According to AAA, the price of a gallon of regular, unleaded gas across gas stations in North Carolina is normally distributed with a mean of $2.39 and a standard deviation of $0.15. Find the price such that the probability that a randomly chosen gas station charges more than that price is 20%.
Answers
Answer:
The price at which the probability that a randomly chosen gas station charges more than that price is 20% is $2.52.
Step-by-step explanation:
We are given that the price of a gallon of regular, unleaded gas across gas stations in North Carolina is normally distributed with a mean of $2.39 and a standard deviation of $0.15.
Let X = price of a gallon of regular, unleaded gas across gas stations in North Carolina.
SO, X ~ Normal(\(\mu=\$2.39,\sigma^{2} =\$0.15^{2}\))
The z score probability distribution for the normal distribution is given by;
Z = \(\frac{X-\mu}{\sigma}\) ~ N(0,1)
where, \(\mu\) = population mean = $2.39
\(\sigma\) = stnadard deviation = $0.15
Now, we have to find the price such that the probability that a randomly chosen gas station charges more than that price is 20%, that means;
P(X > x) = 0.20 {where x is the required price}
P( \(\frac{X-\mu}{\sigma}\) > \(\frac{x-2.39}{0.15}\) ) = 0.20
P(Z > \(\frac{x-2.39}{0.15}\) ) = 0.20
Now in the z table, the critical value of x which represents the top 20% area is given as 0.8416, that is;
\(\frac{x-2.39}{0.15}= 0.8416\)
\(x-2.39} = 0.8416 \times 0.15\)
x = 2.39 + 0.13 = $2.52
Hence, the price at which the probability that a randomly chosen gas station charges more than that price is 20% is $2.52.
Related Questions
Find an equation of the line passing through the points.
(−6, 1), (−6, 6)
Answers
9514 1404 393
Answer:
x = -6
Step-by-step explanation:
Both of these points are on the vertical line x = -6.
guidance counselor compiles data relating a student's English grade to the number of languages studied. The results are shown in the frequency table below.
A 4-column table with 3 rows titled English grade versus number of languages studied. The first column has no label with entries English only, English and another language, total. The second column is labeled 90 or above with entries 15, 110, 125. The third column is labeled lower than 90 with entries 105, 270, 375. The fourth column is labeled total with entries 120, 380, 500.
The counselor converts the frequency table to a conditional relative frequency table by column.
A 4-column table with 3 rows titled English grade versus number of languages studied. The first column has no label with entries English only, English and another language, total. The second column is labeled 90 or above with entries 0.12, 0.88, 1.0. The third column is labeled lower than 90 with entries 0.28, 0.72, 1.0. The fourth column is labeled total with entries X, Y, 1.0.
What is the value of X?
0.16
0.20
0.24
0.40
Answers
Answer:
C:0.24
Step-by-step explanation:
and is this right or do I change to it ?
Answers
please help! NEED IT IMMEDIATELY
Answers
Amy printed a square picture that was 225% the size of the original picture. The length of the side of her original picture was 4 inches. What is the length of the side of Amy’s printed picture
Answers
The length of the side of Amy’s printed picture is 6 inches.
What is defined as a square?A square is a two-dimensional closed shape with four equal sides.
A square is made up of four sides and four vertices.A square's sides are all the same length.All interior angles are identical and correct.The total of all interior angles is 360°.Now, as per the given question;
The original length of the side of the square was 4 inches.
Thus, the area of the old photo was;
A = side²
A = 4²
A = 16 square inch.
Now, as the picture is increased by 225%.
Then, increase the area by 225%.
New area = 225% of old area
= (16×225)/100
New area = 36
The length of the side of the new photograph is;
New area = length²
length = √New area
length = √36
length = 6 inches.
Therefore, the length of the side of Amy’s printed picture is 6 inches.
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Shakira se presentará en la Ruta del Vino, y para ello su anuncio ha aparecido en un espectacular por la Avenida Reforma, si la letra A aparece en el letrero, y el ángulo en la parte superior de la letra es de 40° y su base es de 60 cm, ¿cual es la altura de la letra?
