Answer:
i = 351, j = 0
Step-by-step explanation:
The while loop runs 5 times as indicated by the variable, count.
The variable, i, has an initial value of 10. The first line of the loop code doubles the value of i while the second increments it by 1. This is done 5 times. We have
Iteration 1: i = 10 + 10 + 1 = 21
Iteration 1: i = 21 + 21 + 1 = 43
Iteration 1: i = 43 + 43 + 1 = 87
Iteration 1: i = 87 + 87 + 1 = 175
Iteration 1: i = 175 + 175 + 1 = 351
The third line of the loop code decrements j by 1. However, the fourth line sets j = 0 by subtracting it from itself. Hence, j is always 0 at the end of the loop, no matter its initial value or the number of iterations.
Thus, at the end of the code snippet, i = 351 and j = 0.
The function shown in the graph is
A) f(x) = x - 1
B) f(x) = 2x - 1
C) f(x) = x - 0.5
D) f(x) = 2x - 0.5
Answer:B
Step-by-step explanation:
if you substitute any convenient value of x into f(x)= 2x-1 you see that it holds true when looking for the corresponding value of y.
For example,if you substitute x=5 into function B you get:
f(5)= 2(5) -1 = 10- 1 =9
Now,if you go on x =5 on the graph and check the corresponding value of y you that this value it is indeed 9.
Answer:
B) f(x) = 2x - 1Step-by-step explanation:
Look at the picture.
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept → (0, b)
The formula of a slope:
[tex]m=\dfrac{\Delta y}{\Delta x}=\dfrac{rise}{run}[/tex]
We have:
[tex]rise=4\\run=2\\b=-1[/tex]
The slope:
[tex]m=\dfrac{4}{2}=2[/tex]
Substitute to the equation of a line:
[tex]y=2x+(-1)=2x-1[/tex]
NEED HELP ASAP PLEASE!!
Answer:
5 5/6
Tell me if u got it right
A plastic rod 1.5 m long is rubbed all over with wool, and acquires a charge of -9e-08 coulombs. We choose the center of the rod to be the origin of our coordinate system, with the x-axis extending to the right, the y-axis extending up, and the z-axis out of the page. In order to calculate the electric field at location A = < 0.7, 0, 0 > m, we divide the rod into 8 pieces, and approximate each piece as a point charge located at the center of the piece. 1. What is the length of one of these pieces? 2. What is the location of the center of piece number 2? 3. How much charge is on piece number 2?
Answer:
a) I = 0.1875 m
b) r_2 = 0.46875 m
c) q = -1.125*10^-8 C
Step-by-step explanation:
Given:
- The total Length of rod L = 1.5 m
- The total charge of the rod Q = -9 * 10^8 C
- Total section of a rod n = 8
Find:
1. What is the length of one of these pieces?
2. What is the location of the center of piece number 2?
3. How much charge is on piece number 2?
Solution:
- The entire rod is divided into 8 pieces, so the length of each piece would be:
l = L / n
l = 1.5 / 8
I = 0.1875 m
- The distance from center of entire rod and center of section 2 is 2.5 times the section length
r_2 = 2.5*l
r_2 = 2.5*(0.1875)
r_2 = 0.46875 m
- Assuming the charge on the rod is uniformly distributed. The the charge for each section of rod is given by q:
q = Q / n
q = -9 * 10^8 / 8
q = -1.125*10^-8 C
An album sells for $12.00 through an online music service. If the album is 20% off, and sales tax is 5%, what is the total price of the album including tax?
Answer:
Total price of the album including tax is $10.08
Step-by-step explanation:
Sales price without discount and tax = $12
% discount = 20%
Sales price with discount = 12 - (20/100 × 12) = 12 - 2.4 = $9.6
% sales tax = 5%
Tax = 5/100 × 9.6 = $0.48
Total price of the album including tax = $9.6 + $0.48 = $10.08
Answer:
Final price = 9.6*(105/100) = 9.6*1.05 = 10.08 $
Step-by-step explanation:
The original price of the album is 12 to find out the price after the discount is applied we need to compute 100% - 20% = 80% of the original price. So we can use the following expression:
Price after discount = original price * (80/100)
Price after discount = 12 * (80/100)
Price after discount = 12 * 0.8 = 9.6 $
Now we have to include the sale tax of 5%, since it's a tax we need to add it to the original value so 100% + 5% = 105% of the sale's price:
Final price = Price after discount * (105/100)
Final price = 9.6*(105/100) = 9.6*1.05 = 10.08 $
Let E be the event that a corn crop has an infestation of ear worms, and let B be the event that a corn crop has an infestation of corn borers. Suppose that P(E) = 0.24, P(B) = 0.16, and P(E and B) = 0.13. Find the probability that a corn crop has either an ear worm infestation, a corn borer infestation, or both.
