Answer:
a) The probability of obtaining a sample mean that is less than or equal to 1770 hours is P(M≤1770)=0.0013.
b) It is unusual, as there are only 13 chances in 10,000 (0.13%) of having this outcome.
Step-by-step explanation:
We have a population lifetime with mean of 1800 hours and standard deviation of 100 hours.
Samples of size n=100 are taken and tested.
We can calculate the probability of obtaining a sample mean that is less than or equal to 1770 hours using a z-score for the sample Mean M=1770 and then calculating its probability according to the standard normal distribution:
[tex]z=\dfrac{X-\mu}{\sigma/\sqrt{n}}=\dfrac{1770-1800}{100/\sqrt{100}}=\dfrac{-30}{10}=-3\\\\\\P(X<1770)=P(z<-3)=0.0013[/tex]
True or False? 3+51x=59.1 If x is 1.1
Answer:
true!
Step-by-step explanation:
plug in 1.1
3 + 51(1.1) = 59.1
3 + 56.1 = 59.1
59.1=59.1
Answer:
Truesolution,
[tex]3 + 51x = 59.1 \\ 3 + 51 \times 1.1 = 59.1 \\ 3 + 56.1 = 59.1 \\ 59.1 = 59.1[/tex]
Hence it is true..
Hope it helps..
Q12.
A woman applies for a new job that pays £8.50 a week more (after tax).
She will work 5 days a week and drive to work, as she does in her job now.
The new job is 6 miles further from her house.
Her car travels 8.5 miles per litre of petrol
Petrol costs £1.26 per litre
Will the woman be better off with the new job after she takes the petrol into consideration?
Explain your answer. Include calculations to support your decision.
Decision (yes/no)
8.5x1.295.70
Explanation and supporting calculations
CA
Answer:
Step-by-step explanation:
1l ........8.5 miles
x l .......6 miles
-----------------------
x=6*1/8.5
x=0.70 l
2*0.7=1.4 l petrol/day ( to work and come back home)
5*1.4=7 l/week ( 5 days works in a week)
7*1.26=8.82 L /week
8.82>8.5
The petrol costs more
So the answer is NO
How do you calculate the y-intercept of a line written in Standard Form?
Answer:
y-int = C/B
Step-by-step explanation:
Ax + By = C
y-int = C/B
Answer:
I hope this helps.
Step-by-step explanation:
The snail moved 6 inches in 120 minutes. What was the average speed of the snail in inches per minute
Answer:
0.05 inches per minute
Step-by-step explanation:
The formula for speed is [tex]Speed=\frac{Distance}{Time}[/tex]
The given distance is 6 inches and the time is 120 minutes. Plug in the components into the formula to solve for speed and reduce:
[tex]Speed=\frac{6}{120}[/tex]
[tex]Speed=\frac{1}{20}[/tex]
1/20 in decimal form is 0.05
Grace was given the description “three less than the quotient of a number squared and nine, increased by eight” and was asked to evaluate it when n = 6. Her work is shown below.
Step 1: 3 minus StartFraction n squared Over 9 EndFraction + 8
Step 2: 3 minus StartFraction 6 squared Over 9 EndFraction + 8
Step 3: 3 minus StartFraction 36 Over 9 EndFraction + 8
Step 4: 3 minus 4 + 8
Step 5: 7
In which step did she make an error?
step 1
step 2
step 4
step 5
Answer:
step 1
Step-by-step explanation:
when you say three less than the quotient
you put the quotient first and then subtract 3
Answer: Step 1
Step-by-step explanation: I took it on my quiz and got an 100
What percent of this grid is unshaded?
The grid has 10 columns and 10 rows making 100 equal sized squares 5 rows are
unshaded. The sixth row has 6 squares unshaded.
Answer:
56%
Step-by-step explanation:
We have a grid with 10 columns and 10 rows making 100 equal sized squares, they tell us that 5 rows are unshaded. Therefore half is unshaded, like so:
5 rows = 50 squares
They also tell us that the sixth row has 6 squares unshaded, which means that in total they would be:
50 + 6 = 56 squares
Knowing that the total is 100, the percentage would be:
56/100 = 0.56, that is, 56% are unshaded
Which input value produces the same output value for
the two functions?
O x= -3
0 x = -1
x = 0
O x = 1
Answer: x=1
Step-by-step explanation:
To find which input value that produces the same output value, we are looking for a coordinate pair that is the same on both function tables. If you go through each pair, we find that (1,3) is the same on both tables. Therefore, x=1 is the correct answer.
The input value which produces the same output value for the two functions is x = 1.
What is Function?A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.
