Answer:
[tex]\bar x = 3.545[/tex]
[tex]Median = 3.435[/tex]
Step-by-step explanation:
Given
[tex]x:3.89, 3.51, 3.97, 3.31, 3.21, 3.36, 3.67, 3.24, 3.27[/tex]
[tex]10th: 4.02[/tex]
Solving (a): The mean
This is calculated as:
[tex]\bar x = \frac{\sum x}{n}[/tex]
So, we have:
[tex]\bar x = \frac{3.89 +3.51 +3.97 +3.31 +3.21 +3.36 +3.67 +3.24 +3.27+4.02}{10}[/tex]
[tex]\bar x = \frac{35.45}{10}[/tex]
[tex]\bar x = 3.545[/tex]
Solving (b): The median
First, we sort the data; as follows:
[tex]3.21, 3.24, 3.27, 3.31, 3.36, 3.51, 3.67, 3.89, 3.97, 4.02[/tex]
[tex]n = 10[/tex]
So, the median position is:
[tex]Median = \frac{n + 1}{2}th[/tex]
[tex]Median = \frac{10 + 1}{2}th[/tex]
[tex]Median = \frac{11}{2}th[/tex]
[tex]Median = 5.5th[/tex]
This means that the median is the average of the 5th and 6th item
[tex]Median = \frac{3.36 + 3.51}{2}[/tex]
[tex]Median = \frac{6.87}{2}[/tex]
[tex]Median = 3.435[/tex]
51
What is the inverse of the function f(x) = 2x + 1?
Oh(x) =
1
2x-
o h«x)= kx +
- 3x-2
Oh(x) =
Oh(x) =
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81
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10:49 AM
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mamman
Answer:
let inverse f(x) be m:
[tex]m = \frac{1}{2x + 1} \\ 2x + 1 = \frac{1}{m} \\ 2x = \frac{1 - m}{m} \\ x = \frac{1 - m}{2m} [/tex]
substitute x in place of m:
[tex]{ \bf{ {f}^{ - 1}(x) = \frac{1 - x}{2x } }}[/tex]
At a hockey game, a vender sold a combined total of 228 sodas and hot dogs. The number of sodas sold was two times the number of hot dogs sold. Find the number of sodas and the number of hot dogs sold.
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Answer:
152 sodas76 hot dogsStep-by-step explanation:
Of the items sold, sodas were 2/(2+1) = 2/3 of the total.
(2/3)(228) = 152 . . . sodas were sold
152/2 = 76 . . . . hot dogs were sold
13, 5, 4, 9, 7, 14, 4 The deviations are _____.
A. "5, -3, -4, 0, 1, 6, 4"
B."5, -3, -4, 1, -1, 6, -4"
C."6, -3, -4, 1, 2, 6, -4"
D."-5, 3, 4, -1, 1, 6, 4 "
Answer:
B."5, -3, -4, 1, -1, 6, -4"
Step-by-step explanation:
We are given that
13,5,4,9,7,14,4
We have to find the deviation.
Mean=[tex]\frac{sum\;of\;data}{total\;number\;of\;data}[/tex]
Using the formula
[tex]Mean,\mu=\frac{13+5+4+9+7+14+4}{7}[/tex]
[tex]Mean,\mu=\frac{56}{7}=8[/tex]
Deviation=[tex]x_i-\mu[/tex]
[tex]x_i-\mu[/tex]
13 5
5 -3
4 - 4
9 1
7 -1
14 6
4 - 4
Hence, option B is correct.
An electronic system contains three cooling components that operate independently. The probability of each component's failure is 0.05. The system will overheat if and only if at least two components fail. Calculate the probability that the system will overheat.
Answer:
[tex]Pr= 0.00725[/tex]
Step-by-step explanation:
Given
[tex]p = 0.05[/tex] ---- probability that each component fails
[tex]n = 3[/tex]
Required
[tex]P(System\ Overheats)[/tex]
We understand that the system will overheat if at least 2 component fails; Assume the components are: x, y and z
The events that the system will overheat are: xyz', xy'z, x'yz and xyz
Where ' means that the component did not fail, and the probability is 1 - p (i.e. complement rule)
So, we have:
[tex]xyz' \to 0.05 * 0.05 * (1 - 0.05) = 0.002375[/tex]
[tex]xy'z \to 0.05 * (1 - 0.05)* 0.05 = 0.002375[/tex]
[tex]x'yz \to (1 - 0.05)* 0.05 * 0.05 = 0.002375[/tex]
[tex]xyz \to 0.05 * 0.05 * 0.05 =0.000125[/tex]
So, the required probability is:
[tex]Pr= 0.002375 +0.002375 +0.002375 + 0.000125[/tex]
[tex]Pr= 0.00725[/tex]
(Will mark brainliest!!!) 20 PTS !!
Sixty percent of all children in a school do not have cavities. The probability, rounded to four decimal places, that in a random sample of 9 children selected from this school, at least 6 do not have cavities is:
Answer:
probability[Number of 6 random sample do not have cavities] = 0.8
Step-by-step explanation
Given:
Number of student do not have cavities = 60%
Number of random sample = 9 children
Find:
Probability[Number of 6 random sample do not have cavities]
Computation:
n = 9
p = 60% = 0.6
P(At least 6)
Probability[Number of 6 random sample do not have cavities] = 1 - P(Less than 6)
Probability[Number of 6 random sample do not have cavities] = 1 - P(Less than or equal to 6)
Probability[Number of 6 random sample do not have cavities] = 0.8
Round 948070 to the nearest hundred? Hurry please
Answer:
9.48
Step-by-step explanation:
The equation y - 5 = 6X + 1 is written as point-slope form. What is the equation written in slope intercept form
Answer:
y = 6x + 6
Step-by-step explanation:
The general formula is y = mx +cso; the y as seen will be constant as well as the x
With change of subject the 5 will be moved to the other side having y= 6x +1 + 5 .Given us y = 6x + 6.
Write the quadratic equation in standard form:
3x2 – 3x = 11
Answer:
[tex]3x^{2} -3x-11 = 0[/tex]
Step-by-step explanation:
100 POINTS!!!!!
Directions: Respond to this question to demonstrate your understanding of the topic/content. Be sure to provide adequate and relevant details learned in the module to support your response. Pay close attention to organizing your response so it makes sense and uses correct grammar. Your response should be at least 5-7 sentences at a minimum.
Question: Given answer the questions that follow.
a. Your friend claims the graph of f(x)=2x increases at a faster rate than the graph of g(x)=x2 when x ≥ 0. Is your friend correct? Explain your reasoning.
b. How are the 2 functions different?
Answer:
a. The friend is incorrect.
2(x) is the same as x(2). PEMDAS does not apply to the same order of operation under normal conditions and both are directly proportional functions.
b. The parentheses are the only thing making the functions different. After you simplify from the parentheses, both values have the same priority.
Step-by-step explanation:
The owners of a baseball team are building a new baseball field for their team and must determine the number of seats to include. The average game is attended by 6,500 fans, with a standard deviation of 450 people. Suppose a random sample of 35 games is selected to help the owners decide the number of seats to include. Identify each of the following and be sure to round to the nearest whole number:
Provide your answer below:
μ =------------
μx=-----------
σx=-----------
σ=------------
n=------------
Answer:
μ = 6500
μx= 6500
σx= 76
σ= 450
n= 35
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
The average game is attended by 6,500 fans, with a standard deviation of 450 people.
This means that [tex]\mu = 6500, \sigma = 450[/tex]
35 games:
This means that [tex]n = 35[/tex]
Distribution of the sample mean:
By the Central Limit Theorem, we have [tex]\mu_x = \mu = 6500[/tex] and the standard deviation is:
[tex]\sigma_x = \frac{450}{\sqrt{35}} = 76[/tex]
The length of the box is 15 centimeters, the breadth of the box is 20 centimeter, the height of a box, 20 centimeter fine its volume. Step by step
Answer:
volume=length×width×height
v=15×20×20
v=6000
A sociologist claims the probability that a person picked at random in Times Square in New York City is visiting the area is 0.83. You want to test to see if the claim is correct. State the null and alternative hypotheses.
Answer:
The answer is:
[tex]H_0: p=0.83\\\\H_a: p \neq 0.83[/tex]
Step-by-step explanation:
Now, we're going to test if sociologists claim to be have visited a region of 0.83 by a person picked randomly on Time In New York City.
