it will take 6 cleaners working at the same rate to clean all the rooms in the hotel in 5 hours.
If 4 cleaners can clean all the rooms in a hotel in 7 1/2 hours, we can start by using the concept of work rate. Work rate is a measure of how much work is completed in a certain amount of time. If we assume that the work rate of each cleaner is constant, we can set up a proportion to find how long it will take 6 cleaners to clean the same amount of rooms:
4 cleaners can clean all the rooms in 7 1/2 hours.
Therefore, 1 cleaner can clean all the rooms in (4 x 7 1/2) hours = 30 hours.
So, if 1 cleaner takes 30 hours to clean all the rooms, then 6 cleaners working at the same rate will take:
(time for 1 cleaner) / (number of cleaners) = (30 hours) / (6 cleaners) = 5 hours
Therefore, it will take 6 cleaners working at the same rate to clean all the rooms in the hotel in 5 hours.
It is important to note that this assumes that the work rate of each cleaner is constant and that there are no factors that may affect the cleaning time, such as interruptions or changes in the number of rooms to be cleaned. Additionally, the optimal number of cleaners may vary depending on the size of the hotel and the specific cleaning needs.
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Fill in the table using this function rule.
y = -2x+3
X. Y
-4. ?
-2. ?
0. ?
2. ?
Answer: (-4,11)(-2,7)(0,3)(2,-1)
Step-by-step explanation:
Put the function into desmos and create a table.
17/21 + 14/21
step by step explanations please.
Answer:
31/21
Step-by-step explanation:
First step is to add 17 and 14 = 31
The denominator of the fraction(bottom number stays the same)
so the answer is 31/21
Let me know if it helps
Answer:
EXACT FORM: 31/21
DECIMAL FORM: 1.476190
MIXED NUMBER FORM: 1 10/21
Step-by-step explanation:
If the number of tolls collected varies directly as the number of vehicles and $129 was collected from 20 vehicles, how many vehicles result in the collection of $3225? Show how you arrived at your answer
Answer:
500 vehicles
Step-by-step explanation:
let t represent number of tolls and v represent number of vehicles.
given that t varies directly with v then the equation relating them is
t = kv ← k is the constant of variation
to find k use the condition t = 129 from v = 20 , then
129 = 20k ( divide both sides by 20 )
6.45 = k
t = 6.45v ← equation of variation
when t = 3225 , then
3225 = 6.45v ( divide both sides by 6.45 )
500 = v
the number of vehicles is 500
antonio rolls the 10-sided die from the example. what is the probabilty of rolling a number 10 or less? a number greater than 10
The probability of rolling a number 10 or less is 1, and the probability of rolling a number greater than 10 is 0.
The 10-sided die has 10 faces, each marked with a unique number from 1 to 10. When we talk about the probability of rolling a particular number, we're asking what the chances are of that number coming up when the die is rolled.
In this case, the question asks for the probability of rolling a number 10 or less, which means we're interested in the probability of rolling any number from 1 to 10. Since all the possible outcomes are numbers from 1 to 10, the probability of rolling a number 10 or less is certain, or 1.
This is because the sum of probabilities of all possible outcomes of an experiment is always 1.
Similarly, the probability of rolling a number greater than 10 is impossible, or 0. This is because there are no possible outcomes greater than 10 on the 10-sided die. In general, the probability of an event that cannot occur is always 0.
So, the probability of rolling a number 10 or less is 1, and the probability of rolling a number greater than 10 is 0.
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Linda has two cats. The difference in weight of her Maine Coon and Siberian is at least 6 pounds. Linda’s Siberian has a weight of 834
pounds. Choose the inequality that represents the possible weight of the Maine Coon
The inequality that represents the possible weight of the Maine Coon is 828 ≤ x ≤ 840
Let x be the weight of Linda's Maine Coon in pounds.
Since the difference in weight between the two cats is at least 6 pounds, we can write the following inequality:
|x - 834| ≥ 6
This inequality can be interpreted as "the absolute value of the difference between the weight of the Maine Coon and 834 pounds is greater than or equal to 6".
Simplifying the inequality, we get:
-6 ≤ x - 834 ≤ 6
Adding 834 to each side of the inequality, we get:
828 ≤ x ≤ 840
Therefore, the possible weight of Linda's Maine Coon is between 828 and 840 pounds, inclusive.
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5. Twenty students in Mr. Martin's class each took a survey about the number of minutes they played outside. The box
plots represent the amount of time the students spent outside playing in the summer and in the winter. Which statement is
best supported by the data?
SUMMER WINTER
30
45
60
NUMBER OF MINUTES
75
90
A. The range of number of minutes outside is the same in the
summer and in the winter.
B. The median number of minutes outside in the summer is
equal to the maximum number of minutes outside in
the winter.
C. The interquartile range for the number of minutes outside is
the same in the summer and in the winter.
D. The minimum number of minutes outside in the summer is
the same as the first quartile in the winter.
The statement "The median number of minutes outside in the summer is equal to the maximum number of minutes outside in the winter" is best supported by the data (option B).
How to find the maximum number of minutes outside?Looking at the plot;
Winter: Minimum= 0 Maximum= 60 Median= 30
Range = 60 - 0 = 60
Summer: Minimum= 20 Maximum= 90 Median= 60
Range = 90 - 20 = 70
So the median number of minutes outside in the summer is
equal to the maximum number of minutes outside in the winter.
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Missing information:
The question is incomplete and the complete question is shown in the attached image.
a) r = 29 cm, b) Angle AOC = 1.39 rad,
c) Shaded Region= 68 cm sq, d) Perimeter = 87.7 cm
a) r = 130 cm, b) Angle AOC = 12.9 rad,
c) Shaded Region= 675 cm sq, d) Perimeter = 867 cm
a) r = 30 cm, b) Angle AOC = 1.29 rad,
c) Shaded Region= 67.5 cm sq, d) Perimeter = 86.7 cm
ABC is the segment of a circle, centre O, radius
r. This segment is enclosed in a rectangle APQC.
Given that AC = 36 cm and AP = 6 cm,
Find
a) r
b) the angle AOC is radian
c) the area of the shaded region
a) r = 30 cm
b) The angle AOC is 0.523598775 radian
c) The area of the shaded region is 541.9 cm²
d) The perimeter of the shaded region is 106.8 cm.
What is area?The area of a circle is a measure of the size of the surface of the circle. It is calculated by multiplying the radius of the circle (the length from the center of the circle to its edge) by itself, and then multiplying the result by the constant pi (3.14). The formula for calculating the area of a circle is A = πr2, where “A” represents the area, “π” is pi, and “r” is the radius of the circle.
The radius of the circle, r, can be determined by the Pythagorean theorem. Since AC = 36 cm and AP = 6 cm, the hypotenuse of the right triangle formed by AC and AP is the radius of the circle, r. By applying the Pythagorean theorem, we get:
r² = 362 + 62
r² = 1296
r = √1296
r = 36 cm
b) The angle AOC is 0.523598775 radians
The angle AOC can be determined using the formula for arc length. The arc length of ABC is 36 cm and the radius of the circle is 30 cm. Therefore, the angle AOC is:
AOC = 36/30
AOC = 1.2 radians
c) The area of the shaded region is 541.9 cm²
The area of the shaded region can be determined using the formula for the area of a sector. The angle AOC is 1.2 radians and the radius of the circle is 30 cm. Therefore, the area of the shaded region is:
Area = (1.2)(30)(30)/2
Area = 541.9 cm²
d) The perimeter of the shaded region is 106.8 cm
The perimeter of the shaded region can be determined using the formula for the circumference of a circle. The radius of the circle is 30 cm. Therefore, the perimeter of the shaded region is:
Perimeter = 2π(30)
Perimeter = 106.8 cm
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which property is shown 16x5x2=2x5x16
Answer:
Commutative property
The Commutative property is most simply shown with: a x b = b x a. In multiplication, the values can shift or "commute" in any order
Let Y have a distribution function given by 0, Fly) = y <0 y 20. - e Find a transformation G(U) such that, if U has a uniform distribution on the interval (0, 1), G(U) has the same distribution as Y. G(U) = |(-In(1–u))(7
Let Y have a distribution function given by 0, Fly) = y <0 y 20.
To find a transformation G(U) such that if U has a uniform distribution on the interval (0, 1), G(U) has the same distribution as Y, follow these steps:
1. Identify the distribution function of Y:
F(y) = 0 for y < 0, and F(y) = 1 - e^(-y) for y ≥ 0.
2. Set F(y) equal to the cumulative distribution function (CDF) of a uniform distribution on the interval (0, 1):
F(y) = U.
3. Solve for y in terms of U to obtain the transformation G(U).
So, for y ≥ 0,
1 - e^(-y) = U
Now, solve for y:
e^(-y) = 1 - U
-y = ln(1 - U)
y = -ln(1 - U)
Therefore, the transformation G(U) is given by G(U) =. ln(1 - U)
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Casper has a balloon with a diameter of
6 inches that is seven times the volume of
his brother's balloon. What is the
volume of Casper brother's
approximate
balloon?
Answer:
The volume of a sphere is given by the formula:
V = (4/3)πr^3
where r is the radius of the sphere.
Since the diameter of Casper's balloon is 6 inches, the radius is 3 inches. Therefore, the volume of Casper's balloon is:
V1 = (4/3)π(3 inches)^3 = 113.1 cubic inches (approx.)
We know that Casper's balloon is seven times the volume of his brother's balloon. Let's call the volume of his brother's balloon V2. We can set up an equation:
V1 = 7V2
Substituting the value of V1, we get:
113.1 cubic inches = 7V2
Dividing both sides by 7, we get:
V2 = 16.2 cubic inches (approx.)
Therefore, the approximate volume of Casper's brother's balloon is 16.2 cubic inches.
Let alpha = phi/2008 . Find the smallest positive integer n such that 2 [cos(alpha) sin(alpha) + cos (4 alpha) sin (2 alpha) + cos (9 alpha) sin (3 alpha) +.....+ cos (n^2 alpha) sin(n alpha)] is an integer
n = ceil(sqrt((2008/4phi)[90 - arccos(k(2 cos(phi/2008)))]))
How to find integer?Simplifying equation:2 [cos(alpha) sin(alpha) + cos(4 alpha) sin(2 alpha) + cos(9 alpha) sin(3 alpha) + ... + cos(n^2 alpha) sin(n alpha)]
= [sin(2 alpha) + sin(8 alpha) + sin(18 alpha) + ... + sin(n^2 alpha)].
Using the formula for the sum of a geometric series:sin(2 alpha) + sin(8 alpha) + sin(18 alpha) + ... + sin(n^2 alpha)
= (sin(2 alpha) - sin(2n^2 alpha))/(1 - sin(2 alpha))
= (2 sin(n^2 alpha) cos(n^2 alpha))/(2 cos(alpha) - 1)
= [sin(2n^2 phi/2008)]/(2 cos(alpha) - 1)
To find an integer value:[sin(2n^2 phi/2008)]/(2 cos(alpha) - 1)
sin(2n^2 phi/2008) = k(2 cos(alpha) - 1)
cos(90 - 2n^2 phi/2008) = k(2 cos(alpha) - 1)
Now, we need to find the smallest positive integer n90 - 2n^2 phi/2008 = ±arccos(k(2 cos(alpha) - 1))
Solving for n, we get:n^2 = (2008/4phi)[90 ± arccos(k(2 cos(alpha) - 1))]
n = ceil(sqrt((2008/4phi)[90 - arccos(k(2 cos(phi/2008)))]))
We can find the smallest positive integer n by incrementing the value of k starting from 1 until ceil(k^2*alpha) is greater than or equal to n.
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1: find the cartesian vector expression for the five forces, respectively. 2: find the cartesian vector expression of the resultant force of these five forces. 3: find the magnitude and direction of the resultant force. there are five forces act along edges of a pentagon plate abc, as shown. ab
The magnitude of the resultant force is given by:
|F| = [tex]sqrt((-7)^2 + 0^2) N|F| = 7 N[/tex]The direction of the resultant force is given by:
[tex]θ = tan^-1(0/-7)θ = tan^-1(0) = 0[/tex]
Therefore, the magnitude of the resultant force is 7 N, and its direction is along the negative x-axis.
1. Cartesian vector expression for five forcesThe five forces acting along the edges of a pentagon plate ABC are shown below:Force acting on AB = (6i + 6j) NForce acting on BC = (8i + 4j) NForce acting on CD = (-5i + 10j) NForce acting on DE = (-10i - 8j) NForce acting on EA = (4i - 12j) N2.
Cartesian vector expression of the resultant force of these five forcesThe resultant force acting on the pentagon plate ABC can be determined by finding the vector sum of the five forces. The cartesian vector expression of the resultant force can be found as follows:[tex]F = F1 + F2 + F3 + F4 + F5F = (6i + 6j) N + (8i + 4j) N + (-5i + 10j) N + (-10i - 8j) N + (4i - 12j) N= (-7i + 0j) N[/tex]
Therefore, the cartesian vector expression of the resultant force is (-7i + 0j) N.3. Magnitude and direction of the resultant forceThe magnitude and direction of the resultant force can be determined by using the cartesian vector expression of the resultant force obtained in the previous step.
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suppose you roll a pair of fair dice repeatedly. what is the probability that by the time the sum has been even three times, the sum has already been 7 twice?
The probability that by the time the sum has been even three times, the sum has already been 7 twice is 1/36.
This is because the total number of possible combinations of two dice is 36, and only one combination, (3,4), has the sum of 7 and is also an even number.
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Find the value of each variable with step by step explanation
The length of the missing side of the geometric system of right triangles is equal to 2√29 units.
How to determine the missing length of the right triangle
In this problem we find a geometric system formed by two right triangles, in which we must determine the length of a missing side. The length can be found by means of Pythagorean theorem, whose formula is now introduced:
r² = x² + y²
Where:
x, y - Legsr - Hypotenuser = 30, x = 28
30² = 28² + y²
y = √(30² - 28²)
y = 2√29
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Five interior angles of a hexagon measure 119°, 129°, 104°, 139°, and 95°. What is the measure of the sixth angle?
Answer:
A
Step-by-step explanation:
Enola has x quarters and y dimes. She has a minimum of 18 coins worth at most $3.60 combined. Solve this system of inequalities graphically and determine one possible solution.
Answer: Let's start by setting up the system of inequalities:
x + y ≥ 18 (Enola has at least 18 coins)
0.25x + 0.10y ≤ 3.60 (The total value of her coins is at most $3.60)
To graph this system of inequalities, we can start by graphing the line x + y = 18 (the boundary for the first inequality). This line represents all the possible combinations of x and y that would give Enola exactly 18 coins. To graph this line, we can plot two points on it and connect them with a straight line. For example, if x = 0, then y = 18, and if y = 0, then x = 18. So the line passes through the points (0, 18) and (18, 0).
Next, we need to shade the region that satisfies the second inequality. To do this, we can rearrange the inequality to get:
y ≤ (3.60 - 0.25x) / 0.10
This inequality represents all the possible combinations of x and y that would give Enola a total value of coins at most $3.60. We can graph this inequality by shading the region below the line y = (3.60 - 0.25x) / 0.10.
Putting both of these graphs together, we get:
Graph of system of inequalities
One possible solution to this system of inequalities is (x, y) = (10, 8). This corresponds to Enola having 10 quarters and 8 dimes, for a total of 18 coins. The total value of her coins is:
0.25(10) + 0.10(8) = 2.50 + 0.80 = 3.30
Since 3.30 is at most $3.60, this solution satisfies both inequalities. Note that there may be other possible solutions as well.
Step-by-step explanation:
The system of inequalities is solved by plotting the inequalities in the xy-plane and finding the overlapping region. One possible solution for the number of quarters (x) and dimes (y) Enola could have that meets the conditions is x = 8 and y = 10.
Explanation:The subject of this question is inequalities. Enola has x quarters and y dimes. Each quarter is worth $0.25 and each dime is worth $0.10. Therefore, the total amount of money she has is $0.25x + $0.10y. Since she has at least 18 coins, we have the inequality x + y >=18. Since the total money is at most $3.60, we have the inequality $0.25x + $0.10y <= 3.60. Because we are dealing with a whole number of coins, x and y should be integers. The solution of this system of inequalities can be found graphically by plotting these inequalities in the xy-plane and finding the overlapping region. One possible solution is x = 8 and y = 10.
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Triangles 1 and 2 are similar. what ratio relates a side length of triangle 1 to the corresponding side length of triangle 2? fill in the box to complete the ratio. triangle a b c is labeled triangle 1. side a c is 17, c b is 15, a b is 8. angle c is 28 degrees and angle a is 62 degrees. triangle d e f is labeled triangle 2. side d f is 25.5, f e is 22.5 and d e is 12. angle d is 62 degrees, f is 28 degrees, and e is 90 degrees. to 12
If triangles 1 and 2 are similar, the ratio relates a side length of triangle 1 to the corresponding side length of triangle 2 is 2:3.
Since Triangles 1 and 2 are similar, their corresponding sides are proportional. This means that the ratio of the length of any corresponding pair of sides in the two triangles will be equal.
To determine the ratio of the side lengths of triangle 1 to the corresponding side lengths of triangle 2, we can choose any two corresponding sides and divide their lengths.
Let's choose side AC of triangle 1 and side DF of triangle 2. We know that these two sides are corresponding because they are both opposite angles that have the same measure.
The length of side AC in triangle 1 is given as 17, and the length of side DF in triangle 2 is given as 25.5. Therefore, the ratio of the length of side AC to side DF is:
AC/DF = 17/25.5 = 0.6667 or 2/3
So the ratio of the length of a side in triangle 1 to the corresponding side in triangle 2 is 2:3. This means that if we multiply any side length in triangle 1 by 2, we will get the length of the corresponding side in triangle 2.
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How many Hamiltonian circuits exists in a complete graph with 11 vertices?
10!
12!
11!
9!
An [tex]11[/tex]-vertex full graph has around [tex]19,958,931,200[/tex] Hamiltonian circuits in a complete graph.
Describe the Hamiltonian circuit with an example.At one vertex, the Hamiltonian route begins, and at another, it finishes. Yet, when following a Hamiltonian route, every vertex is encountered. At the same vertex, the Hamiltonian circuit begins and terminates. For instance, if a Hamiltonian circuit's path began at vertex 1, the loop will also conclude at that vertex.
The Hamiltonian circuit: what is it?Single circuit is the sole trip a Hamiltonian circuit makes to each vertex. It must begin and terminate at same vertex since it is a circuit. A Hamiltonian route does not start and end in a single location, but it does visit each vertex just once with no repetitions.
We have to divide by [tex]2(n-2)[/tex]
[tex]11!/(2(11-2)!) = 11!/2,520[/tex] Hamiltonian circuits we get:
[tex]11!/2,520 = 19,958,931,200[/tex]
Therefore, there are approximately [tex]19,958,931,200[/tex] Hamiltonian circuits in a complete graph with [tex]11[/tex] vertices.
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in 2000, a total of 40,255,000 taxpayers in the united states filed their individual tax returns electronically. by the year 2014, the number increased to 214,014,920. what is the geometric mean annual increase for the period? (round your answer to 2 decimal places.)
Rounding the value to 2 decimal places, the geometric mean annual increase for the period is approximately 1.18.
Geometric mean annual increase for the period:
Let A be the initial value and B be the final value of the given data for the geometric mean annual increase for the period in the United States from 2000 to 2014.
A = 40,255,000 and B = 214,014,920.
To find the geometric mean annual increase for the period, we need to use the formula:
Geometric mean = (B/A)^(1/n), where n = the number of years elapsed.
Therefore, n = 2014 - 2000 = 14 years.
Substituting the values of A, B, and n in the above formula, we get:
Geometric mean = (214,014,920/40,255,000)^(1/14) ≈ 1.1802.
Rounding the value to 2 decimal places, the geometric mean annual increase for the period is approximately 1.18.
Answer: 1.18.
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A certain computer can perform a maximum number of operations per second. If this computer is running at 65%
of the maximum and is performing 30 operations per second, what is the maximum number of operations the
computer can perform per second? Round your answer to the nearest whole number.
1. 20 operations per second
2. 46 operations per second
3. 1,950 operations per second
4. 95 operations per second
Answer:
Let the maximum number of operations the computer can perform per second be x.
According to the problem, the computer is running at 65% of the maximum, so it is performing 0.65x operations per second. We also know that it is performing 30 operations per second. So we can write the equation:
0.65x = 30
Solving for x, we get:
x = 30/0.65
x ≈ 46.1538
Rounding to the nearest whole number, we get:
x ≈ 46
Therefore, the maximum number of operations the computer can perform per second is 46, which is option 2.
Brooke has scores of 84, 72, 90, 95, and 87 on her first five quizzes. After taking the sixth quiz, Brooke’s mean score increased.
Which could be Brooke’s sixth quiz score? Select three options.
85
90
83
86
92
Answer:
90, 86, and 92 are three options
Step-by-step explanation:
(a) Use slope-intercept form to write an equation of the line that passes through the given point and has the given slope.
(b) Write the equation using function notation where .
The equation of the line is y = 3x/2 - 8 and can be rewritten using function notation as f(x) = 3x/2 - 8
Slope intercept form:
The slope-intercept form of a line is given by
y = mx + c
Where 'm' is slope and c in y-intercept
Here we have
The coordinate of points (0, -8) and slope (m) = 3/2
As we know the formula for slope intercept form is y = mx + c
Where 'm' is the slope
=> y = (3/2)x + c
=> -8 = 3/2(0) + c
=> c = - 8
Hence, Equation of the line is y = 3/2(x) + (-8)
=> y = 3x/2 - 8
The equation can be rewritten using function notation as follows
=> f(x) = 3x/2 - 8
Therefore,
The equation of the line is y = 3x/2 - 8 and can be rewritten using function notation as f(x) = 3x/2 - 8
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7
A Geometry textbook has a mass of 50 grams. The textbook is in the shape of a rectangular prism with dimensions shown below.
5 cm
16 cm
10 cm
Find the density of the textbook. Round your answer to the nearest ten-thousandth.
Answer:
Step-by-step explanation:
Answer: 0.0625 g/cm^3
Formula for density: d= mass/volume
we have mass m=50g
volume of rectangular prism = length x height x width
volume of book = 5cm x 16cm x 10cm = 800cm^3
density = mass / volume
density = 50g/800cm^3
density = 0.0625 g/cm^3
using a single composite transformation matrix for k transformations of n points, what is the required number of multiplications?
The required number of multiplications using a single composite transformation matrix for k transformations of n points is n × k.
In computer graphics, composite transformation matrices are used to transform points and shapes. These matrices are created by combining multiple transformations into a single matrix, allowing for efficient processing of large amounts of data. The number of multiplications required to perform a composite transformation depends on the number of points being transformed and the number of transformations being applied.
If there are n points and k transformations, then the required number of multiplications is n × k.
This is because each point needs to be multiplied by the composite transformation matrix k times.
Therefore, the total number of multiplications is n × k.
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Teresa wants to buy 2 new tires for her mountain bike. She has budgeted $120 for the tires, but after researching costs, knows she may end up spending within $25 of that amount
Teresa needs to buy two new tires for her mountain bike.
With a budget of $120, she will likely spend within $25 of that amount.
To help her find the best deal, Teresa should first research what type of mountain bike tire she needs. She can look at the bike's current tires to determine the size, or she can look up the bike model and size online. She should then research prices at a variety of local bike shops and online retailers to compare costs.
Once she finds the best price, Teresa should look for discounts and coupon codes that she can use to reduce the cost of her tires. She should also make sure she is aware of any extra costs, such as shipping and taxes.
With some research and savvy shopping, Teresa should be able to find two mountain bike tires that fit within her budget of $120 and that will keep her bike running smoothly.
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if you are a 54 % free-throw shooter and the random variable y denotes the total number of shots in order to make one free-throw, then:
The expected number of shots required to make one free-throw is approximately 1.85.
To calculate the expected value of Y, denoted by E[Y], we need to consider the probability distribution of Y.
The probability distribution of Y is a geometric distribution, since we are counting the number of trials required until the first success (i.e., making a free-throw). The probability of success on each trial is p = 0.54, since you have a 54% chance of making each free-throw. The probability of failure (missing the free-throw) on each trial is q = 1 - p = 0.46.
The probability mass function (PMF) of a geometric distribution is given by:
P(Y = k) = q^(k-1) * p
where k is the number of trials required to achieve the first success.
In this case, we want to find the expected value of Y, which is defined as:
E[Y] = Σ(k=1 to ∞) k * P(Y = k)
We can simplify this expression using the PMF of the geometric distribution:
E[Y] = Σ(k=1 to ∞) k * q^(k-1) * p
This sum can be evaluated using the formula for the sum of an infinite geometric series:
E[Y] = 1/p
Substituting in the value of p = 0.54, we get:
E[Y] = 1/0.54 ≈ 1.85
This means that on average, you need to take about 2 shots to make one free-throw if you have a 54% free-throw shooting percentage.
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Complete question is:
If you are a 54 % free-throw shooter and the random variable y denotes the total number of shots in order to make one free-throw, then:
Calculate E[Y]
The present shown below is a cube.
Find the surface area of the present.
cm
20
cm
20
Answer:
2400 cm^2
Step-by-step explanation:
we first find the area of a face of the cube, which is a square, with the formula A=L^2, we multiply the result by the number of faces (6) and we have the surface area of the cube
everything is resolved with the expression:
20^2 x 6 = 2400 cm^2
solve these questions
Answer:
a) The perimeter of a rectangle is given by the formula:
P = 2L + 2W
where P is the perimeter, L is the length, and W is the width. We are given that the width of the rectangle is 2x and the length is three times the width. So we can set up an equation that represents the given information:
P = 2L + 2W
168 = 2(3W) + 2W
168 = 8W
b) To solve for W, we can divide both sides of the equation by 8:
168/8 = W
21 = W
Therefore, the width of the rectangle is 21cm.
c) To find the length of the rectangle, we can use the expression that represents the length in terms of the width:
L = 3W
L = 3(21)
L = 63
Therefore, the length of the rectangle is 63cm.
The width and length of the rectangle are 21cm and 63cm, respectively.
Order the angles from greatest to least.
Answer:
∠D, ∠C, ∠E
Step-by-step explanation:
"The angle opposite to the shortest side is the smallest angle and the side opposite to the longest side is the largest angle."
John wants to know the volume of his gold ring in cubic centimeters. He gets a glass in the shape of a rectangular prism with a base
3
cm
3 cm3, start text, space, c, m, end text by
2
cm
2 cm2, start text, space, c, m, end text and fills the glass with
3. 1
cm
3. 1 cm3, point, 1, start text, space, c, m, end text of water. John drops his gold ring in the glass and measures the new height of the water to be
3. 7
cm
3. 7 cm3, point, 7, start text, space, c, m, end text. What is the volume of John's ring in cubic centimeters?
The volume of Laura's gold ring is 21.6 cubic centimeters.
To find the volume of the gold ring, we need to determine the volume of water that is displaced when the ring is dropped into the glass.
The initial volume of water in the glass can be calculated as the product of the base area and the height of the water:
V1 = base area x height of water = 7 cm x 4.5 cm x 8.8 cm = 277.2 cm³
When the gold ring is dropped into the glass, it displaces some of the water, causing the water level to rise. The new volume of water in the glass can be calculated using the same formula, but with the new height of the water:
V2 = base area x height of water with ring = 7 cm x 4.5 cm x 9.2 cm = 298.8 cm³
The volume of the gold ring can be calculated by subtracting the initial volume of water (before the ring was added) from the new volume of water (after the ring was added):
Volume of gold ring = V2 - V1 = 298.8 cm³ - 277.2 cm³ = 21.6 cm³
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Th given question is incomplete, the complete question is:
Laura wants to know the volume of her gold ring in cubic centimeters. She gets a rectangular glass with a base 7 cm by 4.5 cm and fills the glass 8.8 cm high with water. Laura drops her gold ring in the glass and measures the new height of the water to be 9.2 cm. What is the volume of Laura'5 ring in cubic centimeters? cm? 8.8 cm 9.2 cm 4.5 cm 4.5 cm 7cm 7 cm
Answer:
THE OTHER GUY IS WRONG the answer is 3.6cm
Step-by-step explanation:
I had this question on khan