Given two functions, f(x) and g(x).
We get that,
f(-3) = -5 and g(-3) = -13
They are not same.
f(-1) = -1 and g(-1) = -5
They are not same.
f(0) = 1 and g(0) = -1
They are not same.
f(1) = 3 and g(1) = 3
Hence the correct option is D.
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A number is equal to twice a smaller number plus 3. The same number is equal to twice the sum of the smaller number and 1. How many solutions are possible for this situation? (a)Infinitely many solutions exist because the two situations describe the same line. (b)Exactly one solution exists because the situation describes two lines that have different slopes and different y-intercepts. (c)No solutions exist because the situation describes two lines that have the same slope and different y-intercepts. (d)Exactly one solution exists because the situation describes two lines with different slopes and the same y-intercept.
Answer:
The correct answer option is: No solutions exist because the situation describes two lines that have the same slope and different y-intercepts.
The first four terms of a sequence are shown below 9,5,1,-3
Which of the following functions best defines this sequence?
A. f(1)=9, f(n+1)=f(n)-4 for n> or equal to 1
B. f(1)=9, f(n+1)=f(n)+4 for n> or equal to 1
C. f(1)=9, f(n+1)=f(n)-5 for n> or equal to 1
D. f(1)=9, f(n+1)=f(n)+5 for n> or equal to 1
Answer:
A. f(1)=9, f(n+1)=f(n)-4 for n> or equal to 1
Step-by-step explanation:
Given the sequence:
9, 5, 1, -3We can easily calculate the difference of terms:
-3- 1= 1- 5= 5-9= -4As the difference of terms is same and equal to -4, it is the AP (arithmetic progression)
This sequence can be defined In the form of function as:
f(1)= 9, as the first term is 9f(n+1)= f(n)- 4, as it is decreasing function with the difference of -4n ≥ 1, as we count from the first term onAll the above matches the first answer choice:
A. f(1)=9, f(n+1)=f(n)-4 for n> or equal to 1Two functions are graphed on the coordinate plane.
Which represents where f(x) = g(x)?
10
ger
8
f(4) = g(4) and f(0) = g(0)
f(-4) = g(4) and f(0) = g(0)
f(4) = 9(-2) and f(4) = g(4)
f(0) = g(4) and f(4) = g(-2)
6
to 54 -3 -2 -12
1 2 3 4 5 6 X
o)
-8
-124
Answer:
f(4) = g(4) and f(0) = g(0)
Step-by-step explanation:
In order for f(x) = g(x), the value of x must be the same in both functions:
f(4) = g(4) . . . corresponds to x=4
f(0) = g(0) . . . corresponds to x=0
The graph is not shown here, so we cannot say if these are the appropriate solutions. We can only say that the other choices are not.
f(x) = g(x) if ...
f(4) = g(4) and f(0) = g(0)
__
Something like f(0) = g(4) is useless for finding solutions to f(x) = g(x).
Which list orders the angles of triangle ABC from smallest to largest measure?
Answer:
B
Step-by-step explanation:
120 is less than 130 and 130 is less than 180
The orders that the angles of triangle ABC from smallest to largest measure is C. ∠B, ∠C, ∠A
What is a triangle?A triangle is a polygon that has three sides and three vertices. It is one of the basic figures in geometry. A right-angled triangle is a triangle having one of its angles with a measure of 90°. The slanted side of that triangle is called Hypotenuse and it is the longest side in that triangle.
We can see that angle A is the largest angle in the triangle, so it's going to be last in order.
Then the side AB is the second biggest , so the angle C is the second largest angle.
And then the last is angle B.
Therefore, the order must be ∠B < ∠C < ∠A
Hence, The orders that the angles of triangle ABC from smallest to largest measure is C. ∠B, ∠C, ∠A
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Which feature of a database displays data in a certain sequence, such as alphabetical order? Chart Filter Search Sort
Answer:
data bar
Step-by-step explanation:
Answer:
chart
Step-by-step explanation:
Find all points (if any) of horizontal and vertical tangency to the curve. Use a graphing utility to confirm your results. (If an answer does not exist, enter DNE.)
