Answer:
The probability that sample mean is less than 2 is 0.1423.
Step-by-step explanation:
Let X denote the number of accidents per week at a hazardous intersection.
It is provided that the mean and standard deviation of X are, μ = 2.2 and σ = 1.4.
(a)
According to the Central Limit Theorem if an unknown population is selected with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from this population with replacement, then the distribution of the sample means will be approximately normally.
Then, the mean of the sample means is given by,
[tex]\mu_{\bar x}=\mu[/tex]
And the standard deviation of the sample means is given by,
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]
As the sample size is not large enough, i.e. n = 9 < 30, the Central Limit Theorem cannot be applied to approximate the sampling distribution of the mean number of accidents per week at the intersection.
And since the distribution of X is not specified, the probability cannot be computed.
(b)
In this case, the sample size is large enough, i.e. n = 52 > 30, the Central Limit Theorem can be applied to approximate the sampling distribution of the mean number of accidents per week at the intersection.
Compute the probability that sample mean is less than 2 as follows:
[tex]P(\bar X<2)=P(\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}<\frac{2-2.2}{1.4/\sqrt{56}})\\\\=P(Z<-1.07)\\\\=0.14231\\\\\approx 0.1423[/tex]
Thus, the probability that sample mean is less than 2 is 0.1423.
Max pays a flat rate of $85 for his cell phone. He is also charged $0.15 for every text that he sends. His cell phone bill can be no more than the amount he has budgeted for it each month. If x represents the number of texts and y represents his budgeted amount, which inequality represents Max's cell phone budget each month? (3 points)
a $0.15x + $85 ≥ y
b $0.15x + $85 ≤ y
c $0.15x - $85 ≥ y
d $0.15x - $85 ≤ y
If x² + xy – 3y = 3, then at the point (2, 1), dy/dx
(A) 5
(B) 4
(C) 7/3 (D) 2
Answer:
A
Step-by-step explanation:
We are given the equation:
[tex]x^2+xy-3y=3[/tex]
And we want to find dy/dx at the point (2, 1).
Find dy/dx. We can take the derivative of both sides with respect to x:
[tex]\displaystyle \frac{d}{dx}[x^2+xy-3y]=\frac{d}{dx}[3][/tex]
Implicitly differentiate:
[tex]\displaystyle 2x+y+x\frac{dy}{dx}-3\frac{dy}{dx}=0[/tex]
Solve for dy/dx:
[tex]\displaystyle \begin{aligned} x \frac{dy}{dx} - 3\frac{dy}{dx} & = -2x - y \\ \\ \frac{dy}{dx}(x - 3) & = -2x - y \\ \\ \frac{dy}{dx} & = \frac{-2x-y}{x-3} \\ \\ & = \frac{2x+y}{3-x} \end{aligned}[/tex]
To find dy/dx at (2, 1), evaluate dy/dx for x = 2 and y = 1. Hence:
[tex]\displaystyle \frac{dy}{dx}\Big|_{(2, 1)}=\frac{2(2)+1}{3 - (2)}=\frac{5}{1}=5[/tex]
Hence, our answer is A.
We want to find the differential dy/dx for the given expression at the given point. We will see that the correct option is A.
How to differentiate the expression?
We have:
x^2 + xy - 3y = 3
First, we need to isolate the variable y in one side of the equation, so we get:
xy - 3y = 3 - x^2
y*(x - 3) = 3 - x^2
y = (x - x^2)/(x - 3)
Now we can differentiate this, remember that if:
f(x) = g(x)*h(x)
then:
f'(x) = g(x)*h'(x) + g'(x)*h'(x)
Using that rule.
dy/dx = (1 - 2x)/(x - 3) - (x - x^2)/(x - 3)^2
Now we need to evaluate this in x = 2 (the x-value of the point) so we get:
(1 - 2*2)/(2 - 3) - (2 - 2^2)/(2 - 3)^2
= (-3)/(-1) - (-2)/(1) = 5
So the correct option is A.
If you want to learn more about differentiation, you can read:
https://brainly.com/question/24898810
How many gallons of a 70% antifreeze solution must be mixed with 100 gallons of 30% antifreeze to get a mixture that is 60% antifreeze?
Answer:
350 gallons
Step-by-step explanation:
Let x = number of gallons of 70% solution
100 = number of gallons of 25% solution
Then, x + 100 = number of gallons of 60% solution
0.70x + 0.25(100) = 0.60(x + 100)
0.70x + 25 = 0.60x + 60
0.10x = 35
x = 350 gal
Mix 350 gal of 70% solution with 100 gal of 25% solution to obtain 450 gal of 60% solution.