Answer:
The probability that a corn crop has either an ear worm infestation, a corn borer infestation
P(EUB) = 0.27
Step-by-step explanation:
Explanation:-
Addition theorem on probability:-
If S is a sample space, and E , F are any events in S then
P(EUF) = P(E) +P(F) -P(E n F)
Let 'E' be the event that a corn crop has an infestation of ear worms
let 'B' be the event that a corn crop has an infestation of corn bores
P(EUB) = P(E) +P(B) -P(E n B)
given P(E) = 0.24 and P(B) = 0.16 and P(E n B) =0.13
P(EUB) = P(E) +P(B) -P(E n B)
P(EUB) = 0.24 + 0.16 - 0.13
= 0.27
The probability that a corn crop has either an ear worm infestation, a corn borer infestation
P(EUB)=0.27
The probability that a corn crop has either an ear worm infestation, a corn borer infestation, or both is 0.27.
Explanation:You are asked to find the probability that a corn crop has either an ear worm infestation, a corn borer infestation, or both. This situation relates to the basic rules of probability, specifically the rule for the probability of the union of two events.
The formula to find the probability of event E (ear worm infestation), event B (corn borer infestation) or both happening is: P(E or B) = P(E) + P(B) - P(E and B).
Plugging in the given values, we get: P(E or B) = 0.24 + 0.16 - 0.13 = 0.27.
Therefore, the probability that a corn crop has either an ear worm infestation, a corn borer infestation, or both is 0.27.
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Click through and select the graph that is not a direct variation.
PLEASE HELP
Answer:
The last one, the one which is not passing through the origin
Step-by-step explanation:
y = mx + c (generally)
For direct proportion, c has to be 0.
The last graph is the one which is not passing through the origin.
How to solve for the variation?Using the slope of a line, a positive slope tells us that the line is increasing.
From the left to the right of graph, it shows that a person is climbing. A negative slope tells us that there is a fall.
We have;
y = mx + c
For direct proportion, c has to be zero.
Therefore, we can conclude that the last graph is the one that's not passing through the origin.
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An investor purchased 100 shares of Fifth Third Bank stock and 100 shares of Santee Electric Cooperative stock. The probability the bank stock will appreciate over a year is 0.70. The probability the electric utility will increase over the same period is 0.60. Assume the two events are independent.a. What is the probability both stocks appreciate during the period?
b. What is the probability the bank stock appreciates but the utility does not?
c. What is the probability at least one of the stocks appreciates?
Answer:
(a) 0.42
(b) 0.28
(c) 0.88
Step-by-step explanation:
Let probability that the bank stock will appreciate over a year, P(A) = 0.70
Probability that the electric utility will increase over the same period, P(B) = 0.60
Also, it is given that the two events are independent.
(a) Probability that both stocks appreciate during the period = Bank stock will appreciate * Electric utility will appreciate = P(A) * P(B)
= 0.70 * 0.60 = 0.42 .
(b) Probability that the bank stock appreciates but the utility does not is given by;
P(A) * (1 - P(B)) = 0.70 * (1 - 0.60) = 0.70 * 0.40 = 0.28 .
(c) Probability that at least one of the stocks appreciates = P(A [tex]\bigcup[/tex] B)
P(A [tex]\bigcup[/tex] B) = P(A) + P(B) - P(A [tex]\bigcap[/tex] B)
= 0.70 + 0.60 - (0.70 * 0.60) { because both events are
independent }
= 1.3 - 0.42 = 0.88 .
What is the measure of DE?