Answers
Answer:
82.4 cm
Step-by-step explanation:
The computation of the height is given below:
As we know that each right triangle contains the top angle of 20 degrees
So, the right angle & the bottom corner angle equivalent to
= 180 - 90 - 20
= 70 degrees
Now the height is
tangent = opposite leg ÷ adjacent leg
tan (70°) = height ÷ 30 cm
height = 30 cm × tan (70°)
= 82.4 cm
Insurance cost is to be distributed among manufacturing, selling and administration in the ratio of 1/10 to 1/3 to 1/9. If the total cost was $12,005 how should it be distributed to these departments
Answers
Manufacturing should pay $2206.80, Selling should pay $7356.0and Administration should pay $2452.00
What is the distribution?Generally, To find out how much each department should pay, you can use the proportion of the cost that corresponds to their respective ratio.
First, calculate the total ratio by adding the three ratios together:
1/10 + 1/3 + 1/9 = 0.544
Then, divide the total cost by the total ratio to find the unit cost:
$12,005 / 0.544 = $22068.01
Next, multiply the unit cost by the ratio for each department to find out how much they should pay:
Manufacturing: $22068.01 x 1/10 = $2206.80
Selling: $22068.01 x 1/3 = $7356.0
Administration: $22068.01 x 1/9 = $2452.00
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What is the slope of the line through? (-4, 2) and (3, -3)?
Answers
Answer:
c. -5/7
Step-by-step explanation:
someone please help!!!!
Answers
Answer:
60
Step-by-step explanation:
Suppose the prices of a certain model of new homes are normally distributed with a mean of 150,000. Use the 68-95-99.7 rule to find the percentage of buyers who paid between $149,000 and $151,000 if the standard deviation is $1000
Answers
The percentage of buyers is approximately 68.26% of buyers of new houses paid between \($149,000\) and \($151,000\) .
We are given that the prices of the new homes are normally distributed with a mean of \($150,000\) and a standard deviation of $1000.
Using the 68-95-99.7 rule, we know that: approximately 68% of the data falls within one standard deviation of the mean approximately 95% of the data falls within two standard deviations of the mean, approximately 99.7% of the data falls within three standard deviations of the mean.
In order to determine the proportion of customers who spent between $149,000 and , we must first determine the z-scores for these values:
z1 = (149,000 - 150,000) / 1000 = -1 z2 = (151,000 - 150,000) / 1000 = 1
Now, we can determine the proportion of data that falls between z1 and z2 using the z-table or a calculator. The region to the left of z1 is 0.1587, and the area to the left of z2 is 0.8413, according to the z-table. Thus, the region bounded by z1 and z2 is:
0.8413 - 0.1587 = 0.6826
We can get the percentage of consumers who spent between by multiplying this by 100% is \($149,000\) and \($151,000\):
0.6826 x 100% = 68.26%
Therefore, the standard deviation of customers who paid between is \($149,000\) and \($151,000\) for this model of new homes.
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A random sample of 40 college professors is selected from all professors at a university. The following list gives their ages.
64, 40, 45, 43, 33, 50, 47, 49, 42, 28, 55, 64, 55, 41, 65.
64, 50, 45, 51, 23, 35, 64, 43, 45, 37, 37, 47, 34, 27, 49,
62, 39, 35, 44, 23, 36, 42, 34, 32, 52.
D
Answers
The required leaves values for the given stems are calculated below.
What is Stem-and-Leaf plot?A plot where every information esteem is parted into a "leaf" (typically the last digit) and a "stem" (different digits). For instance "32" is parted into "3" (stem) and "2" (leaf). The "stem" values are recorded down, and the "leaf" values are recorded close to them.
For example , 42, 34, 48, and so on.
Here 42 and 48 qualities will be written in stem 4 as their most memorable digit is 4, while 2 and 8 will be placed in the leaf side.
Likewise, 3 will be the stem, and 4 will be the leaf for esteem 34.