Answer: Add 315 gallons of 70% antifreeze to 90 gallons of 25% antifreeze to make a 60% mixture.
What if it like this
Answer:
The answer is 4:1
Step-by-step explanation:
16:3 goes to 4:1
What equation shows how to use equivalent fractions to evaluate 2/5 + 3/4
Answer:
Step-by-step explanation:
Exact form: 23/20
Decimal form: 1.15
what is the are in square feet of a 100 yard by 60 yard football field
Marlene made a table to relate the number of T-shirts to the total cost. How can
you tell from the table that the relationship is not proportional?
Number of T-shirt
1
2
3
4
A
The number of T-shirts increases in intervals of one.
B
The rule of multiplying by 8 works for all but 4 T-shirts.
C
The number of T-shirts increases by a different amount than the total cost does.
D
All of the numbers of T-shirts can be multiplied by the same amount to get the cost.
Answer:
The Correct answer would be B.
The rule of multiplying by 8 works for all but 4 T-shirts
Step-by-step explanation:
Answer: B) The rule of multiplying by 8 works for all but 4 T-shirts.
Step-by-step explanation:
Got ir right on Time4Learning
6.) The average delivery charge for a refrigerator is $54. The standard deviation is 53. Find the
range in which at least 75% of the data values will fall.
1
Answer:
88.9%
Step-by-step explanation:
The number of miles driven by a truck driver falls between 300 and 700, and follows a uniform distribution.
a. Find the probability that the truck driver goes more than 650 miles in a day.
b. Find the probability that the truck drivers goes between 400 and 650 miles in a day.
c. At least how many miles does the truck driver travel on the furthest 10% of days?
Answer:
(A) 0.125 probability
(B) 0.625 probability
(C) 660 miles
Step-by-step explanation:
The distance driven by a truck driver daily, falls between 300miles and 700miles and follows a uniform distribution.
(A) The probability that the truck driver goes more than 650 miles a day is:
[700 - 650] / [700 - 300] = 50/400 = 0.125
(B) The probability that the truck driver goes between 400 and 650 miles a day is:
[650 - 400] / [700 - 300] = 250/400 = 0.625
(C) The minimum number of miles the truck driver travels on the furthest 10% of days is given thus:
10% of 400 = 40
Subtract this from the farthest distance;
700miles - 40miles = 660miles
What is the solution to -3 m 49 771-49
Answer:
49722
Step-by-step expla Reste los número 49722 solucion
Alterna entre 4,9722 x 10 a la 4
There are 18 girls and 24 boys who want to participate in a trivia challenge. If each team must have the same ratio of girls and boys, what is the greatest number of teams that can enter? Find how many boys and girls each team would have.
Answer:
4 team could enter 5 people in each team
Step-by-step explanation:
there will be 6 teams, each team having 3 girls and 4 boys
Step-by-step explanation:
6*3=18
6*4=24
a line has the equation 3x-4y=1 choose the equation of a line that is parallel to the given line
Step-by-step explanation:
The equation of the given line is 3x - 4y = 1
A line parallel to the given line will have slope that is the same as this one.
The equation of a straight line is expressed as;
y = mx + c
y and x are the coordinates
m is the slope
c is the y-intercept
Now, we write the given line in the slope - intercept form;
3x - 4y = 1
-4y = -3x + 1
Divide through by -4
[tex]\frac{-4y}{-4}[/tex] = [tex]\frac{-3x}{-4}[/tex] + [tex]\frac{1}{-4}[/tex]
y = [tex]\frac{3}{4} x[/tex] - [tex]\frac{1}{4}[/tex]
The slope of this line is [tex]\frac{3}{4}[/tex]
Any line with the slope [tex]\frac{3}{4}[/tex] will be parallel to the given line.
I need this at 8 hurry guys I’ll give brainlyest
Answer:
1 [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
Evaluate the following expression. Express your answer in simplest form.
3
16
+
5
18
1
2
5
16
10
32
Answer:
518125161348
Step-by-step explanation:
316
518125161032
-------------------------
518125161348
Is 13 a solution to the compound inequality d>5 and x<10
Answer:
Step-by-step explanation:
13>5 is correct but 13 < 10 is not correct
so 13 is not a solution
Calculate the insurance costs.
The Greene family obtains bodily injury and property damage automobile insurance in the amount of 50/100/10. The car
that they insure is not driven to work, and no male drivers under twenty-five use the car.
a. What does the Greene family pay as an annual premium?
b. How much would it cost him to purchase insurance in the amount of 100/300/25?
c. What is the difference in cost?