A. 12
B. 16
C. 20
D. 10
Answer:
c
Step-by-step explanation:
A school district need 3 teachers for every 70 children . They expect to have 14,700 in the district next year. At this time they have 612 teachers so how many more do they need
Answer: They need 18 teachers more.
Step-by-step explanation:
Hi, to solve this problem, first, we have to divide the expected number of children (14,700) by 70.
14,700 / 70 = 210 groups of 70 childrenWe obtain that they are expecting 210 groups of 70 children each. Since the school district needs 3 teachers for every 70 children, we have to multiply the number of groups (210) by the number of teachers per group (3).
210 x 3 = 630 teachersWe obtained the total number of teachers needed for 14,700 children.
Since at this time the district has 612 teachers, to find the teachers missing we have to subtract the actual number of teachers (612) to the number of teachers needed (630).
630 - 612 = 18They need 18 teachers more.
Write a statement that declares and initializes two integer variables. Call the first one age and initialize it to 15, and call the second one weight and initialize it to 90.
Answer:
First is to define the language in which to make the statement, I chose the language C, because it is the most common. To initialize the variable, the first thing is to define the type, in this case it is an integer type.
In language C, that is determined by int, then the name of the variable, in this case it would be age. We close with; To finish the order. Then we give the courage that asks us to initiate.
In the end, it would look like this:
int age;
age = 15;
int weight;
weight = 90;
Final answer:
To declare and initialize two integer variables called age and weight, one can use the code 'int age = 15, weight = 90;'.
Explanation:
To declare and initialize two integer variables in most programming languages, you can use a single line of code. For the variables age and weight, the statement might look like this:
int age = 15, weight = 90;
This line of code creates two variables of type integer named age and weight. The variable age is initialized with the value 15, and weight is initialized with the value 90.
The use of the comma in the statement allows for both variables to be declared and initialized in one concise statement.
Each of the 50 students participating in a workshop is either an undergraduate or a graduate student. If P is the probability that a randomly selected participant will be a female graduate student, is P less than \small \frac{1}{2} ?
Answer:
no
Step-by-step explanation:
no
In a return-standard deviation space, which of the following statements is(are) true for risk-averse investors? (The vertical and horizontal lines are referred to as the expected return-axis and the standard deviation-axis, respectively.) I) An investor's own indifference curves might intersect. II) Indifference curves have negative slopes. III) In a set of indifference curves, the highest offers the greatest utility. IV) Indifference curves of two investors might intersect.
Answer:
Option iii) and iv) are the correct option
Step-by-step explanation:
Correct option is - III and IV only
I) investors indifference curves are parallel they canno be intersect (False)
II) Indifference curve always be in a positive slope hence the statement is (False)
III) In a set of indifference curves, the higher the risk , the higher the return and as such the highest offers the greatest utility. (True)
IV) Indifference curve of investors with a same risk return trade off might intersect . (True)
An SRS of size n was taken to estimate mean body mass index (BMI) for girls between 13 and 19 years of age. The 95% confidence interval obtained had lower limit 19.5 and upper limit 26.3. Which of the following is NOT true? 1. A total of 95% of all teenage girls have BMI between 19.5 and 26.3. 2. The margin of error is 34. 3. The value z in the margin of error is 1.96. 4. A total of 95% of all SRS of size n contain the true mean BMI
Answer:
Option 1 is the only untrue statement of the 4 statements.
The only wrong statement about the confidence interval above is the one about the total of 95% of all teenage girls having BMI between 19.5 and 26.3.
Step-by-step explanation:
The question provides that for the BMI of girls with age between 13 and 19, the 95% confidence interval has a lower limit of 19.5 and an upper limit of 26.3.
We will take the statement one after the other.
Statement 1: A total of 95% of all teenage girls have BMI between 19.5 and 26.3.
This is a wrong statement. It doesn't not follow the definition for confidence interval for a set of sample.
Rather confidence interval, expresses that the true value (mean) exists in the (lower limit, upper limit) range with a confidence level of 95%.
Statement 2: The margin of error is 34.
The margin of error is usually used to calculate the lower and upper limit of the confidence interval.
Basically, the interval is usually between
(Sample mean ± margin of error)
If the sample mean = xbar
And the margin of error = α
xbar - α = lower limit of the confidence interval = 19.5
xbar + α = upper limit of the confidence interval = 26.3
xbar - α = 19.5
xbar + α = 26.3
summing these together
xbar = (19.5+26.3)/2 = 22.9
and the margin of error = (22.9 - 19.5) or (26.3 - 22.9) = 3.4.
So, this statement is correct!
Statement 3: The value z in the margin of error is 1.96.
The margin of error is given as the product of the z-multiplier (from the z-tables) and the sample standard deviation.
The z-multiplier for a 95% confidence interval, as obtained from literature and the z-tables is truly 1.96.
This statement is very true.
Statement 4: A total of 95% of all SRS of size n contain the true mean BMI.
Just like I described the meaning of confidence interval in the explanation under the first statement, this is as close to the meaning of confidence interval as can be. This statement is also very true.
Hence, only statement 1 is not correct of the 4 statements.
The voltage across the capacitor increases as a function of time when an uncharged capacitor is placed in a single loop with a resistor and a battery.
What mathematical function describes this behavior?
1. Exponential2. Linear 3. Quadratic 4. Power
Answer:
1. Exponential
Step-by-step explanation:
The problem statement is insufficient to describe the behavior.
_____
The capacitor's voltage is described by a differential equation such that its rate of change is proportional to the difference of the battery voltage and the capacitor voltage. The solution to the differential equation is a function that is exponential with time.
Each month, Miss Patrick spends $60 on transportation to work, and earns $24.50 per hour.Each month, Mr. Shah spends $150 on lab equipment and earns $32.50 per month. How many hours do they have to work during the same amount
Answer:
3 hours for miss patrick 5 hours for mr shah
Step-by-step explanation:
Answer: they have to work for 11.25 hours.
Step-by-step explanation:
Let x represent the number of months for which they have to work to make the same amount.
Each month, Miss Patrick spends $60 on transportation to work, and earns $24.50 per hour. This means that if she works for x hours in a month, the total amount that she would have is
24.5x - 60
Each month, Mr. Shah spends $150 on lab equipment and earns $32.50 per month. This means that if he works for x hours in a month, the total amount that he would have is
32.5x - 150
For them to have the same amount, the number of months would be
32.5x - 150 = 24.5x - 60
32.5x - 24.5x = - 60 + 150
8x = 90
x = 90/8
x = 11.25 hours
Bill spent 60 dollars on fertilizer and weed killer for his lawn. Each pound of fertilizer costs 75 cents, and each ounce of weed killer costs $2.50. What equalion can represent the relationship between the number of pounds of fertilizer bill bought, x , and the number of ounces of weed killer he bought, y?
The equation 0.75x + 2.5y = 60 represents the relationship between the number of pounds of fertilizer (x), and the number of ounces of weed killer (y) that Bill bought with his $60.
Explanation:The question is asking for an equation that could describe how the 60 dollars was spent on fertilizer and weed killer. To represent this relationship, we can set up a linear equation, with x representing the pounds of fertilizer and y representing the ounces of weed killer. Given that each pound of fertilizer costs 75 cents and each ounce of weed killer costs $2.50, the total amount spent on these two items can be represented as 0.75x + 2.5y = 60. This equation depicts how Bill's 60 dollars were allocated to the two items.
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how to solve for 8^x=2 (I know the answer is 1/3 but i have to show work and i don't know the process to solve it)
Answer:
x = 1/3 . . . . math facts or logarithms are involved; take your pick
Step-by-step explanation:
When you are solving for a variable that is in an exponent, logarithms are often useful. Taking the log of both sides of this equation, you have ...
log(8^x) = log(2)
Using the rules of logarithms, that is ...
x·log(8) = log(2)
x = log(2)/log(8) . . . . . divide by the coefficient of x
You can find the value of this on your calculator, and it will tell you the value is 0.333333333333 or as many digits as your calculator displays. That is a clue that the exact answer is probably 1/3.
__
You should recognize that 8 = 2·2·2 = 2^3, so log(8) = 3log(2) and the above solution becomes ...
x = log(2)/(3log(2)) = 1/3
__
Recognizing that 8 = 2^3, you can make that substitution into the original equation to get ...
(2^3)^x = 2
2^(3x) = 2^1
3x = 1 . . . . . . . matching exponents; equivalent to taking logs base 2
x = 1/3 . . . . . . divide by 3
__
All of the above using 2 as a base of exponents is just dancing around the fact that you already know the math fact ...
8^x = 2 = 8^(1/3)
x = 1/3 . . . . . equating exponents; equivalent to taking logs base 8
The perimeter of a square must be greater than 148 inches but less than 196 inches. Find the range of possible side lengths that satisfy these conditions. (Hint: The perimeter of a square is given by P=4s, where s represents the length of a side).
The possible range for the side length of the square is that it is greater than 37 inches, but less than 49 inches.
Explanation:The perimeter of a square is given by the formula P=4s, where s is the length of one side of the square. Since we know the perimeter must be greater than 148 and less than 196 inches, we can create inequality equations to solve for the side lengths, s.
Given the lowest limit, 148 < 4s. Divide both sides by 4, we get 37 < s.
Given the highest limit, 4s < 196. Again, divide both sides by 4, we get s < 49.
So, we conclude that the length of a side, s, must be less than 49 inches but greater than 37 inches to meet the required conditions of the question.
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In the cafeteria 100 milk cartons were put out for breakfast. After breakfast there were 40 milk cartons left. What is the ratio of milk cartons left over to milk cartons taken?
The ratio of milk cartons left over to milk cartons taken from the 100 initially provided in the cafeteria is 2:3.
Explanation:The number of milk cartons put out for breakfast in the cafeteria was 100 and after breakfast, there were 40 milk cartons left. This means that the number of milk cartons taken at breakfast is 100 - 40, which is 60. Thus, the ratio of milk cartons left over to milk cartons taken is 40:60.
We can simplify this ratio by finding the greatest common divisor (GCD) of both numbers. In this case, the GCD of 40 and 60 is 20, so by dividing both numbers by 20, we get a simplified ratio of 2:3. Therefore, the ratio of milk cartons left over to milk cartons taken is 2:3.
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Need help on the last problem please...
Answer:
y = 97°
Step-by-step explanation:
z = 180 - 55 - 42 = 83
Total angle in a triangle is 180°
y = 180 - z = 180 - 83 = 97°
Supplementary angles
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A parking space is in the shape of a parallelogram. The figure below is a model of the parking space. The measure of Angle B is 80°. What are the measures of the other 3 angles?
In a parallelogram with one given angle of 80°, the opposite angle equals 80°, and the two adjacent angles are 100° each, resulting from the properties of parallelograms.
Explanation:The subject of this question is Mathematics, specifically geometry involving angles in a parallelogram. Given that one angle (Angle B) is 80° in a parallelogram, we can determine the measures of the remaining angles using the properties of parallelograms. Adjacent angles in a parallelogram are supplementary, meaning they add up to 180°. Therefore, if Angle B is 80°, then Angle C (adjacent to B) is 180° - 80° = 100°. Since a parallelogram has two pairs of parallel sides, opposite angles are equal. Therefore, Angle D equals Angle B (80°), and Angle A equals Angle C (100°).
Find the area of the shaded region. With steps
Answer: the area of the shaded region is 21.5 cm²
Step-by-step explanation:
The formula for determining the area of a circle is expressed as
Area = πr²
Where
r represents the radius of the circle.
π is a constant whose value is 3.14
From the information given,
Diameter of circle = 10 cm
Radius = diameter/2 = 10/2 = 5 cm
Area of circle = 3.14 × 5² = 78.5 cm²
The length of each side of the square is 10 cm. The area of the square would be
10² = 100 cm²
Therefore, the area of the shaded region would be
100 - 78.5 = 21.5 cm²
Aldo took out a loan for $2500 and was charged simple interest at an annual rate of 9.3%. The total interest he paid on the loan was $186. How long was the loan for, in days? Assume that there are 365 days in a year, and do not round any intermediate computations.
Answer: 291.6 days
Step-by-step explanation:
The formula for determining simple interest is expressed as
I = PRT/100
Where
I represents interest paid on the loan.
P represents the principal or amount taken as loan
R represents interest rate
T represents the duration of the loan in years.
Considering Henry's loan,
P = 2500
R = 9.3%
I = 186
186 = (2500 × 9.3 × T)/100
186 = 232.5 T
T = 186/231.6
T = 0.8 years
Assume that there are 365 days in a year, it would be
0.8 × 3645 = 291.6 days
Person A can complete a job in 6 hours. Person B can complete the same job in 4 hours. Working at the same rate, how many hours will it take both of them to complete the job?
Answer: it will take both of them 2.4 hours to complete the job.
Step-by-step explanation:
Person A can complete a job in 6 hours. This means that the rate at which Person A can complete the job per hour is 1/6
Person B can complete the same job in 4 hours. This means that the rate at which Person A can complete the job per hour is 1/4
If they work together, they would work simultaneously and their individual rates are additive. This means that their combined working rate would be
1/6 + 1/4 = 5/12
Assuming it takes t hours for both of them to clean the room working together, the working rate per hour would be 1/t. Therefore,
5/12 = 1/t
t = 12/5
t = 2.4 hours
Let p: A number is greater than 25. Let q: A number is less than 35. If p ∧ q is true, then what could the number be? Select two options. 24 28 32 36 40
Answer:
The correct answer are 28 and 32.
Step-by-step explanation:
Given p: A number is greater than 25, that is, the possible numbers are 26, 27, 28, 29, 30, 31, 32, 33, 34, .... and so on. And
q: A number is less than 35, that is the possible numbers are 34, 33, 32, 31, 30, 29, 28, 27, 26, .... and so on.
Now, p ∧ q is true when both p and q are true, this means that we have to find numbers that follow the criterion of both p and q.
So, p ∧ q = {26, 27, 28, 29, 30, 31, 32, 33, 34}. Therefore, the correct answers are 28 and 32.
Austin scored 85 on the calculus midterm. If the final exam counts twice as much as the midterm exam, then for what range of scores on the final would Austin get an average between 85 and 96? Both tests have a maximum of 100 points.
Answer:
Austin should score between 85 and 100 in the final exam to have an average between 85 and 95, since reaching 96 is mathematically impossible.
Step-by-step explanation:
The problem has to be solved in two parts, the first to obtain an average of 85 and the second to obtain an average of 96.
In the first part with an average of 85 would be as follows.
Let x be the final exam grade.
Weighted average = (85 + 2 * X) / 3
85 = 85/3 + (2/3) * X
Rearranging
X = (3/2) * (85- (85/3))
Resolving
X = 85, therefore you must take 85 in the final test to get an average of 85.
The second part with an average of 96:
96 = 85/3 + (2/3) * X
Rearranging
X = (3/2) * (96- (85/3))
Resolving
X = 101.5, therefore you must take 101.5 in the final test to get an average of 96, therefore it is impossible to have an average of 96, because the highest score is up to 100.
Taking 100 your average would be:
Weighted average = (85 + 2 * 100) / 3 = 95
Then Austin should score between 85 and 100 in the final exam to have an average between 85 and 95, since reaching 96 is mathematically impossible.
Austin should score between [tex]85[/tex] and [tex]100[/tex] in the final exam to have an average between [tex]85[/tex] and [tex]95[/tex].
Average :Let us consider that [tex]X[/tex] be the final exam grade.
So that, Weighted average [tex]= \frac{85 + 2 * X}{3}[/tex]
[tex]85 =\frac{85}{3} + \frac{2}{3} X\\\\\frac{2}{3} X=85-\frac{85}{3} \\\\X=85[/tex]
Thus, you must take 85 in the final test to get an average of 85.
The second part with an average of 96:
[tex]96 = \frac{85}{3} + \frac{2}{3} X\\\\\frac{2}{3}X=96-\frac{85}{3}\\ \\ X=101.5[/tex]
Thus, it is impossible to have an average of 96, because the highest score is up to 100.
Taking 100 your average would be:
Weighted average [tex]=\frac{85 + 2 * 100}{3} =95[/tex]
Hence, Austin should score between 85 and 100 in the final exam to have an average between 85 and 95.
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SOMEBODY CAN YOU HELP?
Answer:
A.
Step-by-step explanation:
Since the line goes down 4 and right 5, your slope would be -4/5 and since your y-intercept is at (0,-5) you would plug that in for b.