x=1-t , y=t^2
Horizontal tangent
(x,y)=________
Vertical tangent
(x,y)=________
Answer:
Horizontal tangent
(x, y) = (1, 0)
Vertical tangent
(x, y) = DNE
Step-by-step explanation:
The equation for the slope (m) of the tangent line at any point of a parametric curve is:
[tex]m = \frac{\frac{dy}{dt} }{\frac{dx}{dt} }[/tex]
Where [tex]\frac{dx}{dt}[/tex] and [tex]\frac{dy}{dt}[/tex] are the first derivatives of the horizontal and vertical components of the parametric curves. Now, the first derivatives are now obtained:
[tex]\frac{dx}{dt} = -1[/tex] and [tex]\frac{dy}{dt} = 2\cdot t[/tex]
The equation of the slope is:
[tex]m = -2\cdot t[/tex]
As resulting expression is a linear function, there are no discontinuities and for that reason there are no vertical tangents. However, there is one horizontal tangent, which is:
[tex]-2\cdot t = 0[/tex]
[tex]t = 0[/tex]
The point associated with the horizontal tangent is:
[tex]x = 1 - 0[/tex]
[tex]x = 1[/tex]
[tex]y = 0^{2}[/tex]
[tex]y = 0[/tex]
The answer is:
Horizontal tangent
(x, y) = (1, 0)
Vertical tangent
(x, y) = DNE
Repair calls are handled by one repairman at a photocopy shop. Repair time, including travel time, is exponentially distributed, with a mean of 1.1 hours per call. Requests for copier repairs come in at a mean rate of 1.6 per eight-hour day (assume Poisson). Determine the following:
Required:
a. Determine the average number of customers awaiting repairs.
b. Determine system utilization.
c. Determine the amount of time during an eight-hour day that the repairman is not out on a call.
d. Determine the probability of two or more customers in the system.
Answer and Step-by-step explanation:
Data provided in the question
Mean = 1.1 hours per call =
R = Mean rate = 1.6 per eight hour day
[tex]\mu[/tex] = [tex]\frac{8}{1.6}[/tex] = 5 per day
Based on the above information
a. The average number of customers is
[tex]= \frac{R^2}{\mu(\mu- R)}[/tex]
[tex]= \frac{1.6^2}{5(5- 1.6)}[/tex]
= 151
b. The system utilization is
[tex]= \frac{R}{\mu}[/tex]
= [tex]\frac{1.6}{5}[/tex]
= 0.32
c. The amount of time required is
= 1 - system utilization
= 1 - 0.32
= 0.68
And, there is 8 hours per day
So, it would be
= [tex]0.68 \times 8[/tex]
= 5.44 hours
d. Now the probability of two or more customers is
[tex]= 1 - (0.68 + 0.68 \times 0.32)[/tex]
= 0.1024
Therefore we simply applied the above formulas
A) The average number of customers awaiting repairs is; 0.06
B) The system utilization is; 21.98%
C) The amount of time during an eight-hour day that the repairman is not out on a call is; 6.24 hours
D) The probability of two or more customers in the system is; P₂ = 0.0483
A) We are given;
Arrival rate; a = 1.6 calls per 8 hours = 1.6/8 = 0.2 calls per hour
Repair time; s = 1.1 hours per call = 1/1.1 = 0.91 call per hour
Formula for average number of customers waiting repairs is;
a²/(s( s - a))
⇒ (0.2²)/(0.91 × (0.91 – 0.2)
= 0.04/(0.91 × 0.71)
= 0.06
B) Formula for System utilization is; a/s × 100
⇒ (0.2/0.91) × 100 = 21.98%
C) Percentage of time the repairman is not out on a call = 100 – 21.98% = 78.02%
∴ amount of time in a 8 hour day repairman is not on a call = 78.02% of 8 hours = 6.24 hours
D) Probability that zero customers are in the system; P₀ = 1 – (a/s)
P₀ = 1 – (0.2/0.91)
P₀ = 1 – 0.2198
P₀ = 0.7802
Probability that 1 customer is in the system; P₁= ( a/s ) × P₀
P₁ = (0.2/0.91) × P₀
P₁ =0.2198 × 0.7802
P₁ = 0.1715
Probability that 2 or more customers are in the system;
P₂ = 1 - (P₀ + P₁)
P₂ = 1 – (0.7802 + 0.1715)
P₂ = 0.0483
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Which statement is true about the diagram?
Write the first four terms in the following sequences. A(n+1)=1/2 A(n) for n≥1 and A(1)=4 .
Answer:
4,2,1 and 1/2
Step-by-step explanation:
The first term is 4 since A(1)=4
● A(2) = (1/2)*A(1) = (1/2)*4 = 2
So the second term is 2
● A(3) = (1/2)*A(2) = (1/2)*2= 1
The third term is 1
●A(4) = (1/2)*A(3) = (1/2) *1 = 1
5) What is the correct answer to "2+5*4-8--4/5 =?"
a) 12
b) 17,5
c) 75
Answer:
14.8
Step-by-step explanation:
2 + 5 × 4 - 8 - (-4/5)
Solve for brackets.
