Approximately 86.5% of customers will be served in less than 10 minutes and only 13.5% of customers will take more than 10 minutes to check out.
Exponential Checkout Time ProportionTo find the proportion of customers who take more than 10 minutes to check out, we need to calculate the cumulative distribution function (CDF) of an exponential distribution at 10 minutes and subtract it from 1. The CDF for an exponential distribution with mean (lambda) 5 minutes is given by:
CDF = 1 - e^(- λ * x)
Plugging in λ = 0.2 (1/mean) and x = 10, we get:
CDF = 1 - e^(-0.2 * 10) = 1 - e^(-2) = 1 - 0.135 = 0.865
So, approximately 86.5% of customers will be served in less than 10 minutes and only 13.5% of customers will take more than 10 minutes to check out.
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GEOMETRY The area of the base of a rectangular box measures 2x² + 4x-3 square units. The height of the box measures x units. Find a polynomial expression for the volume of the box.
Answer:
The area of the base of the rectangular box is 2x² + 4x - 3 square units and the height is x units.
So the volume of the box can be found by multiplying the area of the base by the height:
V = (2x² + 4x - 3) x (x)
V = 2x³ + 4x² - 3x
Therefore, the polynomial expression for the volume of the box is 2x³ + 4x² - 3x.
Answer:
2x^3 + 4x^2 - 3x
Step-by-step explanation:
area of base = 2x^2 + 4x - 3 = Length x Breadth
Height of box = x
volume of box = Height x Length x Breadth
= (2x^2 +4x - 3) x
= 2x^3 + 4x^2 - 3x
Triangle DEF is congruent to Triangle DFG by the
A.ASA Postulate
B.SSS Postulate
C.SAS Postulate
D.SSA Postulate
Answer: SSS Postulate
Step-by-step explanation:
Since DF is congruent to FD, there are three congruent sides.
P=(prime numbers less than 20) and Q=(odd numbers less than 10) find PnQ
Answer:
Step-by-step explanation: P = (2, 3, 5, 7, 11, 13, 17, 19), Q = (1, 3, 5, 7, 9)
PnQ = (3,5,7)
(I think your N means intersection)
the fourth term in the geometric sequence in part (a) appears as the $n$th term in the arithmetic sequence. find the value of $n$.
The value of n is 30.33. The thirty-fourth term can be found by solving for the common difference (d) and the number of terms (n) in the arithmetic sequence and then using the formula for the nth term of an arithmetic sequence.
Let's assume that the common ratio of the geometric sequence is r. Then, the terms of the geometric sequence are given by:
[tex]a_2 = a_1 * ra_{10} = a_1 * r^8a_{34} = a_1 * r^{32}[/tex]
Since these terms also appear in the arithmetic sequence, we can write:
[tex]a_2 = a_1 + da_{10} = a_1 + 9da_{34} = a_1 + 33d[/tex]
Substituting the expressions for a_2 and a_{10} from the geometric sequence into the arithmetic sequence, we have:
[tex]a_1 * r = a_1 + da_1 * r^8 = a_1 + 9d[/tex]
Solving for d, we get:
[tex]d = a_1 * (r - 1)d = a_1 * (r^8 - 1) / 9[/tex]
Next, we use the expression for a_{34} from the arithmetic sequence and substitute the expression for d to obtain:
[tex]a_{34} = a_1 + 33d = a_1 + 33a_1 * (r^8 - 1) / 9[/tex]
Since the first term of the arithmetic sequence is 1, we have:
[tex]a_{34} = 1 + 33 * 1 * (r^8 - 1) / 9[/tex]
The value of n can be found by using the formula for the nth term of an arithmetic sequence:
[tex]a_n = a_1 + (n-1)d[/tex]
Setting n = 34 and substituting the expression for d, we have:
[tex]a_{34} = 1 + (33) * (a_1 * (r^8 - 1) / 9)[/tex]
So the thirty-fourth term of the arithmetic sequence is:
[tex]a_{34} = 1 + 33 * (1 * (r^8 - 1) / 9) = 34 - 33/9.[/tex]
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Complete Question:
An arithmetic sequence with first term 1 and common difference not equal to 0 has second, tenth, and thirty-fourth terms that form a geometric sequence.
What is the thirty-fourth term of the arithmetic sequence?
The fourth term in the geometric sequence above appears as the nth term in the arithmetic sequence. Find the value of n.
I need help with this please
Answer:
the answer is B or 12x +18
Answer:
first option: 12x+18
Step-by-step explanation:
You are finding the area of a rectangle so the formula you use will be
length * height
length = 4x+6
height= 3
you multiply them:
=3*(4x+6)
=3*4x + 3*6
=12x+18
Members of the Standing Rock Sioux Tribe write a letter of protest to the federal government. What most likely would be a topic of the letter?
The letter of protest from the Standing Rock Sioux Tribe to the federal government is likely to concern the construction of the Dakota Access Pipeline, which threatened the Tribe's water supply and cultural sites.
Who are the Standing Rock Sioux Tribe?The Standing Rock Sioux Tribe is a Native American tribe located primarily in North and South Dakota. The tribe is known for its opposition to the Dakota Access Pipeline, a controversial oil pipeline that would cross the tribe's reservation and potentially impact its water supply and cultural sites. In 2016, the Standing Rock Sioux Tribe and its supporters held a series of protests and demonstrations against the pipeline, attracting national attention and leading to its temporary halt.
The Dakota Access Pipeline (DAPL) is a
n oil pipeline that runs from the Bakken oil fields in North Dakota to Illinois. The tribe and its supporters held protests, leading to confrontations with law enforcement. In 2016, the US Army Corps of Engineers declined to grant the pipeline an easement, but this decision was later reversed by the Trump administration.
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in a survey one fourth young girl like sour taste only and one third like chilly taste. if 50 of them do not like both the taste, find the total number of young girl
6. A clothing store has reduced their prices on swim wear by 20%. A swimming costume normally costs R124,95. Maria has a loyalty card which entitles her to a further 7,5% discount. How much would Maria pay for the swimming costume?
Answer:
R92.463
Step-by-step explanation:
100% - 20% = 80% = 0.8
0.8 times 124.95 = R99.96
7.5% = 0.075
99.96 - (99.96 x 0.075) = R92.463
So, Maria pay R92.463 for the swimming costume.
URGENT: WILL MARK BRAINLIEST!!!!
Jacob wrote a two digit number and then wrote an additional digit to its right. He added 230 to the obtained number and got 1011. What is the original number Jacob wrote?
Answer:
original number Jacob wrote = 78
Step-by-step explanation:
basically Jacob wrote a 3 digit number, let's call it "x" and then he added 230 to x which resulted in 1011.
this can be written simple as an equation:
x + 230 = 1011
now just solve for x:
x = 1011 - 230
x = 781
finally we know that Jacob initially wrote a two digit number and then an additional digit to its right, hence the original number Jacob wrote would be:
78
Use the image below to answer questions 3 and 4.
What is the value of x?
Answer: x =
Answer:
x=18
Step-by-step explanation:
2 teas and 3 coffees have a total cost of £6.90
4 teas and 7 coffees have a total cost of £15.30
Work out the cost of one tea and the cost of one coffee.
Answer:7
Step-by-step explanation:
7
Pls answer this question! Question down below.
First, find the product of the numbers:
3 · 7 · 13 · 37 = 10101Now, rewrite the given expression as:
x·10000 + y·100 + x + y·10000 + z·100 + x + z·10000 + x·100 + y = x(10000 + 100 + 1) + y(10000 + 100 + 1) + z(10000 + 100 + 1) = 10101x + 10101y + 10101z = (x + y + z)·10101 = (x + y + z)·3·7·13·37Proved that the given expression is divisible by 3, 7, 13 and 37.
Please show all your work. I will give brainiest if done.
The Takac Family decided to join an online music membership site where they can download individual songs, or entire albums and get them at discount prices. Anna downloaded 5 individual songs and 1 album and paid $14.90. Owen downloaded 3 individual songs and 2 albums and paid $21.75.
Mrs. T was a little upset when these charges came up on her bank statement, so she wanted to know how much they were actually being charged for each individual song that was downloaded and for each full album that was downloaded.
Can you help?
Set up an solve a system of equations that models this situation. Be sure to explain what each of your variables represents and also give a detailed explanation of what your solution represents in the context of this situation.
Do you think this membership site is a good deal?
Show all the work using the RACE to display your solution and make sure to answer all that the problem asks for. Scan and upload below.
a) A system of equations that models this situation and helps Mrs. T to know how much the family is being charged for each individual song and each full album downloaded is:
5x + y = 14.903x + 2y = 21.75.b) From the solution of the simultaneous equations, we can determine that each individual song downloaded costs $1.15 while each full album costs $9.15.
What is a system of equations?A system of equations is two or more equations or simultaneous equations, solved concurrently.
Individual Songs Album Total Costs
Anna's download 5 1 $14.90
Owen's download 3 2 $21.75
Let individual songs = x
Let Album = y
Equations:5x + y = 14.90... Equation 1
3x + 2y = 21.75... Equation 2
Multiply Equation 1 by 2:
10x + 2y = 29.80... Equation 3
Subtract Equation 2 from Equation 3:
10x + 2y = 29.80
-
3x + 2y = 21.75
7x = 8.05
x = 1.15
= $1.15
From Equation 1, substitute x = 1.15 to get y:
5x + y = 14.90
5(1.15) + y = 14.90
5.75 + y = 14.90
y = 9.15
y = $9.15
Check Equation 2:
3x + 2y = 21.75
3(1.15) + 2(9.15) = 21.75
3.45 + 18.3 = 21.75
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Find the measures of two supplementary angles if one angle is 40 degrees more than the measure of the supplement.
The measures of two supplementary angles are 110° and 70°.
What is Supplementary angle?The sum of two or more angle is 180 degree then the angle is called the supplementary angle.
We have to given that;
One angle is 40 degrees more than the measure of the supplement.
Let measure of one angle = x
Then, Measure of its supplement = 180 - x
Here, One angle is 40 degrees more than the measure of the supplement.
Hence, We get;
⇒ x = 40 + (180 - x)
⇒ x + x = 220
⇒ 2x = 220
⇒ x = 110
Thus, Measure of one angle = x = 110°
Then, Measure of its supplement = 180 - x
= 180° - 110°
= 70°
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there are 22 boys and 32 girls on a school bus. if 6 boys and 4 girls get off the bus at the next bus stop, what will be the ratio of girls to total students
If 6 boys and 4 girls get off the bus at the next bus stop, the ratio of girls to total students will be 14/27.
There are 22 boys and 32 girls on a school bus, 6 boys and 4 girls get off the bus at the next bus stop.
Total boys = 22
Total girls = 32
Total Student = Total boys + Total girls
Total Student = 22 + 32
Total Student = 54
The girls gets off = 4
Now remaining girls in bus = Total girls - The girls gets off
Now remaining girls in bus = 32 - 4
Now remaining girls in bus = 28
The ratio of girls to total students = Now remaining girls in bus/Total Students
The ratio of girls to total students = 28/54
The ratio of girls to total students = 14/27
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a car starts off 163 miles directly north from the city of johnstown. it travels due east at a speed of 33 miles per hour. after travelling 63 miles, how fast is the distance between the car and johnstown changing? (do not include units in your answer, and round to the nearest hundredth.)
The distance between the car and Johnstown is decreasing at a rate of 33 miles per hour.
After travelling 63 miles, the distance between the car and Johnstown is changing at a rate of 33 miles per hour, and the distance between the car and Johnstown is 100 miles
To calculate the distance between the car and Johnstown after travelling 63 miles, we need to first find the starting distance.
The car starts off 163 miles directly north from the city of Johnstown, so the starting distance is 163 miles.
We then need to subtract the distance travelled from this starting distance. Since the car is travelling at a rate of 33 miles per hour, it has travelled 63 miles in the given time.
Therefore, the distance between the car and Johnstown is 100 miles
(163 - 63 = 100).
Finally, we need to calculate the rate of change of this distance. Since the car is travelling at a rate of 33 miles per hour, the rate of change of the distance between the car and Johnstown is also 33 miles per hour.
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>
54
♡
ܘ
1
-5 -4 -3 -2 -19
-2
-3
GA
2 3 4 5
What is the gradient of the blue line?
X
Answer:
-0.25
Step-by-step explanation:
rise/run=2/8
= 0.25
ans is negative because line is going down
Answer:
2/-8 = -1/4 or -0.25 in decimal
Step-by-step explanation:
To find the slope take two distinguishable points on the graph(integer values preferred).
Find the difference in the y values and divide by the corresponding difference in the x values
You can identify 2 points with integer coordinates as
(-5, 3) and (3, 1)
Difference in y values = 3 - 1 = 2
Corresponding difference in x values : -5 - 3 = -8
So slope is 2/-8 = -1/4 or -0.25 in decimal
use the definition of continuity and the properties of limits to show that the function is continuous at the given number a. f(x) = x 3x4 5 , a = −1
Using the definition of continuity and the properties of limits to show that the function is continuous at the given number f(x)=-5
continuity of a real function is provided generally in a calculus’s introductory course in terms of a limit’s idea.
First, a function f with variable x is continuous at the point “a” on the real line, if the limit of f(x), when x approaches the point “a”, is equal to the value of f(x) at “a”, i.e., f(a).
Second, the function (as a whole) is continuous, if it is continuous at every point in its domain.
We know that the value of f near x to the left of a, i.e. left-hand limit of f at a and the value of f near x to the right f a,
i.e. right-hand limit are equal, then that common value is called the limit of f(x) at x = a. Also,
a function f is said to be continuous at a if limit of f(x) as x approaches a is equal to f(a).
A function f is continuous at a number a if
[tex]\lim_{x \to\n} f( x) = f(a)[/tex]
f(x) = [tex]x ^3x^4 5[/tex]
= [tex]\lim_{x \to \ a} x^3 * \lim_{x \to \ a} x^4 *5\\= (-1)^3 * (-1)^4 *5\\= -1 * 1* 5\\= -5[/tex]
Using the definition of continuity and the properties of limits to show that the function is continuous at the given number f(x)=-5
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Which ordered pair represents point D?
(4, -4)
(-4, -4)
(4, 4)
(-4, 4)
The point must be (-4,-4)
what is the Cartesian coordinate system?A Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates,
Given here : the Point D in the graph.
Each point can be identified by an ordered pair of numbers; that is, a number on the x-axis called an x-coordinate, and a number on the y-axis called a y-coordinate. Ordered pairs are written in parentheses (x-coordinate, y-coordinate). The origin is located at (0,0).
we can clearly read that the point D is -4 points away from the y-axis and -4 units away from the x-axis to the right. It also lies in the third quadrant in the co-ordinate plane.
Hence, The point must be (-4,-4)
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the starlight diner's lunch special includes a choice of one each from 6 appetizers, 5 different salads, 4 meat dishes, 4 sides, 4 breads, and 5 drinks. how many different ways are there to choose a lunch special at the diner?
There are 9600 different ways to choose a lunch special at the starlight diner.
In the given question, there are:
Number of appetizers = 6
Number of salads = 5
Number of meat dishes = 4
Number of sides = 4
Number of breads = 4
Number of drinks = 5
We know that the number of ways to choose r elements from n elements is equal to nCr.
Since, the starlight diner's lunch special includes a choice of one each, then the number of ways in which we can choose a lunch special at the diner will be:
6C1 x 5C1 x 4C1 x 4C1 x 4C1 x 5C1 = 9600
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The surface area of a cylinder with a radius of 3 inches is 78pi square inches. What is the height of the cylinder in inches? (Do not enter units)
The height of the cylinder in inches is 10 inch.
What is Surface Area?The total area of an object's external facing surfaces is its surface area. The base, top, and lateral surfaces (sides) of the object's surface are added together to get the object's overall surface area.
Given:
radius = 3 inch
Surface Area of cylinder = 78π
So, Surface Area of cylinder = 2πr (h+ r)
78π = 2π x 3 ( h+ 3)
78 = 6 (h+ 3)
13 = h+ 3
h= 10 inch
Hence, the height is 10 inch.
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A cylindrical rod measures 4 inches long and the circumference of one of its bases is 12π inches. the rod is cut into two equally-sized pieces and then all surfaces are painted. what is the area that is painted? use π≈3.14. enter your answer, rounded to the nearest tenth, in the box.
The area painted is 376.8 sq. inches (approximately)
We can start solving the problem by calculating the radius of the base of the rod. We can use the formula for the circumference of a circle:
circumference = 2πr
Where r is the radius of the circle.
Given that the circumference of one of the bases of the rod is 12π inches, we can set up the equation:
12π = 2πr
r = 12π/2π = 6
So the radius of the base of the rod is 6 inches.
Now we can use the radius to find the area of one base of the rod. The area of a circle is given by the formula:
A = πr²
So the area of one base of the rod is:
A = π × 6² = 36π
Now we can use the length and radius of the rod to find the lateral surface area of the rod.
The formula for the lateral surface area of a cylinder is :
L.S.A = 2πrh
Where h is the height of the cylinder. In this case, the height of the cylinder is 4 inches.
L.S.A = 2π × 6 × 4 = 48π
So the lateral surface area of the rod is 48π inches.
Finally, to find the total area painted, we can add the area of the two bases and the lateral surface area.
Total area painted = 2 × 36π + 48π = 120π sq inches.
Now we can use π≈3.14 and get the area painted to the nearest tenth.
Total area painted = 120×3.14 = 376.8 sq. inches
Therefore, the area painted is 376.8 sq. inches (approximately)
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karen purchased a DVD player on sale. the original price was $175.80. the sale price was 153.67 what is the first step in finding the percent markdown? find the percent markdown.
The percent markdown is 22.58% for the given DVD player.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
We can determine the value of the percent markdown by the following formula,
percentage decrease = (initial value - reduced value) / initial value × 100%
As per the given question, we have
initial value = $175.80, and reduced value = $153.67
Substitute the values in the above formula, and we get
percent markdown = (175.80 - 153.67) / 175.80 × 100%
percent markdown = (22.13) / 175.80 × 100%
percent markdown = 0.1258 × 100%
Apply the multiplication operation, and we get
percent markdown = 12.58 %
Thus, the percentage decrease of the given item would be 12.58%.
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Peter scored 40 goals at soccer practice his ratio of goals to misses was 5:7 how many times did he miss
The number of times that he misses will be 56.
What are ratio and proportion?A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.
Peter scored 40 goals at soccer practice his ratio of goals to misses was 5: 7.
Let 'm' be the number of miss. Then the equation is given as,
40 / m = 5 / 7
Simplify the equation, then we have
40 / m = 5 / 7
8 / m = 1 / 7
m = 7 x 8
m = 56
The number of times that he misses will be 56.
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Which of the following are factor pairs for 63? Select all that apply.
A.
2
×
126
B.
3
×
21
C.
4
×
13
D.
4
×
16
E.
7
×
9
The required factors of the number 63 is 21×3.So, option(B) is correct.
What is factors?A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them.
How to find factors?Algebraic expressions are written as the sum of two or more expressions using factoring formulas. The following are some crucial factoring formulas: (a + b)2 = a2 + 2ab + b.
According to question:We have to find the factors of the number 63
= 63
= 9×7
= 3×3×7
= 21×3
Thus required factors of the 63 are 21×3.
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1.) if angle a and angle b are supplements, and angle a and angle c are supplements, what can you conclude about angle b and angle c? explain how you know. (2 pts)
If angles a and b are supplemented, they add up to 180 degrees. If angles a and c are supplements, they add up to 180 degrees.
Since angle a is a common angle in both of these equations, you can conclude that angles b and c must also be supplemented and add up to 180 degrees. Supplemented means that two angles add up to 180 degrees. In other words, they are supplementary angles.
Supplementary angles are two angles that add up to 180 degrees. They are considered "complementary" to each other as they "complete" a straight line, which measures 180 degrees. A straight line is a geometric object with no curvature, consisting of an infinite set of points that extends infinitely in both directions. It is the shortest distance between two points and has the property of being perfectly straight. In geometry, straight lines are a basic building block to define and measure other shapes and figures.
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jars of pickles are sampled and weighed. sample measures are plotted on control charts. the ideal weight should be precisely 11 oz. which type of chart(s) would you recommend?
To demonstrate the given situation, the type of chart(s) that is best to use is both an x-bar chart and an R-chart.
An x-bar chart is a statistical process control chart used to monitor the mean of a continuous data set over time. The chart plots the average (x-bar) of each subgroup of data points, rather than plotting individual data points, and provides information about process stability and control. The x-bar chart is often used in conjunction with an R-chart.
An R-chart (Range chart) is a type of statistical process control chart that is used to monitor the variability of a process by plotting the range (difference between the maximum and minimum values) of a subgroup of samples at different time periods. The R-chart provides a measure of process variability and helps detect changes in variability, which may indicate a change in the underlying process mean. The R-chart is typically used in conjunction with an X-bar chart, which monitors the process mean, to provide a comprehensive view of process performance.
The question seems incomplete, it must have been...
"Jars of pickles are sampled and weighed. Sample measures are plotted on control charts. The ideal weight should be precisely 11 oz. Which type of chart(s) would you recommend?
-both an x-bar chart and an R-chart
-p-chart
-an x-bar chart, but not an R-chart
-c-chart
-both a p-chart and a c-chart"
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3
An arrow is shot with an angle of elevation of 20°. When the arrow reaches an altitude of 482 feet, how far has the arrow flown through the air? Round
your answer to the nearest whole foot.
Type your answer...
1 point
figuro holow. To the nearest tenth of a foot
Answer:
1409.3
Step-by-step explanation:
Let the distance flown by the arrow in feet be [tex]d[/tex].
[tex]\sin 20^{\circ}=\frac{482}{d} \\ \\ \frac{1}{\sin 20^{\circ}}=\frac{d}{482} \\ \\ d=\frac{482}{\sin 20^{\circ}} \\ \\ d \approx 1409.3[/tex]
una muestra aleatoria de cinco elementos dio como resultado los siguientes valores: 18, 15, 12, 19 y 21. con el nivel de significancia 0.01,
The calculated t-value of 8.77 is not statistically significant with a confidence level of 99%. This indicates that the sample does not differ significantly from the mean.
The formula for calculating a one-tailed test of significance with a sample size of 5 elements is as follows:
First, calculate the mean of the sample:
Mean = (18 + 15 + 12 + 19 + 21) / 5 = 17
Second, calculate the sample variance:
Variance = [(18-17)2 + (15-17)2 + (12-17)2 + (19-17)2 + (21-17)2] / 4 = 16
Third, calculate the standard deviation:
Standard Deviation = √16 = 4
Fourth, calculate the t-value:
t-value = (17 - 0) / (4 / √5) = 8.77
Finally, calculate the p-value:
p-value = 1 - (2 * 0.01) = 0.98
Thus, the p-value for the sample of five elements with a significance level of 0.01 is 0.98. This means that the calculated t-value of 8.77 is not statistically significant with a confidence level of 99%. This indicates that the sample does not differ significantly from the mean.
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find a unit vector that has the same direction as the given vector. −9i 2j − k
The unit vector with the same direction as the given vector is (−0.45i, 0.9j, −1k). This vector has been normalized so that the magnitude is equal to 1, while still preserving the direction of the original vector.
To find the unit vector with the same direction as the given vector, we need to normalize the vector. This means we need to divide each component of the vector by its magnitude. The magnitude of the vector is the square root of the sum of the squares of its components, which in this case is the square root of (9^2 + 2^2 + 1^2), or 9.64. Dividing each component of the vector by its magnitude gives us the unit vector (−0.45i, 0.9j, −1k). The magnitude of this vector is equal to 1, and the direction is the same as the original vector.
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