The American Automobile Association reported that families planning to travel over the Labor Day weekend would spend an average of $735. Assume that the amount spent is normally distributed with a standard deviation of $230. What is the probability of family expenses for the weekend being: a. more than $580
Answers
Answer:
0.7486 = 74.86% probability of family expenses for the weekend being more than $580.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
The American Automobile Association reported that families planning to travel over the Labor Day weekend would spend an average of $735.
This means that \(\mu = 735\)
Assume that the amount spent is normally distributed with a standard deviation of $230.
This means that \(\sigma = 230\)
What is the probability of family expenses for the weekend being: a. more than $580
This is 1 subtracted by the pvalue of Z when X = 580. So
\(Z = \frac{X - \mu}{\sigma}\)
\(Z = \frac{580 - 735}{230}\)
\(Z = -0.67\)
\(Z = -0.67\) has a pvalue of 0.2514
1 - 0.2514 = 0.7486
0.7486 = 74.86% probability of family expenses for the weekend being more than $580.
Related Questions
Find the value of x
Answers
Answer: The value of x is 49.
Step-by-step explanation:
To find the value of x, you will first need to cross multiply the fractional variables together.
5x - 80 = 3x + 18
Then, move the numerical term 80 to the right side of this equation and add it to 18.
5x - 80 = 3x + 98
Move 3x to the left side of the equation and subtract it this time to the variable 5x.
2x = 98
Finally, you divide both of the equation's sides by 2 and you will get 49.
x = 49
When you actually add x to this problem, you would get 33/55.
49 - 16/49 +6 = 33/55
You can then simplify 33/55 and get the same answer 3/5.
3/5
Therefore, the value of x for this variable equation with the fractions would be equal to x = 49. Hope this helps!
-From 5th Grader Honors Student
Match the following. Match the items in the left column to the items in the right column. 1. domain the first element of a relation or function; also known as the input value. 2. output a relation in which every input value has exactly one output value. 3. input the x-value of a function. 4. relation any set of ordered pairs (x, y) that are able to be graphed on a coordinate plane. 5. function the y-value of a function. 6. range the second element of a relation or function; also known as the output value.
Answers
The matching of items and their corresponding descriptions are 1. Domain, 2.Output, 3. Input, 4. Relation, 5. Function, and 6. Range.
What is the appropriate matching of the following items?1. Domain - the first element of a relation or function; also known as the input value.
3. Input - the x-value of a function.
6. Range - the second element of a relation or function; also known as the output value.
4. Relation - any set of ordered pairs (x, y) that are able to be graphed on a coordinate plane.
2. Output - a relation in which every input value has exactly one output value.
5. Function - the y-value of a function.
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Find the end time.
Start time: 12:13 A.M.
Elapsed time: 3 hr 10 min
End time: : A.M.
Answers
Answer:
3:23
Step-by-step explanation:
Answer:
12:13 - 01:13=1 hour
01:13-01:13= 1 hour
02:13-03:13= 1 hous
03:13-03:23= 10 minutes
12:13-03:23= 3hr 10min
This month my metro water services bill was $36.34 and my Madison Suburban Utilty District bill was $26.03. My total water bill was $
Answers
Total water bill for the month is $62.37.
It seems that you may have accidentally left out the total amount of your water bill.
The total amount by simply adding the amounts of the individual bills together:
Total water bill =\($36.34 + $26.03\)
= \($62.37\)
You have not provided enough information to determine your total water bill.
You have only given the amounts of your individual bills from Metro Water Services and Madison Suburban Utility District.
To find your total water bill, you simply need to add the two bills together.
So, the total amount you owe for water this month would be:
Total water bill = \($36.34 + $26.03\)
= \($62.37\)
It appears that you may have forgotten to include the full amount of your water bill by accident.
Simple addition of the separate bill amounts yields the following sum:
Water bill total = \($36.34 + $26.03\)
= \($62.37\)
Your total water bill cannot be calculated because not enough information has been given.
Only the amounts of your individual Metro Water Services and Madison Suburban Utility District bills have been provided.
You just need to combine the two invoices together to get your total water bill.
As a result, this month's total water bill for you would be:
Water bill total = \($36.34 + $26.03\)
= \($62.37\)
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Percy prepared 22 kilograms of dough after working 5 hours.How many hours did Percy work if he prepared 35.2 kilograms of dough?
Answers
Given data:
The amount of cake Percy prepared after working 5 hours is 22 kg.
The expression for the given statement is,
\(\begin{gathered} 22\operatorname{kg}\text{ =5 hours} \\ 1\operatorname{kg}\text{ =}\frac{5}{22}\text{ hours} \end{gathered}\)Multiplied the above expression by 35.2 on both sides.
\(\begin{gathered} 35.2(\text{ 1 kg)=35.2(}\frac{5}{22}\text{ hours)} \\ 35.2\text{ kg= 8 hours} \end{gathered}\)Thus, Percy need 8 hours to prepare 35.2 kg cake.
What is the mean ? 50, 55, 58, 58, 90, 92, 99
Answers
sum of observations
mean =..........................no. of observations
50+55+58+90+58+92+99 502
....................................... = .........= 71.77 7
awnser is 71.7
hope this helpeduse the formula v = u + t to find the velocity when the initial velocity is 3 m/s, the accelaration is 1.5 m/s and the time is 7 seconds. What is the formula for each one?
Answers
The final velocity of the parameters is 13.5m/s
How to determine the final velocity of the parameter?In this question, the given parameters are represented as
Formula: v = u + at
Initial velocity = 3m/s
Acceleration = 1.5m/s²
Time = 7 seconds
When these parameters are represented using their required notation, we have the following representations
u = 3m/s
a = 1.5m/s²
t = 7 s
Next, we substitute the above parameters in the above equation
So, we have the following representation
v = 3 + 1.5 * 7
Evaluate the products
This gives
v = 3 + 10.5
Evaluate the sum
So, we have the following representation
v = 13.5
The notation v represents the final velocity
Hence, the final velocity is 13.5m/s
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What number should go in the space? Multiplying by 0.65 is the same as decreasing by _____%
Answers
Answer: 35%
Step-by-step explanation:
If no is 10, 10 x 0.65 = 6.5. OR
10 - 35% of 10 = 6.5
Multiplying by 0.65 is the same as decreasing by 35%
Conversion of statements into algebraic expression:To convert the statement into algebraic expression choose the variables first.Then form the expression or equation as per given statements.
Let the number is 'a' and percentage decrease is 'b',
Expression for the given statement will be,
a × 0.65 = a - (b% of a)
\(0.65a=a(1-\frac{b}{100})\)
\(0.65=1-\frac{b}{100}\)
\(\frac{b}{100}=1-0.65\)
\(b=100(0.35)\)
\(b=35\)
Therefore, Multiplying by 0.65 is the same as decreasing by 35%.
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Match each letter to its correct term. Efficiency Unobtainable Impossible Inefficiency Underutilization 1. A 2. B 3. C
Answers
Each letter should be matched to its correct term as follows;
1. A ⇔ Efficiency.
2. B ⇔ Impossible.
3. C ⇔ Inefficiency.
What is a production possibilities curve?In Economics and Mathematics, a production possibilities curve (PPC) can be defined as a type of graph that is typically used for illustrating the maximum and best combinations of two (2) products that can be produced by a producer (manufacturer) in an economy, if they both depend on the following two (2) factors;
Technology is fixed.Resources are fixed.Based on the production possibilities curve shown in the image attached above, we can reasonably infer and logically deduce that each of the letters represent the following terminologies;
A ⇔ Efficiency: it represent points on the production possibilities curve.B ⇔ Impossible: it represent points outside the production possibilities curve.C ⇔ Inefficiency: it represent points on the interior of a production possibilities curve.Read more on production possibilities here: brainly.com/question/26460726
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Students and teachers at a school were asked if they preferred blue, green, red, or yellow. The table shows the results of the survey. Blue Green Red Yellow Total Students 5 10 20 15 50 Teachers 15 10 5 20 50 Total 20 20 25 35 100 Choose three statements that can be inferred from the data in the table. A. 20% of all people surveyed chose blue. B. 20% of the students surveyed chose red. C. 20% of the students surveyed chose blue. D. 20% of the teachers surveyed chose green. E. 20% of those who chose red were teachers. F. 20% of those who chose yellow were teachers.
Answers
20% of all people surveyed chose blue and 20% of the teachers surveyed chose green. Then the correct options are A and D.
What is probability?Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.
Students and teachers at a school were asked if they preferred blue, green, red, or yellow.
The table shows the results of the survey.
\(\begin{matrix}&\rm Blue &\rm Green &\rm Red &\rm Yellow &\rm Total \\\\\rm Students &5 &10 &20 &15 &50 \\\\\rm Teachers &15 &10 &5 &20 &50\\\\\rm Total &20 &20 &25 &35 &100\end{matrix}\)
A. The probability of the people who chose blue will be
\(\rm P = \dfrac{20}{100} = 0.2 \ or \ 20\%\)
B. The probability of the student who chose red will be
\(\rm P = \dfrac{20}{50} = 0.4 \ or \ 40\%\)
C. The probability of the student who chose blue will be
\(\rm P = \dfrac{5}{50} = 0.1 \ or \ 10\%\)
D. The probability of the teachers who chose green will be
\(\rm P = \dfrac{10}{50} = 0.2 \ or \ 20\%\)
E. The probability of the teachers who chose red will be
\(\rm P = \dfrac{5}{50} = 0.1 \ or \ 10\%\)
F. The probability of the teachers who chose yellow will be
\(\rm P = \dfrac{20}{50} = 0.4 \ or \ 40\%\)
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Please help with this math question!
Answers
Answer:
5. Proofs attached to answer
Step-by-step explanation:
Proofs attached to answer
HI PLEASE HELP ON QUESTION ASAP USING AVERAGE (MEAN) TO ANSWER QUESTION! IF UR ANSWER AND EXPLAINATION IS CORRECT ILL RATE YOU FIVE STARS, A THANKS AND MAYBE EVEN BRAINLIEST. PLEASE MAKE SURE YOU ANSWER MY QUESTION USING AVERAGES.
1) a meal for 6 cost £12 per person. as it is one of the diners birthday , the other 5 decided to pay for his meal. how much do each of the five friends need to pay?
Answers
Each of the five friends needs to pay £14.40 to cover the cost of the birthday person's meal.
To calculate how much each of the five friends needs to pay, we can use the concept of averages or mean.
The total cost of the meal for 6 people is £12 per person. This means that the total cost of the meal is 6 * £12 = £72.
Since the other five friends have decided to pay for the birthday person's meal, they will evenly divide the total cost of £72 among themselves.
To find the average amount each friend needs to pay, we divide the total cost by the number of friends paying, which is 5:
£72 / 5 = £14.40
Using the concept of averaging or finding the mean allows us to distribute the cost equally among the friends, ensuring fairness in sharing the expenses.
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What percent of 2 is 32? If necessary, round your answer to the nearest tenth.
Answers
Answer:
Below
Step-by-step explanation:
32/2 x 100% = 1600 %
After 4years the car has a value of $ 9200
Find the average rate of change (in dollars per year) of car value for the given points.
$ __
Answers
The average rate of change of the car value is given as follows:
Rate = (9200 - Initial Value)/4.
How to obtain the average rate of change?The average rate of change of a function is given by the change in the output divided by the change in the input.
The change in the output is of:
9200 - Initial value.
The change in the input is of:
4.
(4 years).
Hence the rate is given as follows:
Rate = (9200 - Initial Value)/4.
Missing InformationThe initial value is missing, hence the answer was given in terms of the initial value.
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The sum of 2 numbers s 1 and the diffreance is 5 what are th 2 numbers
Answers
Answer:
note ;sum of two no. is not 1.
let no. be x and y.
we have
x+y=11.......(1)
x-y=5........(2)
adding equation 1&2
x+y+x-y=11+5
2x=16
x=16/2=8
again
8-y=5
y=8-5=3
:.
x=8,y=3
For the equation f(x) = 1.1 * (0.44) ^ x state the initial value C, the growth or decay factor a, and percent change R for each unit increase in x
c = (Type an integer or a decimal)
a = (Type an integer or a decimal)
R = % (Simplify your answer. Type an integer or a decimal)
Answers
The parameters of the exponential function in this problem are given as follows:
c = 1.1.a = 0.56.R = -56%.What is an exponential function?The standard format of an exponential function is given as follows:
y = c(1 - a)^t.
This is the case for a decaying exponential function, and the meaning of each parameter is given as follows:
c is the initial value, value assumed by y when t = 0.a is the decay rate.In this problem, the function is given as follows:
f(x) = 1.1(0.44)^x.
Hence the values for the parameters are given as follows:
c = 1.1, which is the initial value.a = 0.56, as 1 - a = 0.44 -> a = 0.56.Then the percent of change is of -56%, as it is a decaying exponential function with a = 0.56.
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Please give me examples to use
Answers
Answer:
cy+d to the middle of the problem
store A charges 12.50 for a custom shirt with 0.40 per each custom character store b charges 14.75 for the same shirt but charges 0.25 per each custom characyer would make the cost from both stores the same
Answers
Answer:
15 shirts
Step-by-step explanation:
Store A charges 12.50 for a custom shirt with 0.40 per each custom character. Store B charges 14.75 for the same shirt but charges 0.25 per each custom character would make the cost from both stores the same
A: 12.5 + 0.40x
B: 14.75 + 0.25x
12.5 + 0.40x = 14.75 + 0.25x
subtract 12.5 from both sides:
12.5 + 0.40x - 12.5 = 14.75 + 0.25x - 12.5
0.40x = 2.25 + 0.25x
subtract 0.25x from both sides:
0.40x - 0.25x = 2.25 + 0.25x - 0.25x
0.15x = 2.25
divide both sides by 0.15:
0.15x/0.15 = 2.25/0.15
x = 15
a die is tossed twice and the number of dots facing up in each toss is counted and noted in the order of occurrence. (a) find the sample space. (b) find the set a corresponding to the event “number of dots in first toss is not less than number of dots in second toss.” (c) find the set b corresponding to the event “number of dots in first toss is 6.” (d) does a imply b or does b imply a? (e) find and describe this event in words. (f) let c correspond to the event “number of dots in dice differs by 2.”
Answers
A die is tossed twice and a number of dots facing up in each toss are counted and noted in the order of occurrence.
a) The sample space is given as:
Sample Space (S)= {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5),(2,6),(3,1),(3,2),(3,3)(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1)(5,2)(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),c),(6,6)}.
What is the sample space?A sample space is a collection of a set of possible outcomes of a random experiment. The sample space is represented using the symbol S.
b) the set corresponding to the event number of dots in the first toss is not less than the number of dots in the second toss.
{(6,6),(6,5)(6,3)(6,2)(6,1)(6,4),(5,1)(5,2)(5,3),(5,4),(5,5),(4,1),(4,2),(4,3),(4,4),(3,1),(3,2), (2,1), (2,2),(1,1)}
c) find the set b corresponding to the event number of dots in the first toss is 6.
{(6,1),(6,2),(6,3),(6,4),c),(6,6)}.
e) a does not imply b or does b imply a.
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Pam, the CEO of Zettabyte Tek, set up a $750,000 education fund. She wants to give each employee who takes a computer security class a $350 reimbursement toward the cost of the class. You can use a function to describe the amount of money left in the fund after x employees receive the reimbursement.
Write an equation for the function. If it is linear, write it in the form f(x)=mx+b. If it is exponential, write it in the form f(x)=a(b)x.
Answers
The formula for this linear function is f(x) = mx + b, where m is the slope (in this example, -350), and b is indeed the y-intercept (750,000 in this case).
What does a simple equation represent?An equation expressing the connection between the expressions on either side of a sign. Normally, it has an equal sign and just one variable. such as: 2x - 4 is equal to 2. The variable x is present in the example above.
Workers who complete the computer security course will each receive a reimbursement of $350.
We deduct $350x from of the initial $750,000 to determine how much money will remain inside the education fund once x employee gets the reimbursement.
Thus, f(x) = 750,000 - 350x is the equation again for function that describes that amount of money still in the fund when x employees receive the refund.
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I Need Help please!!
Slope of one of the dotted lines:
Slope of the line of reflection:
Answers
Answer:
see explanation
Step-by-step explanation:
calculate slope m using the slope formula
m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)
consider the middle dotted line
with
(x₁, y₁ ) = (- 5, - 3) and (x₂, y₂ ) = (6, 8) ← 2 points on the line
m = \(\frac{8-(-3)}{6-(-5)}\) = \(\frac{8+3}{6+5}\) = \(\frac{11}{11}\) = 1
consider the line of reflection ( the solid line )
with
(x₁, y₁ ) = (0, 3) and (x₂, y₂ ) = (- 1, 4) ← 2 points on the line
m = \(\frac{4-3}{-1-0}\) = \(\frac{1}{-1}\) = - 1
PLEASE I NEED HELP WITH THIS
Answers
Answer: \(m\angle 2+m\angle 5=180^{\circ}\)
Step-by-step explanation:
You are ending by proving \(\angle 2\) and \(\angle 5\) are supplementary, so right before that, you need to prove their measures add to 180 degrees.
One number is six times as large as a certain smaller number. Let x represent the smaller number.
Write the number that is 20 more than the smaller number.
Answers
Answer:
24
Step-by-step explanation:
6x = x + 20
Subtract x from both sides
5x = 20
Divide by 5 on both sides
x = 4
Confirm
4 times 6 equals 24, and 4 + 20 is 24 as well.
divide 4 on both sides
The weather person said that the temperature was "seventeen degrees below zero." How should this number be written?
Answers
Answer:
-17
Step-by-step explanation:
Answer:
You can write this three different ways. The first way is -17. The second way is 17 degrees below zero. The third way is simply negative seventeen.
Step-by-step explanation:
Hope this helps!
Have a blessed day and remember to keep smiling! :)
PLEASE MARK ME AS BRAINLIEST I REALLY WANT TO LEVEL UP.
I know this was 5 days ago, but I just now saw this and decided to help. Sorry it was so late.
The right rectangular prism below has a square base?Select yes or no.
Answers
Answer:
no
Step-by-step explanation:
if it's a prism then it wont have a square bottom
Cars enter a car wash at a mean rate of 3 cars per half an hour. What is the probability that, in any hour, at least 3 cars will enter the car wash
Answers
Answer:
0.938
Step-by-step explanation:
Using the poisson probability relation:
P(x = x) = (e^-λ * λ^x) ÷ x!
λ = 3 per half an hour = 6 cars per hour
P(x ≥ 3) = 1 - [p(x = 0) + p(x = 1). + p(x = 2)]
P(x ≥ 3) = (e^-6* (6^0 + 6^1 + 6^2/2!))
P(x ≥ 3) = 1 - (e^-6 * (1 + 6 + 18)
P(x ≥ 3) = 1 - (e^-6 * 25)
P(x ≥ 3) = 1 - (0.0024787 * 25)
P(x ≥ 3) = 1 - 0.0619688
P(x ≥ 3) = 0.9380311
= 0.938
Find equation of the line shown
Answers
The equation of the line is y = x + 6
How to detemrine the equatiin of the lineFrom the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we have the following highlights
The graph intersect the y-axis at y = 6
This means that the intercept c is 6
Also, as x changes by 1, the y values changes by 1
This mean sthat the slope is 1
So, we have
y = mx + c
This gives
y = x + 6
Hence, the equation is y = x + 6
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The linear equation on the graph can be written as:
y = (3/2)*x + 6
How to find the equation in the graph?A general linear equation can be written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
If the line passes through two points (x₁, y₁), then the slope will be:
a = (y₂ - y₁)/(x₂ - x₁)
In this case we can see the points (0, 6) (so the y-intercept is b = 6) and (4, 10)
Then the slope will be:
a = (10 - 6)/(4 - 0) = 6/4 = 3/2
Then the linaer equation is:
y = (3/2)*x + 6
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\Look at the two equations:
-3x + 6 = 21
-3x + 6 < 21
Which statement best describes the process used to solve the equations?
In both cases, subtract 6 from both sides, but reverse the inequality sign when doing that for the inequality.
In both cases, divide by –3 on both sides, but reverse the inequality sign when doing that for the inequality.
The process is exactly the same for solving the equation and solving the inequality.
The process for solving the equation is entirely different from solving the inequality.
Answers
The statement "In both cases, subtract 6 from both sides, but reverse the inequality sign when doing that for the inequality" best describes the process used to solve the equations.
In the equation -3x + 6 = 21, to isolate the variable x, we subtract 6 from both sides of the equation, which yields -3x = 15. Then, we divide both sides by -3 to solve for x, resulting in x = -5. This process is applicable to equations where we aim to find the exact value of the variable.
Similarly, in the inequality -3x + 6 < 21, we want to find the range of values for x that satisfy the inequality. By subtracting 6 from both sides, we obtain -3x < 15.
However, since we performed the same operation on both sides of the inequality, the direction of the inequality sign remains the same.
Thus, the correct inequality is -3x < 15. To isolate x, we divide both sides by -3. However, since we reversed the inequality sign, we must also reverse it again, resulting in x > -5.
This process allows us to determine the range of values for x that satisfy the inequality.
Therefore, the statement accurately describes the process for solving both the equation and the inequality, highlighting the significance of reversing the inequality sign when manipulating inequalities.
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y = 3x. How do you graph it???
Answers
Answer:
If you go to desmos.com, select the graphing calculator, and enter in y = 3x you should be able to see how it's graphed! Hope this helps!
Answer:
(0, 0) and (1, 3)
happy to help!
Complete this sequence of numbers such that the difference between any two adjacent numbers is the same : 3/k, _, _, 9/2k.
Answers
The completed sequence is: 3/k, 3/k, 3/k, 9/2k.To complete the sequence of numbers with a constant difference between adjacent numbers, we can calculate the common difference by subtracting the first term from the second term.
Let's denote the missing terms as A and B.
The given sequence is: 3/k, A, B, 9/2k.
The common difference can be found by subtracting 3/k from A or B. Therefore:
A - 3/k = B - A = 9/2k - B.
To simplify, we can equate the two expressions for the common difference:
A - 3/k = 9/2k - B.
Next, we can solve for A and B using this equation.
Adding 3/k to both sides gives:
A = 3/k + 9/2k - B.
Now, we can substitute the value of A into the equation:
3/k + 9/2k - B - 3/k = 9/2k - B.
Simplifying further, we have:
9/2k - 3/k = 9/2k - B.
Cancelling out the common terms, we find:
-3/k = -B.
Multiplying both sides by -1, we get:
3/k = B.
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