4| 2, 8
3| 4
According to question:65, 40, 47, 47, 33, 55, 44, 49, 46, 22, 58, 65, 56, 41, 63, 65, 54, 42, 58, 29, 39, 66 , 49, 42, 34, 36, 42, 35, 21, 44, 61, 35, 33, 42, 27, 30, 46, 33, 35, 58.
As given in the question that the stem and Leaves are to be separated by a hyphen.
Stem-and-Leaf plot 6 - 5, 5, 3, 5, 6, 1
5 - 5, 8, 6, 4, 8, 8
4 - 0, 7, 7, 4, 9, 6, 1, 2, 9, 2, 2, 4, 2, 6
3 - 3, 9, 4, 6, 5, 5, 3, 0, 3, 5
2 - 2, 9, 1, 7
As we can see above there are 5 stems, where stem 6 has 6 leaves, stem 5 has 6 leaves, stem 4 has 14 leaves, stem 3 has 10 leaves, and stem 2 has 4 leaves.
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Claire made 1⁄2 pound of trail mix. If she puts 1⁄4 pound of trail mix into each bag, how many bags are filled? *
Answers
Answer:
2 bags
Step-by-step explanation:
1/2 half bag is 2/4 when a full bag is 4/4 distributed into each bag
the manager of a bank record of the amount of each Time customer spent waiting in the line during peak business hours on Monday the waiting times are shown below find the mean waiting time Roger answer to one Decimal place 6.8 min 7.5 min 7.2 min brainly
Answers
Answer:
To find the mean waiting time, you need to add up all the waiting times and divide by the number of customers. In this case, the total waiting time is 6.8 + 7.5 + 7.2 = 21.5 minutes. Since there are 3 customers, the mean waiting time is 21.5 / 3 = 7.17 minutes. Rounded to one decimal place, the mean waiting time is 7.2 minutes.
Step-by-step explanation:
Lesson 17: Use the Four Operations to Solve Problems Cool Down: Andre's Balloons Andre has 125 balloons. He and 4 friends hung up some balloons for a party at school and now there are 80 balloons left. If each person hung up the same number of balloons, how many balloons did each person hang up? 1. Write an equation with a letter for the unknown quantity to represent the situation. 2. Solve the problem. Explain or show your reasoning.
Answers
a) Using the four basic mathematical operations, the number of balloons that each person hang up is 9.
b) An equation representing the situation is x = (125 - 80)/5.
What are the mathematical operations?The four basic mathematical operations include addition, subtraction, division, and multiplication.
The mathematical operations provide solutions to mathematical problems using operands.
What is an equation?An equation is a mathematical statement showing that two or more mathematical expressions are equal or equivalent.
The total number of balloons that Andre has = 125
The number of balloons remaining after hanging some for the school party = 80
The difference (number of balloons used) = 45 (125 - 80)
The number of friends who hang the balloons = 5
The number of balloons hung by each friend of Andre = 9 (45/5)
Thus, we can conclude that each of the 4 friend and Andre hung 9 balloons, with 80 remaining.
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NO LINKS!! URGENT HELP PLEASE!!!
9. Find the equation of the PARABOLA with a vertex at (-2, 6) and passing through the point (1, -3)
Answers
Answer:
y= -x²-4x+2
Step-by-step explanation:
write in vertex form
a(x-h)²+k
in our case h = -2 and k= 6
y=a(x+2)²+6
now we just need to solve for a. we know that when x= 1 y = -3. plug these values in and solve for a
-3= a(1+2)²+6
-9=9a
a= -1
thus the formula is -(x+2)²+6
generally, teachers want things in standard form, so expand the exponent and simplify.
-(x²+4x+4)+6
y= -x²-4x+2
Answer:
\(y = -x^2 - 4x + 2\)
Step-by-step explanation:
The equation of a parabola in vertex form is:
\(y = a(x - h)^2 + k\)
where (h, k) is the vertex of the parabola.
In this case, the vertex is (-2, 6), so h = -2 and k = 6.
We also know that the parabola passes through the point (1, -3).