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please help with areas
Answer:
Step-by-step explanation:
7) The formula for determining the area of a parallelogram is expressed as
Area = base × height.
Length of base = Area/height
Therefore,
Length of base = 7/2 = 3.5 feet
8) The formula for determining the area of a trapezoid is expressed as
Area = 1/2(a + b)h
Where
a and b are the length of the bases
h is the height. Therefore
21 = 1/2(2 + 4)h
21 = 3h
h = 21/3 = 7 inches
9) Area = base × height.
Height = Area/Length of base
Height = 28/14 = 2 inches
10) a and b are 10 inches each.
Area = 1/2(a + b)h
Therefore,
35 = 1/2(10 + 10)h
35 = 10h
h = 35/10
h = 3 inches
what is the domain of y=3^x -2
Answer:
All real numbers
Step-by-step explanation:
The given exponential function is
[tex]y = {3}^{x} - 2[/tex]
This function is obtained by shifting, the parent function down by 2 units.
The parent function is
[tex]y = {3}^{x} [/tex]
The domain is the values of x for which the function is defined.
The exponential function is defined everywhere and the same applies to the transformed function.
Therefore the domain is all real numbers.
A study of the checkout lines at the Safeway Supermarket in the South Strand area revealed that between 4 and 7 P.M. on weekdays there is an average of four customers waiting in line. What is the probability that you visit Safeway today during this period and find?
a. No customers are waiting?
b. Four customers are waiting?
c. Four or fewer are waiting?
d. Four or more are waiting?
Answer:
(a) The probability of no customers are waiting in a line is 0.01832.
(b) The probability of 4 customers are waiting in a line is 0.19537.
(c) The probability of 4 or fewer customers are waiting in a line is 0.62885.
(d) The probability of 4 or more customers are waiting in a line during the visit is 0.56652.
Step-by-step explanation:
The number of customers waiting in a line between 4 PM and 7 PM (X) follows a Poisson distribution with parameter λ = 4.
The probability mass function of a Poisson distribution is:
[tex]P(X=x)=\frac{e^{-4}(4)^{x}}{x!} ;\ x=0, 1, 2,...[/tex]
(a)
Compute the probability that no customers are waiting in a line during the visit as follows:
[tex]P(X=0)=\frac{e^{-4}(4)^{0}}{0!}=\frac{0.01832\times1}{1}=0.01832[/tex]
Thus, the probability of no customers are waiting in a line is 0.01832.
(b)
Compute the probability that 4 customers are waiting in a line during the visit as follows:
[tex]P(X=4)=\frac{e^{-4}(4)^{4}}{4!}=\frac{0.01832\times256}{24}=0.19537[/tex]
Thus, the probability of 4 customers are waiting in a line is 0.19537.
(c)
Compute the probability that 4 or fewer customers are waiting in a line during the visit as follows:
P (X ≤ 4) = P (X = 0) + P (X = 1) + P (X = 2) + P (X = 3) + P (X = 4)
[tex]=\frac{e^{-4}(4)^{0}}{0!}+\frac{e^{-4}(4)^{1}}{1!}+\frac{e^{-4}(4)^{2}}{2!}+\frac{e^{-4}(4)^{3}}{3!}+\frac{e^{-4}(4)^{3}}{3!}+\frac{e^{-4}(4)^{4}}{4!}\\=0.01832+0.07326+0.14653+0.19537+0.19537\\=0.62885[/tex]
Thus, the probability of 4 or fewer customers are waiting in a line is 0.62885.
(d)
Compute the probability of 4 or more customers are waiting in a line during the visit as follows:
P (X ≥ 4) = 1 - P (X < 4)
= 1 - P (X = 0) - P (X = 1) - P (X = 2) - P (X = 3)
[tex]=1-\frac{e^{-4}(4)^{0}}{0!}+\frac{e^{-4}(4)^{1}}{1!}+\frac{e^{-4}(4)^{2}}{2!}+\frac{e^{-4}(4)^{3}}{3!}+\frac{e^{-4}(4)^{3}}{3!}\\=1-0.01832-0.07326-0.14653-0.19537\\=0.56652[/tex]
Thus, the probability of 4 or more customers are waiting in a line during the visit is 0.56652.