Therefore, null or other hypotheses are:
[tex]H_0: p=0.83\\\\H_a: p \neq 0.83[/tex]
A paper weight is made in the shape of a triangular pyramid.The dimensions of the paper weight are shown The formula for the volume of a triangular pyramid is V = 1/3 Bh .Which expression can be usef to find the value of B the area of the base of the pyramid
Answer:
[tex]B = \frac{3V}{h}[/tex]
Step-by-step explanation:
Given
[tex]V = \frac{1}{3}Bh[/tex]
Required
Solve for B
We have;
[tex]V = \frac{1}{3}Bh[/tex]
Multiply by 3
[tex]3V = Bh[/tex]
Make B the subject
[tex]B = \frac{3V}{h}[/tex]
HELP PLSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS
Answer:
12
Step-by-step explanation:
10 - 1/2 x = 12-4/3x
60 - 3x = 72-2x
-12 = - x
Which of the following is a polynomial
A. 1-5x^2/x
b. 11x
c. 2x^2- square root x
d. 3x^2+6x
Answer:
B and D are polynomial
Step-by-step explanation:
An algebraic expression with non-zero coefficients and variables having non-negative integers as exponents is called a polynomial.
A)
If it is [tex]1 -\frac{5x^{2}}{x }=1-5x[/tex] , then it is a polynomial.
But if it is [tex]\frac{1-5x^{2}}{x}[/tex] then it is not a polynomial
HW HELP PLZZZZ ASAPPPP
Answer:
[tex]\frac{3v}{a^{2}} = h[/tex]
Step-by-step explanation:
[tex]v = \frac{1}{3} a^{2} h[/tex]
[tex]3v = a^{2} h[/tex]
[tex]\frac{3v}{a^{2}} = h[/tex]
please answer
Find the area of the polygon.
6 cm6 cm10 cm
Answer:
Area: 360 cm
Perimeter: 44 cm
Step-by-step explanation:
To calculate the area, you must multiply the length x width.
If you need help calculating the perimeter too, just add all your lengths and widths together twice.
which linear inequality represents the graph below?
A. y < -1/4x-4
B. y < 4x-4
C. y < -1/4x+4
D. y < -4x+4
30 students in grade 8 finished their summer packet before August 15.
This was 12% of all the students. How many students are in grade 8?
Step-by-step explanation:
12/100=30/x
12x=3000
x=250
hiii! !!
GIVING OUT BRAINLIEST IF GIVEN AN ANSWER WITH THOUROUGH EXPLANATION AND NOT JUST AN ANSWER! THANKS!
During the first part of a 6-hour trip, you travel 240 miles at an average speed of r miles per hour. For the next 72 miles of the trip, you
increase your speed by 10 miles per hour. What were
your two average speeds?
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Answer:
50 mph for 4.8 hours60 mph for 1.2 hoursStep-by-step explanation:
One way to write the relationship between time, speed, and distance is ...
time = distance/speed
For the first part of the trip, the time is ...
t1 = 240/r
For the second part of the trip, the time is ...
t2 = 72/(r+10)
The total time is 6 hours, so we have ...
t1 +t2 = 6
240/r +72/(r+10) = 6
We can simplify this a bit by multiplying by (r)(r+10)/6 to get ...
40(r+10) +12(r) = r(r+10)
r² -42r -400 = 0 . . . . . . . . subtract the left side and collect terms
(r -50)(r +8) = 0 . . . . . . . . factor
r = 50 . . . . . the positive solution of interest.
The two average speeds were 50 mph and 60 mph.
How many outcomes (sample points) for a deal of two cards from a 52-card deck are possible? Report your answer as an integer.
Answer:
1326
Step-by-step explanation:
[tex]{52\choose2}=\frac{52!}{(52-2)!2!}=\frac{52!}{50!*2!}=1326[/tex]
XYZ has side lengths that measure 20 centimeters each. Which of the
following best describes this type of triangle?
A. Obtuse triangle
B. Right triangle
C. Scalene triangle
D. Equilateral triangle
Answer:
it's and equilateral triangle because
all sides are equal
Answer:
equilateral triangle i have a math proffesor helping me
Step-by-step explanation:
I have a math proffesor helping me
Consumers Energy states that the average electric bill across the state is $39.09. You want to test the claim that the average bill amount is actually different from $39.09. What are the appropriate hypotheses for this test
The null hypothesis is [tex]\mu = 39.09[/tex]
The symbol [tex]\mu[/tex] is the Greek letter mu
The alternate hypothesis is [tex]\mu \ne 39.09[/tex] telling us we have a two-tailed test here. The "not equal" is directly tied to the keyword "different" given in the instructions. In other words, mu being different from 39.09 directly leads to [tex]\mu \ne 39.09[/tex]
So either mu is 39.09 or it's not 39.09
You can use H0 and H1 to represent the null and alternate hypotheses respectively.
----------------------
Summary:
The two hypotheses are
H0: [tex]\mu = 39.09[/tex]
H1: [tex]\mu \ne 39.09[/tex]
This is a two tailed test.
Solve by graphing. Round each answer to the nearest tenth.
6x2 = −19x − 15
a: −2, 1.7
b: −1.7, −1.5
c: −1.5, 1.5
d: −1.5, 1.7
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Answer:
b: -1.7, -1.5
Step-by-step explanation:
The graph is shown below. We have annotated the x-intercepts for the equivalent equation ...
6x^2 +19x +15 = 0
ANSWER ASAP IM BEING TIMED
IF I GET AN A ON THIS I WILL DO ANOTHER POINT FREE DROP, PLEASE SHOW YOUR WORK
The side of a square measures (4x − 7) units.
Part A: What is the expression that represents the area of the square? Show your work to receive full credit. (4 points)
Part B: What are the degree and classification of the expression obtained in Part A? (3 points)
Part C: How does Part A demonstrate the closure property for polynomials? (3 points)
(10 points)
Step-by-step explanation:
Area of a square = s x s
(4x-7)x(4x-7)
Open brackets
4x(4x-7)-7(4x-7)
16x^2-28-28x+49
16x^2-28x+21
Two vectors and are given by and . If these two vectors are drawn starting at the same point, what is the angle between them
Answer: hello your question is incomplete below is the complete question
The Two vectors; A = 5i + 6j +7k and B = 3i -8j +2k.
answer;
angle = 102°
Step-by-step explanation:
multiplying the vectors
A.B = |A| * |B|* cosθ
hence : Cosθ = (Ai*Bi )+ (Aj*Bj) + ( Ak*Bk/ (√A^2 *√B^2 )
= 15 - 48 + 14 /(√25+26+29) * (√9+64+4)
= -0.206448454
θ = cos^-1 ( -0.206448454) = 101.9° ≈ 102°
2/5 e +4 = 9
Help please
Answer:
e=12.5 or e=25/2
Step-by-step explanation:
A little help?? It’s trig
Answer:
12 [tex]\pi[/tex] = 37.699 f/s
Actually, the more interesting question
would have been how fast is the ball going in MPH?
25.7 MPH
Step-by-step explanation:
C = 2[tex]\pi r[/tex]
C = 2 [tex]* \pi * 1.2[/tex]
C = 2.4 [tex]\pi feet[/tex]
C (per second) = (5)(2.4 [tex]\pi feet[/tex])
C(per second) = 12 [tex]\pi[/tex] = 37.699 f/s
Julie and Mona know that that Earth’s average distance from the Sun is approximately 93 million miles and it takes 1 year to complete an orbit of the Sun. A new asteroid has been discovered orbiting the Sun at an average distance of 1,488 million miles. How long will it take for the asteroid, in Earth years, to complete one orbit of the Sun.
Answer:
16 years
Step-by-step explanation:
Given that :
Earth's distance from sun = 93 million miles
Number of years to complete an orbit = 1 year
Average orbiting distance of new asteroid = 1488 million miles
Number of years to complete an orbit = x
93,000,000 Miles = 1
1488000000 miles = x
Cross multiply :
93000000x = 1488000000
x = 1488000000 / 93000000
x = 16 years
Period taken to orbit the sun = 16 years
Answer: 64 Earth years...
A canning factory turns out 568 tins of jam on a certain day. How many tins will be produced in 297 working days?