Answer:
a. What does the Greene family pay as an annual premium? $450.60
b. How much would it cost him to purchase insurance in the amount of 100/300/25? $480.70
c. What is the difference in cost? $30.10
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Jaden and his family are using a map to drive down to Napa Valley. On the map, the distance is given by the equation c = 1.3m, where c is the number of centimeters on the map and m is the corresponding real-world distance in miles. If they cover a distance of 18 miles, that would mean a distance of centimeters on the map.
Answer:13.84
Step-by-step explanation:
Answer:
13.84
Step-by-step explanation:
In ΔIJK, j = 7.6 cm, k = 7.8 cm and ∠I=27°. Find the length of i, to the nearest 10th of a centimeter.
Answer:
3.6
Step-by-step explanation:
TRUST ME LOL
Compare using <, > or = 7 2/5 _ 7 3/7
Answer:
<
Step-by-step explanation:
7 2/5 = 37/5
7 3/5 = 52/7
~~~~~~~~~~~
37/5 times 7 = 259/35
52/7 times 5 = 260/35
~~~~~~~~~~~~~~~~~
Subtract then you difference is one, therefor 7 3/5 is greater.
I WILL MARK BRAINLIST
Answer:
the Answer is C. A and B
Step-by-step explanation
plot the points for each figure
Jen is single and owns a condo. Her condo costs $120,000 and she has a $100,000 mortgage at 5%. She pays $3,600 in property tax and contributes $500 to ber church per year. Does she use Iternized Deduction or Standard Deduction?
Answer:
`298,483
Step-by-step explanation:
Use the information mZ1 = (3x + 30), m42 = (5x – 10°, and x = 20, and the theorems you have learned to
show that 1 || m.
Answer:
Step-by-step explanation:
First you have to do 2 + 2=
Write an equation for 51 divided by 3 is k
Answer:
51/3 = 17
Step-by-step explanation:
3 can go into 5 one time (1)
5 minus 3 equals 2.
Bring down the one, make sure the 2 and 1 are beside. (21)
How many times can 3 go in to 21 ?
7 !
So, put 1 and 7 together, and get 17!
Please hurry please
Answer:yes
Step-by-step explanation:
44/4=11
11 is less than 27
Kyle invests $11200 in two different accounts. The first account paid 10 %, the second account paid
7 % in interest. At the end of the first year he had earned $958 in interest. How much was in each
account?
$____at 10 %
$____at 7 %
Answer:
Kyle invested 5,800 at 10% and 5,400 at 7%.
Step-by-step explanation:
Let x be the amount Kyle invests in the 10% account.
0.1x + 0.07(11200 - x) = 958
0.1x + 784 - 0.07x = 958
0.03x = 174
x = 5800
Kyle invests $5,800 at 10% and $5,400 at 7%.
What is the simple interest?Simple interest is the borrowing amount added only to the principal amount.
The Formula to calculate the simple interest is;
S.I. = P x T x R / 100,
Where S.I. is simple interest, P is principal amount, T is time period and R is interest rate in a year.
Given:
Kyle invests $11200 in two different accounts.
The first account paid 10 %.
The second account paid 7 % in interest.
At the end of the first year,
he had earned $958 in interest.
Let n be the amount Kyle invests in the 10% account.
0.1n + 0.07(11200 - n) = 958
0.1n + 784 - 0.07n = 958
0.03n = 174
n = 5800
Therefore, $5,800 at 10% and $5,400 at 7%.
To learn more about the simple interest; https://brainly.com/question/25845758
#SPJ2
What should be subtracted from 538 to get reminder 3 when divided by 11
Answer:
4
Step-by-step explanation:
Answer: 7
Step-by-step explanation: 538÷11=48 + 10
so to get remainder 3 subtract 7 from 538
complete the point-slope equation of the line through (1,0) and (6,-3)
Answer: y- (-3)= -3/5 (x-6)
Step-by-step explanation:
Find the exact value of tan^-1(1)
A. Pi/4
B. 7pi/4
C. 5pi/4
D. 3pi/4
helppppp please I will give brainliest
Answer:
y=3/4x
Step-by-step explanation:
What is the purpose of a pilot sample?
a. To help clarify how the sampling process will be performed.
b. To provide an idea of what the population standard deviation might be.
c. To save time and money instead of having to carry out a full sampling plan.
d. To provide a better idea of what the population mean will be.
Answer:
b. To provide an idea of what the population standard deviation might be
Step-by-step explanation:
Pilot sample can be regarded as the
small scale preliminary experiment whereby a smaller size of samples which is smaller compare to expected size is taken population of interest which gives the estimate for the population standard deviation.
The population standard mean is a parameter and it's been calculated from every entity of the population and
can be calculated using below formula
σ =√Σ (xi -μ)^2 /N
Where N= size of the population
σ= population standard mean
μ= population mean
Xi=each sample from the population