2 + 5 × 4 - 8 + 4/5
Multiply.
2 + 20 - 8 + 4/5
Add or subtract.
= 74/5
The function h(x)=12/x-1 is one to one. Algebraically find it’s inverse, h^-1(x).
Answer:
Step-by-step explanation:
hello,
I assume that you mean
[tex]h(x)=\dfrac{12}{x-1}[/tex]
so first of all let's take x real different from 1 , as this is not allowed to divide by 0
[tex](hoh^{-1})(x)=x=h(h^{-1}(x))=\dfrac{12}{h^{-1}(x)-1} \ \ \ so\\h^{-1}(x)-1=\dfrac{12}{x} \\\\h^{-1}(x)=1+\dfrac{12}{x}[/tex]
and this is defined for x real different from 0
hope this helps
Provide an appropriate response.
In a recent survey, 72% of the community favored building a health center in their neighborhood. If 14 citizens
are chosen, find the probability that exactly 10 of them favor the building of the health center.
0.001
0.714
0.720
0.230
Answer:
0.230
Step-by-step explanation:
Given
Estimate = 72%
Number of citizens = 14
Required
Find the probability that exactly 10 of the citizens will be in favor
This question can be solved using binomial expansion of probability which states;
[tex](p + q)^n = ^nC_0 .\ p^n.\ q^{0} + ....+ ^nC_r .\ p^r.\ q^{n-r}+ .. +^nC_n .\ p^0.\ q^{n}[/tex]
Where p and q are the probabilities of those in favor and against of building a health center;
n is the selected sample and r is the sample in favor
So; from the above analysis
[tex]n = 14[/tex]
[tex]r = 10[/tex]
[tex]p = 72\% = 0.72[/tex]
[tex]q = 1 - p[/tex]
[tex]q = 1 - 0.72[/tex]
[tex]q = 0.28[/tex]
Since, we're solving for the probability that exactly 10 citizens will be in favor;
we'll make use of
Substituting these values in the formula above
[tex]Probability = ^nC_r .\ p^r.\ q^{n-r}[/tex]
[tex]Probability = ^{14}C_{10} .\ 0.72^{10}.\ 0.28^{14-10}[/tex]
[tex]^{14}C_{10} = 1001[/tex]
So, the expression becomes
[tex]Probability =1001 * \ 0.72^{10}.\ 0.28^{14-10}[/tex]
[tex]Probability =1001 * \ 0.72^{10}.\ 0.28^4[/tex]
[tex]Probability =1001 * 0.03743906242 * 0.00614656[/tex]
[tex]Probability =0.23035156495[/tex]
[tex]Probability =0.230[/tex] ----Approximated
Hence, the probability that exact;y 10 will favor the building of the health center is 0.230
A psychology professor assigns letter grades on a test according to the following scheme. A: Top 8% of scores B: Scores below the top 8% and above the bottom 61% C: Scores below the top 39% and above the bottom 16% D: Scores below the top 84% and above the bottom 8% F: Bottom 8% of scores Scores on the test are normally distributed with a mean of 65.4 and a standard deviation of 9.7 Find the numerical limits for a D grade. Round your answers to the nearest whole number, if necessary.
Answer:
it a
Step-by-step explanation:
just took test
Could someone help? Not sure if my answer is right.
Answer:
Your answer is right
Step-by-step explanation:
Don't second guess your self
Suppose a shipment of stereos contained 6% defectives. If a sample of size 285 is selected, what is the probability that the sample proportion will differ from the population proportion by less than 4%? Round your answer to four decimal places. 20 points.
Answer:
0.9954
Step-by-step explanation:
For normal distribution z score is
= [tex]\frac{\hat p-p}{\sigma p}[/tex]
Population proportion (p) = 0.060
Sample size (n) = 285
the standard error of proportion is
= [tex]\sigma p = \sqrt{\frac{p\times (1 - p)}{n}}[/tex]
After putting the values into the above formula we will get
= 0.0141
Probability as the sample proportion will different from the population proportion by lower than the 4% that is
Probability = P(0.02<X<0.1) = P(-2.84<Z<2.84) = 0.9977 - 0.0023
= 0.9954
Write an equation in point-slope form for each line
Answer: y=x+1
Step-by-step explanation:
y+1=1(x+2)
y+1=x+2
y=x+1
Hope this helps:)
If f(x) = 5x – 2 and g(x) = 2x + 1, find (f - g)(x).
