation
x-5+5 = 5±√3
x = 5±√3
Hence, from the options above, the right answer is
B. x = 5±√3
What is net cash flow
A merchant keeps marble in a cylindrical plastic container that has a diameter of 28cm and height of 35cm. A marble has a diameter of 25mm. Determine the number of marbles that can be stored in such a container if air space accounts for 20% between marbles.
Answer:
2107 marbles can be stored in the container.
Step-by-step explanation:
Since a merchant keeps marble in a cylindrical plastic container that has a diameter of 28cm and height of 35cm, and a marble has a diameter of 25mm, to determine the number of marbles that can be stored in such a container if air space accounts for 20 % between marbles, the following calculation must be performed, knowing that the volume of a cylinder is equal to height x π x radius²:
35 x 3.14 x (28/2) ² = X
109.9 x (14 x 14) = X
109.9 x 196 = X
21,540.4 = X
In turn, the volume of each 25mm diameter marble is equal to:
25mm = 2.5cm
4/3 x 3.14 x 1.25³ = X
4.18666 x 1.953125 = X
8.1770 = X
21,540.4 x 0.8 = 17,232.32
17,232.32 / 8,177 = 2,107.41
Therefore, 2107 marbles can be stored in the container.
3. The size of a red blood cell is 0.000007 m and the size of a plant
cell is 0.0000127 m. Compare these two.
Given:
Size of a red blood cell = 0.000007 m
Size of a plant cell = 0.0000127 m
To find:
The comparison of these two values.
Solution:
We have,
Size of a red blood cell = 0.000007 m
Size of a plant cell = 0.0000127 m
Clearly, [tex]0.0000127>0.000007[/tex]. Now, the difference between these two values is:
[tex]0.0000127-0.000007=0.0000057[/tex]
Therefore, the size of a plant cell is 0.0000057 m more than the size of a red blood cell.
Which point represents the unit rate?
A
B
C
D
Answer:
Point C represents the unit rate
Step-by-step explanation:
You are planning to buy a house for $800,000. City bank offers a 30 year loan at 4.9 % apr ( Annual percentage interest rate) if you put 20 % down. Calculate your expected monthly payment.
Answer:
3396.65
Step-by-step explanation:
Let's start by cacluating the amount the bank is loaning us
800000*.8=640000
Let's now calculate the effective rate: .049/12= .004083333333
let x= payment
[tex]640000=x\frac{1-(1+.004083333333)^{-30*12}}{.004083333333}\\x=3396.651012[/tex]
The speed (S) an object falls varies directly with time. If the speed is 49.0m/s after 5 seconds, then what is the speed after 3 seconds
9514 1404 393
Answer:
29.4 m/s
Step-by-step explanation:
Speed is proportional to time, so we have ...
speed / time = s/3 = 49/5
s = 3/5(49) = 29.4
The speed of the object is 29.4 m/s after 3 seconds.
The MD orders 50mg of an elixir to be given every 12 hours. Available is 125mg/5ml. How much should be administered every 12 hours?
Answer:
2ml
Step-by-step explanation:
50mg of some potent agent has to be given every 12 hours.
there is a solution that has a concentration of that agent of 125mg/5ml
we need to administer some part of this solution, which we cannot (or should not) change in its structure.
that means the ratio of agent to overall solution stays the same, no matter how much of the solution we administer.
all we need to do is to transit the ratio of 125/5 to represent 50/x (maintaining the said ratio).
in other words, we need to find how many ml we need to administer, so that 50mg of the agent enter the body.
so,
125/5 = 50/x
125x/5 = 50
25x = 50
x = 50/25 = 2
2ml of the solution needs to be administered every 12 hours.
Solve the equation for x.
2/3x-1/9x+5=20
Answer:
x = 27
Step-by-step explanation:
I'm assuming the equation looks like this:
[tex]\frac{2}{3}x-\frac{1}{9}x+5=20[/tex]
Here's how to solve for x:
[tex]\frac{2}{3}x-\frac{1}{9}x+5=20[/tex]
(subtract 5 from both sides)
[tex]\frac{2}{3}x-\frac{1}{9}x=15[/tex]
(Find the GCF of 3 and 9, which is 3. Multiply 2/3 by 3/3. You get 6/9)
[tex]\frac{6}{9}x-\frac{1}{9}x=15[/tex]
(add like terms)
[tex]\frac{5}{9}x=15[/tex]
(multiply 9/5 to both sides, which is the same as dividing both sides by 5/9)
x = 27
Hope it helps (●'◡'●)
95, 86, 78, 71, 65, 60 _____
Answer:
hello there here is your answer
51 is your next term.
Step-by-step explanation:
you are subtracting 9 from each number
95-9= 86
86-9=78
78-9=65
65-9=60
60-9=51
so on and so on
Hope this help
have a good day
bye
Step-by-step explanation:
[tex]here \: is \: your \: solution: - \\ \\ given \: number \: = 95.86.78.71.65.60 \\ \\ = > 95 - 9 = 86 \\ \\ = > 86 - 8 = 78 \\ \\ = > 78 - 7 = 71 \\ \\ = > 71 - 6 = 65 \\ \\ = > 65 - 5 = 60 \\ \\ \: now \: follow \: the \: sequence \: \\ \\ subtract \: 4 \: from \: 60 \\ \\ = > 60 - 4 = 56 \\ \\ = > \: \: 56 \: \:( ANSWER✓✓✓)[/tex]
Draw a triangle ABC, where AB = 8 cm , BC = 6 cm and angle B=70^ and locate its circumcentre and draw the circumcircle.
Step-by-step explanation:
ΔABC, where AB = 8 cm, BC = 6 cm, B = 70° Construction: (i) Draw the ∆ABC with the given measurements. (ii) Construct the perpendicular bisector at any two sides (AB and BC) and let them meet at S which is the circumcircle. (iii) S as centre and SA = SB = SC as radius, draw the circumcircle to pass through A, B, and C. Circum radius = 4.3cm .draw-triangle-abc-where-cm-bc-and-70-and-locate-its-circumcentre-and-draw-the-circumcircle
Police Chase: A speeder traveling 40 miles per hour (in a 25 mph zone) passes a stopped police car which immediately takes off after the speeder. If the police car speeds up steadily to 55 miles/hour in 10 seconds and then travels at a steady 55 miles/hour, how long and how far before the police car catches the speeder who continued traveling at 40 miles/hour
Answer:
a. 18.34 s b. 327.92 m
Step-by-step explanation:
a. How long before the police car catches the speeder who continued traveling at 40 miles/hour
The acceleration of the car a in 10 s from 0 to 55 mi/h is a = (v - u)/t where u = initial velocity = 0 m/s, v = final velocity = 55 mi/h = 55 × 1609 m/3600 s = 24.58 m/s and t = time = 10 s.
So, a = (v - u)/t = (24.58 m/s - 0 m/s)/10 s = 24.58 m/s ÷ 10 s = 2.458 m/s².
The distance moved by the police car in 10 s is gotten from
s = ut + 1/2at² where u = initial velocity of police car = 0 m/s, a = acceleration = 2.458 m/s² and t = time = 10 s.
s = 0 m/s × 10 s + 1/2 × 2.458 m/s² (10)²
s = 0 m + 1/2 × 2.458 m/s² × 100 s²
s = 122.9 m
The distance moved when the police car is driving at 55 mi/h is s' = 24.58 t where t = driving time after attaining 55 mi/h
The total distance moved by the police car is thus S = s + s' = 122.9 + 24.58t
The total distance moved by the speeder is S' = 40t' mi = (40 × 1609 m/3600 s)t' = 17.88t' m where t' = time taken for police to catch up with speeder.
Since both distances are the same,
S' = S
17.88t' = 122.9 + 24.58t
Also, the time taken for the police car to catch up with the speeder, t' = time taken for car to accelerate to 55 mi/h + rest of time taken for police car to catch up with speed, t
t' = 10 + t
So, substituting t' into the equation, we have
17.88t' = 122.9 + 24.58t
17.88(10 + t) = 122.9 + 24.58t
178.8 + 17.88t = 122.9 + 24.58t
17.88t - 24.58t = 122.9 - 178.8
-6.7t = -55.9
t = -55.9/-6.7
t = 8.34 s
So, t' = 10 + t
t' = 10 + 8.34
t' = 18.34 s
So, it will take 18.34 s before the police car catches the speeder who continued traveling at 40 miles/hour
b. how far before the police car catches the speeder who continued traveling at 40 miles/hour
Since the distance moved by the police car also equals the distance moved by the speeder, how far the police car will move before he catches the speeder is given by S' = 17.88t' = 17.88 × 18.34 s = 327.92 m
Solve the system, or show that it has no solution. (If there is no solution, enter NO SOLUTION. If there are an infinite number of solutions, enter the general solution in terms of x, where x is any real number.)
20x − 80y = 100
−14x + 56y = −70
(x, y) =
Answer:
The system has an infinite set of solutions [tex](x,y) = (x, \frac{x-5}{4})[/tex]
Step-by-step explanation:
From the first equation:
[tex]20x - 80y = 100[/tex]
[tex]20x = 100 + 80y[/tex]
[tex]x = \frac{100 + 80y}{20}[/tex]
[tex]x = 5 + 4y[/tex]
Replacing on the second equation:
[tex]-14x + 56y = -70[/tex]
[tex]-14(5 + 4y) + 56y = -70[/tex]
[tex]-70 - 56y + 56y = -70[/tex]
[tex]0 = 0[/tex]
This means that the system has an infinite number of solutions, considering:
[tex]x = 5 + 4y[/tex]
[tex]4y = x - 5[/tex]
[tex]y = \frac{x - 5}{4}[/tex]
The system has an infinite set of solutions [tex](x,y) = (x, \frac{x-5}{4})[/tex]
Which expression can be used to determine 50% of 42?
42-2 ,42÷2,42÷10,42-10
Answer:
42÷2
Step-by-step explanation:
Write an algebraic expression for the situation. 28 divided by a number n An algebraic expression for the situation is
Answer:
[tex]\frac{28}{n}[/tex]
Step-by-step explanation:
