The best estimate of the volume of this cylindrical water dispenser is 2940 in³. The correct option is b.
To estimate the volume of the cylindrical water dispenser, we can use the formula for the volume of a cylinder, which is given by V = πr²h, where V is the volume, π is a mathematical constant approximately equal to 3.14, r is the radius, and h is the height.
Given that the radius of the water dispenser is 7 inches and the height is 20 inches, we can substitute these values into the formula:
V = π(7²)(20)
V = π(49)(20)
V ≈ 3.14 × 49 × 20
V ≈ 3.14 × 980
V ≈ 3075.2 in³
From the given options, the closest estimate to the calculated volume of approximately 3075.2 in³ is option B: 2940 in³. While it is not an exact match, it is the closest estimate among the options provided.
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21. if you have the raw scores of two individuals on a norm-referenced test, which of the following is important in terms of making meaning of those scores? a. measures of central tendency (mean, median, mode) b. the relative positions of the scores to the rest of the group c. whether higher scores are better than lower scores d. how an individual feels about his or her score e. all of these are important.\
The term which is important in terms of making meaning of those scores is measures of central tendency (mean, median, mode), option A.
A single number that seeks to characterise a set of data by pinpointing the centre location within that set of data is referred to as a measure of central tendency. As a result, measurements of central location are occasionally used to refer to measures of central tendency.
These also fit within the category of summary statistics. You are probably most familiar with the mean (sometimes known as the average), but there are additional central tendency measures, including the median and the mode.
The mean, median, and mode are all reliable indicators of central tendency, however depending on the situation, certain indicators are more useful than others.
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Y’all pls help this is due
Answer: 4.7KL
Step-by-step explanation:
KL=DAL/100
KL=470/100
KL=4.7
what is the percent of 11/20
Answer: 55%
Step-by-step explanation:
To find the percentage of 11/20, we can use the following formula:
Percentage = (Numerator ÷ Denominator) × 100
Substituting the values from 11/20 into the formula, we get:
Percentage = (11 ÷ 20) × 100
Percentage = 0.55 × 100
Percentage = 55%
Therefore, the percentage of 11/20 is 55%.
Answer:
Solution: 11/20 as a percent is 55%
Step-by-step explanation:
First, convert the fraction into a decimal by dividing the numerator by the denominator:
11/20 = 0.55
If we multiply the decimal by 100, we will get the percentage:
00.5 * 100 = 55
We can see that 11/20 is percentage is 55.
10-2 skills practice simplifying radical expressions square root of 5 over 3
Step-by-step explanation:
sqrt (5/3) = sqrt 5 / sqrt 3
multiply by ONE in the form sqrt (3) / sqrt 3
sqrt 5 / sqrt 3 * sqrt 3 / sqrt 3
= sqrt 15 / 3
Or maybe you meant
sqrt (5) / 3 = .745
Si se tiene un recipiente en forma de prisma triangular como el de la figura B, lleno de un líquido que se vierte en otro recipiente cilindro como el de la figura A Después de esa acción, ¿Qué volumen le falta al cilindro para estar completamente lleno?
The number of cones that can be filled with the ice cream from the container is 10.
Let's start with the container. We are given that it is a right circular cylinder with a diameter of 12 cm and a height of 15 cm. To find the volume of this cylinder, we use the formula:
Volume of cylinder = πr²h
where r is the radius of the cylinder (which is half of the diameter), and h is the height. Substituting the given values, we get:
Volume of cylinder = π(6 cm)²(15 cm) = 540π cubic cm
So the container has a volume of 540π cubic cm.
Now, let's move on to the cones. We are given that the cones have a height of 12 cm and a diameter of 6 cm. The cones have a hemispherical shape on the top, so we can consider them as a combination of a cone and a hemisphere. The formula for the volume of a cone is:
Volume of cone = (1/3)πr²h
where r is the radius of the base of the cone, and h is the height. Substituting the given values, we get:
Volume of cone = (1/3)π(3 cm)²(12 cm) = 36π cubic cm
The formula for the volume of a hemisphere is:
Volume of hemisphere = (2/3)πr³
where r is the radius of the hemisphere. Substituting the given values (the radius is half the diameter of the cone, which is 3 cm), we get:
Volume of hemisphere = (2/3)π(3 cm)³ = 18π cubic cm
So the total volume of each cone is:
Volume of cone + hemisphere = 36π + 18π = 54π cubic cm
To find out how many cones can be filled with the ice cream from the container, we divide the volume of the container by the volume of each cone:
Number of cones = Volume of container / Volume of each cone Number of cones
=> (540π cubic cm) / (54π cubic cm) Number of cones = 10
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Complete Question:
A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice cream. The ice cream is to be filled into cones of height 12 cm and diameter 6 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream.
Complete each conversion by dragging a number to each box.
Numbers may be used once, more than once, or not at all.
1,20012012,00012
12,000 g =
kg
120 cm =
mm
1. 2 L =
mL
1,200 cm =
m
0. 12 m =
mm
The value for each conversion is: 12,000 g = 12 kg 120 cm = 1200 mm 2 L = 2000 mL 1,200 cm = 12 m 0.12 m = 120 mm.
Here are the completed conversions using the provided numbers:
1. 12,000 g = 12 kg (To convert grams to kilograms, divide by 1,000)
2. 120 cm = 1,200 mm (To convert centimeters to millimeters, multiply by 10)
3. 1.2 L = 1,200 mL (To convert liters to milliliters, multiply by 1,000)
4. 1,200 cm = 12 m (To convert centimeters to meters, divide by 100)
5. 0.12 m = 120 mm (To convert meters to millimeters, multiply by 1,000)
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a pet store has 115 fish and each tank can hold six fish how many tanks do you nedd
Answer:
20 tanks
Step-by-step explanation:
if each tank holds 6 fish and there are 115 fish, you need to divide the amount of fish total by amount that go in 1 tank:
115/6 = 19.1666666667
Now we round up bc we cant leave any fish out right?
So your answer is 20 tanks will be needed to hold 115 fish if it’s 6 fish per tank.
Check this by multiplying the tanks and fish in every tank:
20 x 6 = 120
Meaning that 115 fish go into 20 tanks, one of the tanks just having 1 fish :D
Answer: 20 is the correct option.
Step-by-step explanation:Given that a pet store has 115 fish that need to be placed into fish tanks and each tank hold 6 fish.
We are to find the number of tanks that the store need.
We will be using the UNITARY method to solve the given problem.
Number of tanks needed to store 6 fishes = 1.
So, number of tanks needed to store 1 fish will be [tex]\frac{1}{6}[/tex]
Therefore, number of tanks needed to store 115 fishes is given by
[tex]\frac{1}{6}[/tex] × 155 =[tex]\frac{115}{6}[/tex]= 19 [tex]\frac{1}{6}[/tex] = 19.16.
Since we cannot have 0.16 tank, so we need one tank more than 19 to store all fishes.
Thus, the store needs 20 tanks for 115 fishes.
Hope this helps :)
8 pound of peanuts cost 24 dollars. 6 pounds of walnuts cost half as much. Which is more expensive and by how much.
Answer:
Step-by-step explanation:
The cost of 1 pound of peanuts can be found by dividing the total cost of 8 pounds by 8:
Cost of 1 pound of peanuts = $24 / 8 pounds = $3 per pound
The cost of 1 pound of walnuts can be found by dividing the total cost of 6 pounds by 6 and then multiplying by 2 (since the cost of 6 pounds is half that of the peanuts for the same weight):
Cost of 1 pound of walnuts = ($24 / 6 pounds) x 2 = $8 per pound
Therefore, we see that walnuts are more expensive than peanuts by $5 per pound ($8 - $3).
In other words, 1 pound of walnuts costs $5 more than 1 pound of peanuts.
Find the measure of Tu in the photo
The value of the tangent TU for the circle with secant through U which intersect the circle at points V and W is equal to 12
What are circle theoremsCircle theorems are a set of rules that apply to circles and their constituent parts, such as chords, tangents, secants, and arcs. These rules describe the relationships between the different parts of a circle and can be used to solve problems involving circles.
For the tangent TU and the secant through U which intersect the circle at points V and W;
TU² = UV × VW {secant tangent segments}
(5x)² = 9 × 16
(5x)² = 144
5x = √144 {take square root of both sides}
5x = 12
x = 12/5
so;
TU = 5(12/5)
TU = 12
Therefore, the value of the tangent TU for the circle with secant through U which intersect the circle at points V and W is equal to 12
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made bracelets with string and beads. she used xx centimeters of string to make 77 bracelets. she used 17.817.8 centimeters of string for each bracelet. how much string did she use in all? write an equation and use it to solve this problem.enter the correct answers in the boxes.show hints
Total string used = Number of bracelets × String used per bracelet
Total string used = 77 × 17.8 = 1370.6 cm
How much string did she use in total?Let's denote the total amount of string used as "T". We know that the girl used xx centimeters of string to make 77 bracelets, and each bracelet required 17.8 centimeters of string.
To find the total string used, we can set up the following equation:
T = 77 * 17.8
Simplifying the equation, we have:
T = 1369.6
Therefore, the girl used a total of 1369.6 centimeters of string to make all the bracelets.
In conclusion, the equation T = 77 * 17.8 can be used to determine the total amount of string used, and the solution to the equation is T = 1369.6 centimeters.
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A circle with center c(2, 4) has radius 13. a) verify that a(14,9) and b(7, 16) are points on this circle. b) if m is the midpoint of ab, show that cm is perpendicular to ab.
a) To verify that the points A(14, 9) and B(7, 16) are on the circle with center C(2, 4) and radius 13, we can use the distance formula:
Distance between point A and C:
d_AC = sqrt[(x_A - x_C)^2 + (y_A - y_C)^2]
= sqrt[(14 - 2)^2 + (9 - 4)^2]
= sqrt[144 + 25]
= sqrt(169)
= 13
Since the distance between point A and C is equal to the radius of the circle, point A is on the circle.
Distance between point B and C:
d_BC = sqrt[(x_B - x_C)^2 + (y_B - y_C)^2]
= sqrt[(7 - 2)^2 + (16 - 4)^2]
= sqrt[25 + 144]
= sqrt(169)
= 13
Since the distance between point B and C is equal to the radius of the circle, point B is also on the circle.
Therefore, points A and B are on the circle with center C(2, 4) and radius 13.
b) The midpoint of line segment AB can be found using the midpoint formula:
M = [(x_A + x_B)/2, (y_A + y_B)/2]
= [(14 + 7)/2, (9 + 16)/2]
= [10.5, 12.5]
The slope of line segment AB can be found using the slope formula:
m_AB = (y_B - y_A)/(x_B - x_A)
= (16 - 9)/(7 - 14)
= -7/-7
= 1
The slope of a line perpendicular to AB will be the negative reciprocal of m_AB:
m_CM = -1/m_AB
= -1/1
= -1
The equation of the line passing through points C(2, 4) and M(10.5, 12.5) can be found using the point-slope form:
y - y_C = m_CM(x - x_C)
y - 4 = -1(x - 2)
y = -x + 6
The slope of line CM is -1, which is the negative reciprocal of the slope of line AB. Therefore, line CM is perpendicular to line AB.
Hence, we have shown that line segment CM is perpendicular to line segment AB.
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[tex]\frac{4}{-2} -\frac{3}{-6}[/tex]
The value of the fraction is 3/-2
What is a fraction?A fraction can simply be described as the part of a whole variable, a whole number or a whole element.
The different types of fractions in mathematics are;
Mixed fractionsProper fractionsImproper fractionsComplex fractionsSimple fractionsFrom the information given, we have that;
4/-2 - 3/-6
find the lowest common factor
12 - 3/-6
subtract the value, we get;
9/-6
Divide the values into simpler forms
3/-2
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PLS HELP ME WITH THIS 2. QUESTIONS, 50 POINTS
( The first 2 images are from the first question, the other one is from the second)
Answer: B g(x)=1/4f(x) odd
Step-by-step explanation:
First Page:
Points from the graph
Points from f(x) points from g(x)
(1,2) (1, 1/2)
(4, 16) (4, 4)
f(x) was multiplied by 1/4 to get to g(x)
Second Page:
Even functions are symmetrical about the y-axis: . Odd functions are symmetrical about the x- and y-axis: f(x)=-f(-x).
lets test for even: does f(x)=f(-x) => f(1)=f(-1) no -2[tex]\neq[/tex]2
see image for plotted points
lets test for odd: does f(x)= -f(-x) => f(1) = -f(-1) yes -2 = -2
Answer:
[tex]\textsf{B)} \quad g(x)=\dfrac{1}{4}f(x)[/tex]
[tex]\textsf{B)} \quad \textsf{odd}[/tex]
Step-by-step explanation:
Functions f(x) and g(x) are exponential functions.
From inspection of the given points on both graphs:
f(4) = 16g(4) = 4When x = 4, the y-value of function f(x) is four times the y-value of function g(x). Therefore, function g(x) is ¹/₄ of function f(x):
[tex]g(x)=\dfrac{1}{4}f(x)[/tex]
[tex]\hrulefill[/tex]
And even function is symmetric about the y-axis:
f(x) = f(-x) for all values of x.According to the table, f(3) = -4 and f(-3) = 4.
Therefore, as f(x) ≠ f(-x), the function is not even.
An odd function is symmetric about the origin:
f(-x) = -f(x) for all values of x.According to the table, f(-3) = 4 and f(3) = -4. So -f(3) = -(-4) = 4.
Therefore, as f(-3) = -f(3), the function is odd.
[tex]\hrulefill[/tex]
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If f(x) = 3x² - 3, find x = 2
Answer:
The answer is 9
Step-by-step explanation:
When x = 2,
f(2) = 3×2^2-3
f(2) = 3×4-3
f(2) = 12-3
f(2)= 9
The total cost C(x) (in dollars) incurred by Aloha Company in manufacturing x surfboards a day is given by the following function.
C(x) = −10x2 + 500x + 110 where (0 ≤ x ≤ 15)
(a)
Find C '(x).
C '(x) = (b)
What is the rate of change of the total cost (in dollars) when the level of production is 7 surfboards a day?
$ per surfboard
(a) First, we need to find the derivative of the cost function, C'(x), with respect to x.
The given function is: C(x) = -10x^2 + 500x + 110
To find the derivative, we will apply the power rule:
C'(x) = d/dx (-10x^2) + d/dx (500x) + d/dx (110)
For each term: d/dx (-10x^2) = -20x d/dx (500x) = 500 d/dx (110) = 0 So, C'(x) = -20x + 500
(b) Now, we need to find the rate of change of the total cost when the level of production is 7 surfboards a day.
To do this, we will substitute x=7 into the derivative function C'(x): C'(7) = -20(7) + 500 C'(7) = -140 + 500 C'(7) = 360
The rate of change of the total cost when the level of production is 7 surfboards a day is $360 per surfboard.
Your answer: a) C'(x) = -20x + 500 b) $360 per surfboard
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100 points Please help asap!
The solution of the system of equations is given by the ordered pair (-2, 2).
Based on the table, a x-value that is a solution to the equation is -2.
The solution to the equations are (-6, 3) and (-4, -5).
An ordered pair which is the best estimate for the solution of the system is: A. (-0.5, -1.75).
How to graphically solve this system of equations?In order to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;
8x - 4y = -24 ......equation 1.
4x - 12y = -32 ......equation 2.
Based on the graph shown in the image attached above, we can logically deduce that the solution to this system of equations is the point of intersection of the lines on the graph representing each of them, which lies in Quadrant II, and it is given by the ordered pairs (-2, 2).
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The answer to this math problem please.
Answer:
C) 6
Step-by-step explanation:
n=6
6( 6 + 1) + 3 =45
36 + 6 + 3 = 45
36 + 9 = 45
The table below shows the number of students in Mr. Jang's class that are taking 1, 2, 3, or 4 AP classes. After a new student joined the class (not shown in the table), the average (arithmetic mean) number of AP classes per student became equal to the median. How many AP classes is the new student taking?
A) 2
B) 3
C) 4
D) 5
Answer:
2
Step-by-step explanation:
To solve this problem, we need to first find the current average and median number of AP classes per student, and then use that information to determine the number of AP classes the new student is taking.
To find the current average number of AP classes per student, we can use the information in the table:
(1 AP class) x 6 students = 6 AP classes
(2 AP classes) x 9 students = 18 AP classes
(3 AP classes) x 5 students = 15 AP classes
(4 AP classes) x 4 students = 16 AP classes
Total number of AP classes = 6 + 18 + 15 + 16 = 55
Total number of students = 6 + 9 + 5 + 4 = 24
Average number of AP classes per student = Total number of AP classes / Total number of students
= 55 / 24
= 2.29 (rounded to two decimal places)
To find the current median number of AP classes per student, we need to order the number of AP classes per student from least to greatest:
1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4
The median is the middle value when the data is ordered in this way. Since there are 24 students, the median is the average of the 12th and 13th values:
Median = (2 + 2) / 2
= 2
Since we know that the current average and median are not equal, the new student must be taking a number of AP classes that will bring the average up to 2. We can set up an equation to represent this:
(55 + x) / (24 + 1) = 2
where x is the number of AP classes the new student is taking. Solving for x, we get:
55 + x = 50
x = -5
This is a nonsensical answer, as the number of AP classes taken by the new student cannot be negative. Therefore, our assumption that the new student is taking a number of AP classes greater than the current average is incorrect. Instead, the new student must be taking a number of AP classes less than the current average, which will bring the average down to 2.
Let y be the number of AP classes the new student is taking. We can set up a new equation to represent this:
(55 + y) / (24 + 1) = 2 - ((2.29 - 2) / 2)
where the term on the right-hand side represents the amount by which the average needs to decrease in order to reach 2. Solving for y, we get:
55 + y = 46.5
y = 46.5 - 55
y = 8.5
So the new student is taking 8.5 AP classes. However, since the number of AP classes must be a whole number, we need to round this value to the nearest integer. Since 8.5 is closer to 9 than to 8, we round up to 9. Therefore, the answer is:
The new student is taking 9 AP classes. Answer: None of the above (not given as an option).
Looking at the spread of your data best fits which step of the statistical process?
Looking at the spread of your data is part of the data analysis step in the statistical process.
In this step, the data is examined to identify patterns, relationships, and trends in the data.
One aspect of data analysis is understanding the distribution and spread of the data, which can be done through measures of central tendency and measures of variability.
Understanding the spread of the data can help in making decisions about what statistical analyses are appropriate and how to interpret the results.
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the line is parallel to the graph of y=-1/2x-1 and contains the point (-4, 5)
The equation of the line parallel to the graph of y = (-1/2)x - 1 and containing the point (-4, 5) is y = (-1/2)x + 3.
What is the equation of the parallel line?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
Given the equation of the graph
y = (-1/2)x - 1
The equation of a line parallel to the graph of y = (-1/2)x - 1 will have the same slope as the given line, which is -1/2.
Now. using the point-slope form, we can find the equation of the line that passes through the point (-4, 5) with slope -1/2:
y - y1 = m(x - x1)
y - 5 = (-1/2)(x - (-4))
y - 5 = (-1/2)x - 2
y = (-1/2)x + 3
Therefore, the equation of the parallel line is y = (-1/2)x + 3.
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Please helpppp
side lengths, surface areas, and volumes fo...
a designer builds a model of a sports car. the finished model is exactly the same shape as the original, but smaller. the scale factor is 3:11
(a) find the ratio of the surface area of the model to the surface area of the original.
(b) find the ratio of the volume of the model to the volume of the original.
(c) find the ratio of the width of the model to the width of the original.
nrite these ratios in the format m:n.
surface area:
volume:
width:
The ratios are: surface area 9:121, volume 27:1331, width 3:11.
(a) The ratio of the surface area of the model to the surface area of the original can be found by using the scale factor to find the ratio of the corresponding side lengths. Since surface area is proportional to the square of the side length, we can use this ratio squared to find the ratio of the surface areas.
The ratio of the corresponding side lengths is 3:11, so the ratio of the surface areas is (3/11)^2, which simplifies to 9/121.
Therefore, the ratio of the surface area of the model to the surface area of the original is 9:121.
(b) The ratio of the volume of the model to the volume of the original can be found using the same method as above, but with volume instead of surface area. Since volume is proportional to the cube of the side length, we can use this ratio cubed to find the ratio of the volumes.
The ratio of the corresponding side lengths is 3:11, so the ratio of the volumes is (3/11)^3, which simplifies to 27/1331.
Therefore, the ratio of the volume of the model to the volume of the original is 27:1331.
(c) The ratio of the width of the model to the width of the original can be found directly from the scale factor, since width is one of the corresponding side lengths.
The ratio of the corresponding side lengths is 3:11, so the ratio of the widths is 3:11.
Therefore, the ratio of the width of the model to the width of the original is 3:11.
Overall, the ratios are: surface area 9:121, volume 27:1331, width 3:11.
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x An investor puts $4,500 into a life insurance policy that pays 8.0% simple annual interest. If no additional investment is made into the policy, how much accumulated interest should the investor expect at the end of 8 years? HELP PLEASE
The amount of accumulated interest the investor can expect in 8 years is $2,880.
How to find the accumulated interest ?To calculate the accumulated interest on the life insurance policy, we can use the simple interest formula:
I = P x r x t
In this case, the principal amount invested is $4,500, the annual interest rate is 8.0% (or 0.08 as a decimal), and the time period is 8 years. Therefore:
I = 4,500 x 0.08 x 8
I = $2,880
Therefore, the investor can expect to earn $2,880 in accumulated interest at the end of 8 years.
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A scientist uses a submarine to study ocean life.
She begins at sea level, which is an elevation of 0 feet.
She travels straight down for 112 seconds at a speed of 0.8 feet per second.
She then travels directly up for 120 seconds at a speed of 0.6 feet per second.
After this 232-second period, how much time, in seconds, will it take for the scientist to travel back to sea level at 3.5 feet per second? If necessary, round your answer to the nearest tenth of a second.
The length of time, in seconds, that it will take for the scientist to travel back to sea level at 3.5 feet per second will be 5.0 seconds.
How to calculate the amount of timeTo calculate the amount of time, we will begin by calculating the distance traveled from sea level in all of the instances.
1. 112 seconds × 0.8 feet per second = 89.6 feet
2. 120 seconds × 0.6 feet per second = 72 feet
The distance from sea level is now: 89.6 feet - 72 feet
= 17.6 feet
The time, in seconds, that it will take for the scientist to travel back to sea level at 3.5 feet per second will be:
17.6 feet ÷ 3.5 feet per second
5.0 seconds to the nearest tenth.
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Sofia owns a small business selling ice cream. She knows that in the last week 56 customers paid cash, 6 customers used a debit card, and 18 customers used a credit card.
Based on these results, express the probability that the next customer will pay with a credit card as a fraction in simplest form
The probability that the next customer will pay with a credit card is 9/40.
To find the probability that the next customer will pay with a credit card, we need to determine the total number of customers and then calculate the fraction of those who used a credit card.
Step 1: Find the total number of customers.
56 customers paid cash, 6 customers used a debit card, and 18 customers used a credit card.
Total customers = 56 + 6 + 18 = 80 customers
Step 2: Calculate the probability of a customer using a credit card.
Number of customers who used a credit card = 18
Total number of customers = 80
Probability = (Number of customers who used a credit card) / (Total number of customers)
Probability = 18 / 80
Step 3: Simplify the fraction.
Divide both the numerator and denominator by their greatest common divisor (GCD). The GCD of 18 and 80 is 2.
18 ÷ 2 = 9
80 ÷ 2 = 40
Simplified fraction: 9/40
So, the probability that the next customer will pay with a credit card is 9/40.
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2. Quadrilateral ABCD is inscribed in a circle. Find the measure of each of the angles of the quadrilateral. Show
your work.
Answer:
(x-4)
(2x-78)
(x+8)
The measure of the quadrilateral are
88 - 4 = 84
2 * 88 - 78 = 98
88 + 8 = 96
How to solve the quadrilateralA quadrilateral is a polygon with four sides and four vertices (corners). There are many different types of quadrilaterals, including squares, rectangles, parallelograms, trapezoids, and kites. The angles and sides of a quadrilateral can vary depending on its specific type, but the sum of the internal angles of any quadrilateral is always 360 degrees.
x - 4 + x + 8 = 180
we have to find the value of x
x = 88
The angles would be
88 - 4 = 84
2 * 88 - 78 =
88 + 8 = 98
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Domain of the rational function.
(5x^2)/(1-x)
Answer:
(-∞, 1) ∪ (1, ∞)
Step-by-step explanation:
1 - x = 0
-x = -1
x = 1
In interval notation, the domain is (-∞, 1) U (1, ∞)
The height h and the base area B of a cone are given. Find the volume of the cone. Write your answer in terms of pi.
H = 9 units
B = 5pi square units
The volume is ____ cubic units
The volume of the cone is (5/3)π(9²) cubic units ≈ 381.7 cubic units.
The formula for the volume of a cone is V = (1/3)πr²h, where r is the radius of the circular base and h is the height of the cone. However, we are given the base area B instead of the radius, so we need to find the radius first.
We know that the area of a circle is A = πr², so if the base area of the cone is B = 5π square units, then πr² = 5π, which means r² = 5. Solving for r, we get r = √5.
Now that we have the height h = 9 units and the radius r = √5 units,
we can use the formula for the volume of a cone:
V = (1/3)πr²h.
Substituting the values, we get
V = (1/3)π(√5)²(9) = (5/3)π(9²) cubic units, which simplifies to ≈ 381.7 cubic units.
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Suppose there is a simple index of two stocks, stock A and stock B. Stock A
opens on Monday with 10,000 shares at $5. 50 per share. Stock B opens on
Monday with 8000 shares at $6. 25 per share. Stock A opens on Tuesday at
$5. 80 per share, and stock B opens on Tuesday at $6. 65 per share. Both
stocks have the same number of shares that they opened with on Monday.
What is the rate of change of this simple index over 1 day?
I
To calculate the rate of change of the simple index over 1 day, we need to first calculate the index value for Monday and Tuesday.
On Monday, the value of stock A is 10,000 x $5.50 = $55,000, and the value of stock B is 8,000 x $6.25 = $50,000. The total value of the index on Monday is $55,000 + $50,000 = $105,000.
On Tuesday, the value of stock A is 10,000 x $5.80 = $58,000, and the value of stock B is 8,000 x $6.65 = $53,200. The total value of the index on Tuesday is $58,000 + $53,200 = $111,200.
To calculate the rate of change, we can use the formula:
(rate of change) = (new value - old value) / old value x 100%
Using this formula, we get:
(rate of change) = ($111,200 - $105,000) / $105,000 x 100% = 5.90%
Therefore, the rate of change of this simple index over 1 day is 5.90%.
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What is the max/min of the quadratic equation in factored form: f(x) = 0. 5(x+3)(x-7)? Is it a maximum or a minimum? Show your workor explain your reasoning.
The quadratic equation in factored form: f(x) = 0. 5(x+3)(x-7) have a minimum point. The minimum value of the function is -11.
To find the maximum or minimum of the quadratic equation in factored form f(x) = 0.5(x+3)(x-7), we need to convert it to standard form by expanding the terms:
f(x) = 0.5(x² - 4x - 21)
f(x) = 0.5x² - 2x - 10.5
The coefficient of x² is positive, so the parabola opens upwards and we have a minimum point.
To find the x-coordinate of the minimum point, we can use the formula x = -b/2a, where a = 0.5 and b = -2:
x = -(-2)/2(0.5) = 2
So the minimum point is at x = 2. To find the y-coordinate, we can substitute x = 2 into the equation:
f(2) = 0.5(2)^2 - 2(2) - 10.5 = -11
Therefore, the minimum value of the function is -11.
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I’m confused as to what the solution is if I follow the first step
Answer:
x = 4, y = 1, z = 5
Step-by-step explanation:
z + x =9....(3) we can say it's x + z = 9
x - z = - 1
x + z = 9
______ -
- 2z= - 10
z = 10/2
z = 5
if z + x = 9
5 + x = 9
x = 9 - 5
x = 4
if x + y = 5
4 + y = 5
y = 5 - 4
y = 1
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