Plugging these values into the equation, we get:
\(-3 = a(1 - (-2))^2 + 6\)
\(-3 = a(3)^2 + 6\)
-9 = 9a
a = -1
Substituting a = -1 into the equation for a parabola in vertex form, we get the equation of the parabola:
\(y = -1(x + 2)^2 + 6\)
This equation can also be written as:
\(y = -x^2 - 4x -4+6\\y=x^2-4x+2\)
What contributes to the movement of air masses?
weather boundaries
natural wind patterns
air pressure differences
rapid changes in weather
Answers
Answer:
B natrul winds
Step-by-step explanation:
The movement of air masses is influenced by a combination of factors, including air pressure differences, weather boundaries, natural wind patterns, and rapid changes in weather.
The movement of air masses is primarily influenced by air pressure differences.Air moves from areas of high pressure to areas of low pressure, creating wind and facilitating the movement of air masses.The pressure gradient force drives the movement of air from regions of higher atmospheric pressure to regions of lower atmospheric pressure.Weather boundaries, such as cold fronts, warm fronts, and stationary fronts, can contribute to the movement of air masses by acting as barriers or transitional zones between different air masses.Natural wind patterns, such as global atmospheric circulation patterns, like the Hadley, Ferrel, and Polar cells, influence the movement of air masses on a larger scale.Rapid changes in weather, such as severe storms or thunderstorms, can cause the movement of air masses due to strong vertical air motion and atmospheric instability.Learn more about Weather here:
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A golf association requires that golf balls have a diameter that is inches. To determine if golf balls conform to the standard, a random sample of golf balls was selected. Their diameters are shown in the accompanying data table. Do the golf balls conform to the standards? Use the level of significance.
Answers
Answer:
Following are the solution to the given question:
Step-by-step explanation:
The data provided
Statistics descriptive: data
Sum of total
Variable Count Mean StDev Variance Sum Squares
Data \(1\ \ 12 \ \ 1.6810 \ \ 0.00429 \ \ 0.00002 \ \ 20.1720 \ \ 33.9093\)
Null hypothesis: \(H_o: \mu= 1.68\)
The alternative hypothesis: \(H_1 : \mu \neq 1.68\) (The tailed two test)
Graph the inequality. y is less than negative one fourth times x minus 3 The graph shows a solid line passing through the point negative 12 comma 0 and 0 comma negative 3, with shading above the line. The graph shows a dashed line passing through the point negative 12 comma 0 and 0 comma negative, 3 with shading above the line. The graph shows a solid line passing through the point negative 12 comma 0 and 0 comma negative 3, with shading below the line. The graph shows a dashed line passing through the point negative 12 comma 0 and 0 comma negative 3, with shading below the line.
Answers
A graph of the inequality "y is less than negative one fourth times x minus 3" is: D. The graph shows a dashed line passing through the point negative 12 comma 0 and 0 comma negative 3, with shading below the line.
How to determine the required ordered pair?In order to determine the ordered pair that is included in the solution to this linear inequality, we would first of all translate the word problem into an algebraic equation as follows;
y is less than negative one-fourth times x minus 3 ⇒ y < -x/4 - 3.
Next, we would use an online graphing calculator to graphically solve the linear inequality. Therefore, the required solution for the given linear inequality is the shaded area below the dashed line, which is given by the ordered pairs (−12, 0) and (0, -3).
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Answer:
it’s D dotted line with shading below
Step-by-step explanation:
i got it on my quiz
I need help solving this
Answers
The cylinder has a volume of 150.796 in³. The cylinder has a surface area of 175.929 in².
What's volume of cylinder ?The quantity of three-dimensional space that an object or closed surface occupies is referred to as volume in mathematics. The cubic units of volume are m³, cm³, in³, and so on.
How does surface area work?The sum of all of an object's faces is its surface area in three dimensions. Wrapping, painting, and finally building things to achieve the best possible design are examples of real-world applications of the concept of surface areas.
Evaluating :Given that a volume of cylinder = h × r² × π
h = 12 in
r = 2 in
volume = ?
Volume of cylinder = h × r² ×π
= =12 × 3.14×(2)²
=37.68 × 4
=150.796 in³
B). Surface area of cylinder= 2πr² + 2πrh
=2× 3.14 × (2)²+2× 3.14× 2×12
=175.929in²
The formula V=r²(h) can be used to determine a cylinder's volume. Simply multiplying the area of the circular base shape by the height is all that is required to determine a cylinder's volume.
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An anonymous survey of college students was taken to determine behaviors regarding alcohol, cigarettes, and illegal drugs. The results were as follows: 854 drank alcohol regularly,644 smoked cigarettes, 199 used illegal drugs,407 drank alcohol regularly and smoked cigarettes,109 drank alcohol regularly and used illegal drugs,108 smoked cigarettes and used illegal drugs,84 engaged in all three behaviors, and 93 engaged in none of these behaviors.
Answers
Based on the information, it can be inferred that the total number of students surveyed is: 2,498.
How to find the number of students surveyed?To find the number of students surveyed we can perform the following operation.
1. Add all the results of each category
854 + 644 + 199 + 407 + 109 + 108 + 84 + 93 = 2,498
According to the above, the total number of students surveyed would be 2,498. Additionally, this information can be classified in a Venn diagram to identify students who belong to two or three categories at the same time.
Note: This question is incomplete because there is some information missing. Here is the complete information
tasks
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Nuts berry farm makes their own trail mix using nuts and berries. Each pack of trail mix has a 3 tablespoon of nuts and 1 tablespoon of berries. Enter the percentage of the trail mix that is berries
Answers
Answer:
25%
Step-by-step explanation:
There's 3 tablespoons of nuts and 1 tablespoon of berries, so 1/4 tablespoons is berries.
Answer:
To sum up, we looked at the important amount devided by the total amount. Finally we solved for p. Which gave us p=75. Furthermore 75 percent of the trail mix is made up out of berries.
Step-by-step explanation:
So the main equation with percentages is W/G = p/100.
So First we look at G. G describes the total amount. In this case the total amount of teaspoons is four. Four because we have three tablespoons of berries and one tablespoon of nuts. That is four tablespoons.
Now we can go further to find out what W is. 2 is the important amount. In the question we are supposed to look at the amount of berries is the trail mix. Which gives us the value three.
So far our equation has no unknowns anymore 3/4=p/100. We multiply both sides of the equation with 100 3*100/4=p. Thus p = 300/4=150/2=75.
The recipe calls for 4 cups of broccoli, but Roselyn has only a 2/3 cup measure. How many measuring cups of broccoli should she add?
Answers
Answer:
6
Step-by-step explanation:
If the recipe calls for 4 cups of broccoli and she only has 2/3 cup measure you have to think how many 1/4 are in a cup there are 3 1/4 in 1 cup and you count 1/4, 2/3, 1 cup. So...you have to count the cups is 6.
hope this helps I maybe be wrong sorry☺️
Identify the Input values: (0,2), (1,3), (5,9), (7,13) *
Answers
Ella invested $4,900 in an account paying an interest rate of 3% compounded monthly. Assuming no deposits or withdrawals are made, how long would it take, to the nearest tenth of a year, for the value of the account to reach $5,920?
Answers
Answer:
It would take 6 years for the value of the account to reach $5,920
Step-by-step explanation:
Principal Amount = $4900
Interest rate r = 3% = 0.03
Compounded monthly = n=12
Time t =?
Future Value = $5920
We can find time using formula: \(A=P(1+\frac{r}{n})^{nt}\)
Putting values and solving:
\(A=P(1+\frac{r}{n})^{nt}\\5920=4900(1+\frac{0.03}{12})^{12t} \\5920=4900(1+0.0025)^{12t}\\5920=4900(1.0025)^{12t}\\\frac{5920}{4900}= (1.0025)^{12t}\\1.21=(1.0025)^{12t}\)
Applying exponent rule; \(a=b^c\\c\:ln(b)=ln(a)\)
\(12t\:ln(1.0025)=ln(1.21)\\12t\:(0.00249)=0.19062\\t=\frac{0.19062}{12*0.00249}\\t=6.3\approx6\)
So, It would take 6 years for the value of the account to reach $5,920
200 students attend Ridgewood Junior High School. 25% of students bring their lunch to school everyday. How many students brought their lunch to school on Thursday?
Answers
sorry est un site Web Internet spécialement conçue 4
25% of 100 is 25 and 200 is twice as much as 100. So then double the 25 to 50.
You can also set up a proportion of 25%/100% = ?/200 and cross multiply and divide.
Another way is to manipulate the numbers. Instead of 25% of 200 you can say 200% of 25. 200% is the same as saying twice as much as the number so what is twice the number 25? 50!
100 Points! Multiple choice Geometry question. Photo attached. Thank you!
Answers
Answer:
2. C. 50.3 ft²
3. A. 75.4 ft²
Step-by-step explanation:
The lateral surface area of a cylinder is the area of the curved surface of the cylinder. It is calculated by multiplying the circumference of the base by the height of the cylinder. The formula for the lateral surface area of a cylinder is:
Lateral Surface Area = 2πrh
Where:
r is the radius of the baseh is the height of the cylinderThe total surface area of a cylinder is the area of the lateral surface plus the area of the two circular bases. The formula for the total surface area of a cylinder is:
Total Surface Area = 2πrh + 2πr^2
Where:
r is the radius of the baseh is the height of the cylinder2.
r=2 ft
h=4 ft
Lateral Surface Area = 2πrh=2*22/7*2*4=50.3 ft²
3.
Total Surface Area = 2πrh + 2πr^2=2*22/7*2*4+2*22/7*2
=50.3+25.1=75.4 ft²
Select the expression that has a value of 13.
9 + 3 x (2 ÷ 3) + 6
(9 + 3) x 2 ÷ 3 + 6
9 − (3 x 2) ÷ 3 + 6
(9 + 3 x 2) ÷ 3 + 6
Answers
Answer:
9 − (3 x 2) ÷ 3 + 6 is the answer
Marta is shopping where there is a sales tax of 8\%8%8, percent on any item she buys.
1. Write an equation that represents how much tax (ttt) Marta pays on an item whose price is ppp dollars.
2. How much tax does Marta pay on an item whose price is \$ 20$20dollar sign, 20?
\$$dollar sign
Answers
1. An equation that represents "the amount of tax on an item of price p",
t = p x X / 100
2. Marta does pay on an item whose price is $20, $1.6
What is the percentage?Percentage is a way to express a number as a fraction of 100. It is often used to represent ratios and proportions in a more convenient and understandable form, especially in financial and statistical contexts. For example, 50% means 50 per 100, or half of a given quantity. It is denoted using the symbol "%".
Given that,
Tax rate = 8%
1. Let's assume that the sales tax rate is X%.
Then, the equation that represents the amount of tax (t) Marta pays on an item whose price is p can be written as:
t = p x X / 100
2. If the price of the item is $20, the amount of tax Marta pays can be calculated as follows:
t = $20 x X / 100
t = $20 x 8 / 100
t = $1.6
So, Marta pays $1.6 in sales tax on an item whose price is $100.
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please ASAP , giving BRAINLIEST if correct.
Answers
Answer:
B. -3(4x + 1) (x - 4)
Step-by-step explanation:
Out of the other answer choices, "B," is the only that factorizes correctly and ends up with the correct factorization (It already gives you the break-down of the trinomial).
However, if you're unsure about the answer, you can always take the end result: -3(4x + 1) (x - 4), and multiply it together to see if you can end up with the original trinomial: \(-12x^2 + 45x + 12\)
Question 1 of 5 Which number line shows the solutions to x < 5? OA. -3 -6 -4 -2 0 2 4 6 8 OB. O C. -8 -6 -4 -2 0 2 4 6 8 -8-6-4-2 0 2 4 6 8 OD. 864 2 0 2 4 6 8
Answers
The number line that shows the solutions of x < 5
B. O What is number line?A number line is a visual representation of the real numbers, ordered from left to right, with zero in the middle. It is typically a straight line that extends infinitely in both directions, with evenly spaced markings that represent specific points along the line.
The solution of x < 5 should consist of number less than 5
The inequality used is less than and hence should have values saying less than
Other options has numbers more than 5 such as 6 except option B
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