A. 3 - 3x
B. 3x-3
C. 7x-1
D. 7x-3
Answer:
The difference of the functions is (f-g)(x) = 3x - 3
Step-by-step explanation:
In the problem, we are asked to find the difference of the two functions, f(x) and g(x). When we see (f-g)(x), this means that we are going to subtract g(x) from f(x).
f(x) = 5x - 2
g(x) = 2x + 1
(f-g)(x) = (5x - 2) - (2x + 1)
Distribute the negative to (2x + 1)
(f-g)(x) = 5x - 2 - 2x - 1
Combine like terms. Make sure your answer is in standard form.
(f-g)(x) = 3x - 3
So, the answer to the equation is (f-g)(x) = 3x - 3
Help I need help with this answer
Answer:
5.4 cm^2
Step-by-step explanation:
Area of a triangle is calculated by multiplying height to the base and that divided by two
5.4 × 2 ÷ 2 = 5.4 cm^2
Need help with this Pythagorean theorem formula. In a right triangle ,find the length not given? c=hypotenuse, a=6,b=8. use radicals as needed
Answer: c = 10
Step-by-step explanation:
Pythagorean Theorem states that in a right triangle [tex]a^2 + b^2 = c^2[/tex], where a and b are the legs of the triangle and c is the hypotenuse. Thus, because a=6 and b=8, 36+64=c². Thus 100=c². Thus 10=c
The human resource department at a certain company wants to conduct a survey regarding worker benefits. The department has an alphabetical list of all 2708 employees at the company and wants to conduct a systematic sample of size 30.A) What is k?B) Determine the indviduals who will be administered the survey.
Answer:
A) 90
B) The individuals in the survey will be 11, 101, 191,...., 2621.
Step-by-step explanation:
Tenemos lo siguiente a partir del enuciado:
A) let, a consider a department has an alphabetical list of all 2708 employees at company and wants to conduct a systematic sample. Substitute the value as:
k = N/n
reemplanzado nos queda:
k = 2708/30 = 90.26
Lo que quiere decir que el valor de k es de aproximadamente 90 B) Randomly select the number between I and 90, Suppose the randomly selected sumber is 11. The individuals in the survey will be; need to find 30th team, hence by using the airthmetic perogression nth term formula:
30th term = 11+ (30 - 1) *90
30th term = 2621
The individuals in the survey will be 11, 101, 191,...., 2621.
The random sample is obtained
You have $60. You want to buy a pair of jeans and a shirt. The pair of jeans cost $27.
You come home with $15. How much did you spend on the shirt?
Answer:
$18
Step-by-step explanation:
Buying the jeans for $27 leaves you with ($60 - $27), or $33.
Buying the shirt for s dollar leaves you with $15. To find s, the price of the shirt, you subtract $15 from $33: $18.
The shirt cost you $18.
During flu season, there were 124 students out of school on a particular day. If there are 775 students in the school, what percent
of them have the flu
Answ
Step-by-step explanation:
soln,
total number of students =775
present students=124
now,
let the % of students who have flu be x%
here,
x% of 775 is 124
x/100*775=124
775x=12400
x=12400/775
x=16%
So, the% of students is 16%.
There are 775 students in the school and the percentage of students who have flu is 16%.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
For example, If Saima obtained a score of 57% on her exam, that corresponds to 67 out of 100. It is expressed as 57/100 in fractional form and as 57:100 in ratio form.
Given that the total number of students = 775
The number of students present = 124
Let the percentage of students who have flu be x %
As per the given data, the solution would be as:
⇒ x% of 775 = 124
x% is expressed as x/100 in fractional form
⇒ (x/100)(775) = 124
⇒ 775x=12400
⇒ x = 12400/775
⇒ x = 16%
Therefore, the percentage of students who have flu is 16%.
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W
5. 26.5 liter air dan 8.25 liter jus oren dicampurkan bersama. Semua campuran itu
dibotolkan dengan saiz setiap botol adalah 1.25 liter. Berapa botolkah diperlukan
untuk mengisi semua campuran jus oren tersebut?
A. 25
B. 26
C.27
D. 28
Answer: D, 28 bottles.
Step-by-step explanation:
This can be translated to:
26.5 liters of water and 8.25 liters of orange juice are mixed together. All that mixture is bottled in bottles of 1.25 liters. How many bottles are needed to fill all the orange juice mixture?
the total mass of mixture that we have is:
26.5 L + 8.25 L = 34.75 L.
if we want to divide it into groups of 1.25 L, we have:
N = 34.75/1.25 = 27.8
So we have 27.8 groups of 1.25L this means that we need 27.8 bottles.
But we can not have a 0.8 of a bottle, so we must round it up to 28 bottles.
Then the correct option is D: