When binomial distribution is used, the probability that at least 275 rooms are occupied is 0.96
Option b. is correct
We have the following parameters:
sample, n=300
proportions of rooms reserved, p=6%
We first get the sample mean,
Sample mean=n*p
=300*6%
=18
Now, we get population mean according to binomial distribution, μ'
μ=n-sample mean
=300-18
=282
We get the standard deviation, σ
σ=(sample mean*(1-p))^1/2
=(18*(1-6%))^1/2
=4.11
We now, calculate z-score:
z=(x-μ)/σ, given x should be at least 275
z=(275-282)/4.11
=-1.703
Now, we have p(x>275)=p(z>-1.703)
From z-score of probabilities, we have p(z>-1.703) as 0.95572
So, p(x>275)=0.95572
=0.96
Hence, the probability that at least 275 rooms are occupied is 0.96
To learn more about binomial distribution; click here:
https://brainly.com/question/14697367
#SPJ4
the length length of a species of plants is normally distributed with expected value 60 cm. it is known from past experience that seventy five percent of theses flowers have length between 50 and 70 cm. what can we say about the standard deviation of the length of this plant?
The standard deviation of the length of this plant be 25.
m = 60(mean)
Let the standard deviation be s,
As, the probability for 50<x<70 be 0.75
Z = (x−m)/s
for x=50,
Z=0
for x=70,
Z=(70−50)/s=20/s
Now, the probability for 50<x<70 be,
P(50<x<70) = 0.75
In the standard form 0<z<(20/s)
using Z-table, the area from 0 to 20/s,
= 0.75
s = 25
Hence, the standard deviation of the length of this plant be 25.
Learn more about Probability here https://brainly.com/question/13604758
#SPJ4
6) Complete the equation so that it has infinitely many solutions.
12x-x+8+ 3x =__x+__
The simplified equation is 14x+8 which has infinitely many solutions as given in the question.
What does the equation mean?Two expressions joined by an equal sign form a mathematical statement known as an equation. An equation is, for instance, 3x - 5 = 16. By solving for x, we discover that x equals 7, which is the value for the variable.How do you solve an equation?1.Remove parenthesis and combine like terms to simplify either side of the equation.
2.Isolate the variable term on one side of the equation using addition or subtraction.
3.To find the variable, use multiplication or division.
Given equation is:
12x-x+8+ 3x
= 11x+3x+8
=14x+8
Therefore, the simplified equation is 14x+8 which has infinitely many solutions.
Learn more about equations here:
https://brainly.com/question/18831322
#SPJ1
please help with this im strugglingggggggg
The dimensions of the kennel and the size of the cylinder indicates;
4.1.1. The two 3D objects which the figure consists of are a triangular prism that lays on top of a rectangular prism at the bottom.
4.1.2. The area of the wood needed to build the dog kennel is approximately 2.85 m²
4.1.3. The number of containers of sealant needed to paint one coat on the dog kennel is approximately 2 containers
4.2. The new height of the water in the container will be approximately 18 cm.
What is the surface area of a solid?The surface area of a solid is found by adding together the area of the surfaces that enclose the solid.
4.1.1. The two 3D objects in the figure are;
A triangular prismA rectangular prism4.1.2. The amount of wood needed is found by finding the surface area, A, of the dog kennel as follows;
A = 2×80×60+2×50×60+50×80+2×0.5×80×40+2×√(40²+40²)×50
A = 22800 + 80·√2×50 = 22800 + 4000·√2
The amount of wood needed = (22800 + 4000·√2) cm²
1 m² = 10,000 cm²
(22800 + 4000·√2) cm² = ((22800 + 4000·√2))/10,000 m²
((22800 + 4000·√2)) cm² = (2.28 + 0.4·√2) m² ≈ 2.85 m²
The amount of wood needed is approximately 2.85 m²4.1.3. 500 milliliters of paint is enough to for 1.5 m² area
The number of containers of paint containers required, n, is therefore;
[tex]n = \dfrac{(2.28 + 0.4\cdot \sqrt{2}) \, m^2 }{1.5 \, m^2/container} = (1.52+0.\overline 6\cdot\sqrt{2} ) \, containers \approx 2 \, containers[/tex]
The number of containers of sealant needed to paint one coat on the dog kennel is approximately 2 containers4.2 Diameter of the base of the water container = 20 cm
Radius of the base = (20 ÷ 2) cm = 10 cm
Height of water in the container = 15 cm
Volume of water added = 1,000 cm³
The new height will be 15 + (1,000/(π×10²)) = (15 + 10/π) cm ≈ 18 cm
The height of the water in the container will rise to approximately 18 centimeters
Learn more about the volume and surface area of regular solids here:
https://brainly.com/question/28822252
#SPJ1
y≥x²+2x-8 factor the quadratic equation to find x intercepts
The factors of the quadratic equation are x≥-4, x≥2 and lies in the interval (-∞, -4]∪[2, ∞)
What is meant by quadratic equation?A quadratic equation is any equation that can be rearranged in standard form as ax²+bx+c=0 where x represents an unknown value and a, b, and c represent known numbers. In general, a = 0; equations with a = 0 are considered degenerate because the equation becomes linear or even simpler. The numbers a, b, and c are the equation's coefficients, and they can be distinguished by referring to them as the quadratic coefficient, linear coefficient, and constant or free term, respectively.
To find x-intercept y=0
y≥x²+2x-8
x²+2x-8≥0
x²+4x-2x-8≥0
x(x+4)-2(x+4)≥0
(x-2)(x+4)≥0
∴x≥-4, x≥2
∴(-∞, -4]∪[2, ∞)
Therefore, the factors of the quadratic equation are x≥-4, x≥2 and lies in the interval (-∞, -4]∪[2, ∞)
To know more about quadratic equation, visit:
https://brainly.com/question/17177510
#SPJ1
Determine the distance between the points (−2, −3) and (2, 0). 2 units 4 units 5 units 10 units
The distance between two points on a 2D coordinate plane can be found using the following distance formula. d = √ (x 2 - x 1) 2 + (y 2 - y 1) 2. where (x 1, y 1) and (x 2, y 2) are the coordinates of the two points involved. The order of the points does not matter for the formula as long as the points chosen are consistent.
Thank me at https://brainly.com/app/profile/49759317
#SPJ1
Answer:
it is 5 units!
Solve the following equation for y. 3y - 7(y + 5) = y - 35 Also Show your work Describe and show each step taken.
A. y = 0
B. y = 1
C. y = 2
D. All real values for y are correct solutions.
The equation is,
→ 3y - 7(y + 5) = y - 35
Now the value of y will be,
→ 3y - 7(y + 5) = y - 35
→ 3y - 7y - 35 = y - 35
→ -4y - y = -35 + 35
→ -5y = 0
→ y = 0/-5
→ [ y = 0 ]
Hence, option (a) is correct.
6 groups of what tenths is 4.2
The answer is 6 groups of 0.7 tenths is 4.2. in the decimal form.
What is Decimals?
Decimals are a form of a number in algebra that have a full integer and a fractional portion separated by a decimal point. The decimal point is the dot that separates the whole number from the fractional element of the number. A decimal is a number with a whole and a fractional component. Decimal numbers, which are in between integers, are used to express the numerical value of full and partially whole amounts.
Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.
6 groups of ____ tenths is 4.2
4.2 ÷ 6 = 0.7
Hence, 6 groups of 0.7 tenths is 4.2
Learn more about Decimals, by the following link.
https://brainly.com/question/1827193
#SPJ1
1. Given that p=5xy + q, express y in terms of p,q and x.
2.Given that p=7x +4q, express x in terms of p and q.
[tex]\huge\mathcal{♨Answer♥}[/tex]
Answer is on the attachment...
☆...hope this helps...☆
_♡_mashi_♡_
The equation p=5xy+q can be expressed in terms of p,q, and x as y = (p-q)/5x.
The equation p=7x+4q can be expressed in terms of p and q as x = (p-4q)/7x.
Given in the first equation, p = 5xy+q
p-q=5xy
y=(p-q)/5x
Here we need to express y in terms of p,q, and x so we need all these three variables on one side of the equation and y on the other side. Initially we more q to the left-hand side of the equation which makes it p-q=5xy. Now we divide the left-hand side and the right-hand side by 5x making the equation y = (p-q)/5x.
Similarly in the second equation, p = 7x+4q
p-4q = 7x
x = (p-4q)/7
Here we need to express x in terms of p and q so we need all these two variables on one side of the equation and the term x on the other side. First, we will move 4q to the left-hand side of the equation which will make it p-4q=7x. Now, we will divide the whole equation by 7 which will make the equation x = (p-4q) / 7.
To learn more about simultaneous, transposing and rearrangement of the equations,
https://brainly.com/question/15165519
if a fair die is rolled, what is the probability of landing on an even number or a number greater than 2
The probability of landing on an even number or a number greater than two is 5/6.
A fair die is rolled. We need to find out the probability of landing on an even number or a number greater than two.
Let the event of landing on an even number be denoted by the variable E1. Let the event of landing on a number greater than two be denoted by the variable E2. We need to calculate P(E1 ∪ E2).
P(E1 ∪ E2) = P(E1) + P(E2) - P(E1 ∩ E2)
P(E1 ∪ E2) = (3/6) + (4/6) - (2/6)
P(E1 ∪ E2) = 5/6
Hence, the probability of landing on an even number or a number greater than two is 5/6.
To learn more about probability, visit :
https://brainly.com/question/11234923
#SPJ4
A regular polygon has 16 sides. If one of its angles measures (5h − 29)°, what is the value of h?
PLEASE I NEED HELP!!
a rancher plans to use 170 yards of fencing to enclose a rectangular corral and to divide it into two parts with a fence parallel to the shorter sides of the corral. find the dimensions of the corral if its area is to be 1200 square yards.
The dimensions of recangle is = 30 yrds.
What is the area of rectangle?Any shape's area can be calculated by counting how many unit squares will fit inside of it. A square with a side of 1 unit is referred to as a unit square in this context. Therefore, the quantity of unit squares that make up a rectangle's perimeter is its area.Alternately, the area of the rectangle is the area contained within the boundary of this shape. The unit-length tiles in your home are a good illustration of a rectangle form. By counting the number of tiles, you can quickly determine how much space the floor takes up. This will also enable you to calculate the rectangular floor's area.acc to our question-
2000 = 160x - 3x^23x^2 -160x + 2000 = 0x = [160 +- sqrt(160^2 - 4*3*2000)]/6x = [160 +- sqrt(1600)]/6Positive solution:x = [160 + 40]/6x = 200/6x = 33 1/3 yrds. (side);Learn more about area of rectangle click here:
https://brainly.com/question/25292087
#SPJ4
given that 3p = 2m - 5q, express m in terms of p and q
Answer:
Step-by-step explanation:
3p. = 2m - 5q
-2m. = -3p - 5q
Divide through by -2
m. = (3p + 5q) \2
The equation can be rearranged and expressed in terms of p and q is m = (3p+5q)/2.
Given equation 3p = 2m - 5q
3p + 5q = 2m
(3p + 5q) / 2 =m
Hence, m = (3p+5q) / 2
To express the equation in terms of p and q we need to put all the p and q terms to one side of the equation and m terms to another side of the equation. It can be easily seen that 3p is already on one side and we just need to bring a q term to this side which can be done by shifting 5q from the right-hand side to left-hand side. The equation is now 3p+5q. Now to get the equation in terms of m we need to divide the whole equation by 2 which will give m = (3p+5q) / 2.
To learn more about rearranging and transposing equations,
https://brainly.com/question/19029120
can somebody please solve this if you send picture please send good quality
What is the solution of the inequality -8(x + 7.5) ≤ 10?
Step-by-step explanation:
-8(x + 7.5) ≤ 10?
expand left side:
-8x - 60 ≤ 10
subtract 60 to both sides:
-8x - 60 + 60 ≤ 10 + 60
-8x ≤ 70
dive both sides by -8: (Remember when dividing by a negative number, you flip the direction of the inequality sign)
-8x/-8 ≥ 70/-8
x ≥ -35/4
reduce right side:
x ≥ -35/4 or x ≥ -8.75 [depends on if you need fractional or decimal format]
so in set builder format: [-35/4 , ∞) or [-8.75 , ∞) [depends on if you need fractional or decimal format]
length of 3 feet, a width of 2 feet, and a height of 5 feet. What is the volume of the refrigerator?
Answer:
30 feet^3
Step-by-step explanation:
length x width x height
3 x 2 x 5
=30
The dot plot shows 20 students' scores on a quiz
in English class.
Quiz Scores
If one student from the class is chosen at
random, what is the probability that he or she
scored MORE than 15 points on the quiz?
Answer:
Probability = A. 2 / 5
Step-by-step explanation:
Probability = ( Number of Favorable Outcomes ) / (Total Number of Outcomes )
So the Total Number of Students = 20
Number of Students ( Dots ) scored more than 15 = 3+2+1+2 = 8
Probability = 8 / 20 = 2 / 5
Glad to Help
Answer: 12/20= 3/5
Step-by-step explanation:
you have to count all the dots on the dot plot to find your denominator which is 20.
then you count all the dots that are fifteen or more and there are 12 so 12/20 is the probability which is simplified into 3/5.
let x be the exam grade of a random student taking calculus 1 at uiuc. suppose professor smith takes a random sample of 140 students from the calculus 1 class to see how they did on the exam. in his sample, he got a mean of 86 and a standard deviation of 11. approximate the probability that (the sample mean) would be higher than 88.4 or smaller than 84.4?
The probability that the sample mean would be higher than 88.4 or smaller than 84.4 is 0.85582
How to get the required probabilityThe probability is calculated using z score, this is used to determine the amount of standard deviations a sample, X is from the mean
The z score is given by the formula
z = (X - μ) / σ
Definition of variables
mean, μ = 86
sample size, n = 140
standard deviation, σ = 11
The probability
P(z > 88.4) + P(z < 84.4)
z score for z < 88.4
z = (88.4 - 86) / 11
= 0.21818 p value = 0.41364
z score for z < 84.4
z = (84.4 - 86) / 11
= -0.14545
p value for z < -0.14545 = 0.44218
The probability required = 0.41364 + 0.44218 = 0.85582
Learn more about p - values at:
https://brainly.com/question/28940355
#SPJ1
To keep in shape, Leah exercises at a track near her home. She requires 84 minutes to do 8 laps running and 10 laps walking. In contrast, she requires 66 minutes to do 2 laps running and 10 laps walking. Assuming she maintains a consistent pace while running and while walking, how long does Leah take to complete a lap? Leah takes minutes to run a lap and minutes to walk a lap.
Using a system of equations, it is found that:
Leah takes 3 minutes to run a lap and 6 minutes to walk a lap.
What is the system of equations?The variables of the system of equations are presented as follows:
Variable x: time required to complete a lap running.Variable y: time required to complete a lap walking.She requires 84 minutes to do 8 laps running and 10 laps walking, hence the first equation is:
8x + 10y = 84.
She requires 66 minutes to do 2 laps running and 10 laps walking, hence the second equation is:
2x + 10y = 66.
Simplifying by 2, we have that:
x + 5y = 33.
x = 33 - 5y.
Replacing in the first equation, we can find the time it takes to walk a lap, as follows:
8(33 - 5y) + 10y = 84.
264 - 40y + 10y = 84
30y = 180
y = 180/30
y = 6 minutes.
Then the time it takes to run a lap is obtained as follows:
x = 33 - 5y = 33 - 5(6) = 33 - 30 = 3 minutes.
More can be learned about a system of equations at https://brainly.com/question/24342899
#SPJ1
Which expression is equivalent to 3x5y?
Answer:
15y
Step-by-step explanation:
3 times 5 is 15 with the variable
Find the length of the missing side in the following examples. Round answers to the nearest tenth, if necessary.
Answer:
Step-by-step explanation:[tex]x2{12}5\\ =18[/tex]
a cashier cannot tell the difference between cilantro and parsley. customers would only buy either cilantro or parsley. he knows that 20% of his customers prefer parsley. these customers will buy parsley 40% of the time when shopping. otherwise, they wouldn't buy either herb. 40% of his customers prefer cilantro and will buy cilantro 15% of the time when shopping. otherwise, they wouldn't buy either herb. the other 40% of his customers don't prefer, and thus don't buy, either herb. given the next customer buys one of the two herbs, what is the probability it is parsley?
Probability that customer buy parsley given buy any of two herb
= 0.5714
What is probability in math?
Probability refers to potential. The subject of this area of mathematics is the occurrence of random events.The range of the value is 0 to 1. To forecast how likely events are to occur, probability has been introduced in mathematics.Parsley ( 0.4 , 0.6 )
buy = B ∩ P = 0.08
Don't buy = DB ∩ P = 0.12
Cilantro = ( 0.15 , 0.85 )
buy = B ∩ C = 0.06
Don't buy = DB ∩ C = 0.34
Don't buy anything = DB = 0.4
P( Buy anything ) = P(B∩P) + P( B ∩ C )
= 0.08 + 0.06 = 0.14
Now, P( P/B) = P( P ∩ B)/P(B)
= 0.08/0.14 = 4/7 = 0.5714
Hence, probability that customer buy parsley given buy any of two herb
= 0.5714
Learn more about probability
brainly.com/question/11234923
#SPJ4
assuming that earth is a sphere of radius 6378 kilometers, what is the difference in latitude of two cities, one of which is 1046 kilometers due north of the other?
The difference between the distance between the two cities if of 14.842 latitudes.
The earth has one latitude running right in the center called the equator. On either side of the equator, there are 90 more latitudes each.
Therefore, the earth has 181 latitudes.
Now if we see the image we can see that all these latitudes fall on the vertical diameter of the Earth.
Hence the distance covered by all 181 latitudes = 2 X radius of the Earth
= 2 X 6378 km
= 12756
Assuming that all the latitudes are equidistant, we get the distance between 2 latitudes to be
12756/181
= 70.475 km
Let the two cities be A and B. It is given that the distance between the two cities is 1046 km and one is due north of the other.
Therefore the difference in latitudes between the two cities is
1046/70.475
= 14.842 latitudes
To learn more about distances visit
https://brainly.com/question/23274198
#SPJ4
what does the adjusted r squared tell us about the relationship between sales, price, and advertising? the model explains about 90% of the variance in sales. the model explains about 60% of the variance in sales. the model explains about 80% of the variance in sales. the model explains about 70% of the variance in sales.
The modified r squared tells us more about the relationship among sales, price, as well as advertising by explaining approximately 60% of a variance in sales.
Define the term adjusted r squared?R-squared (R2) would be a statistical measure that quantifies the proportion of the variation explained from an independent variable other variables within a regression model for a dependent variable.
R-squared describes how much the variance with one variable describes the variance of the other. So, if a model's R2 is 0.50, the model's inputs can explain roughly half of a observed variation.A score of 70 to 100 shows that a specific portfolio closely reflects the underlying stock index, whereas a score of 0 to 40 indicates a relatively poor correlation the with index.Higher R-squared scores also suggest that beta measurements are more reliable. The volatility of either a security or portfolio is measured by beta.Thus, the modified r squared tells us more about the relationship among sales, price, as well as advertising by explaining approximately 60% of a variance in sales.
To know more about the adjusted r squared, here
https://brainly.com/question/14364216
#SPJ4
Write an equation in point-slope form for the line that passes through the
point with the given slope.
(-6, -3), m = -1
Answer:
( y + 3 ) = - ( x + 6 )
Step-by-step explanation:
The Equation of Line in Point-Slope Form is
[tex](y-y_1)=m(x-x_1)\\where\ m \is \ the \ slope\ and \ (x_1 , y_1) \ is \ any \ point \ on \ the \ line[/tex]
So by Substitution by the Givens
( y - (-3) ) = -1( x - (-6) )
( y + 3 ) = - ( x + 6 )
Glad to Help
Can somone help me with this will mark u brainliest
Answer: 2[tex]\sqrt{2}[/tex]
Step-by-step explanation: First plug in the value, which is [tex]\sqrt{8}[/tex]
Then divided to 2[tex]\sqrt{2}[/tex]
Two cars start at the same point and simultaneously drive in opposite directions.
The speed of the first car is s miles per hour. The speed of the second car is 5
miles per hour less than the speed of the first car.
The cars are 315 miles apart 1.5 hours after they start moving. Use the answer
from part (c) to write an equation.
Rhombus EFGH is rotated 90° counterclockwise about vertex G. How many pairs of parallel sides does the rotated figure have?
The number of pairs of the parallel lines after the rotation is 2
How to determine the number of pairs of the parallel lines?The transformation is described by
Rotation by 90° counterclockwise about vertex G
There are four types of transformation, and they are:
DilationRotationReflectionTranslationAs a general rule of rotation:
When a shape, line or an angle is rotated, the size of the properties in the rotated figure remains unchanged
Before rotation, a rhombus has two pairs of parallel sides
This means that the parallel sides would remain parallel after rotation
Read more about rotation at:
brainly.com/question/17809268
#SPJ1
Jade ha 28 triangle card. He ha 4 time a many trading card a jordan. How many trading card do they have altogether
Jade and Jordan both have a total of 35 trading cards altogether.
Given, Jade has 28 trading cards. He has 4 times as many trading cards as Jordan.
As, Jade has 28 trading cards
Let Jordan has 'x' trading cards.
Now, as Jade has 4 times as many trading cards as Jordan.
So, 28 = 4x
4x = 28
x = 7
So, Jordan has 7 trading cards.
Now, they both have a total of 35 trading cards altogether.
Hence, Jade and Jordan both have a total of 35 trading cards altogether.
Learn more about Unitary Method here https://brainly.com/question/28627316
#SPJ4
Beginning with the equation 3m=7 write the new equation produced by multiplying both sides by 3/8
Answer:
9/8 m = 21/8
or
9m/8 = 21/8
Step-by-step explanation:
3m = 7
3/8 × 3m = 3/8 × 7
9/8 m = 21/8
events which can never occur together in probability theories then it is classified as? a. mutually exclusive events b. collectively exclusive events c. mutually exhaustive events d. none of these
In probability theories, events which can never occur together are classified as "mutually exclusive events" that is option A.
What is mutually exclusive event?Two events are mutually exclusive or disjoint in logic and probability theory if they cannot both occur at the same time. The results of a single coin toss, which can result in either heads or tails but not both, serve as an obvious illustration. Events that do not take place at the same time are said to be mutually exclusive. For instance, if a coin is tossed, the outcome will either be head or tail; we cannot get both outcomes. Since they do not occur at the same time, such events are also known as disjoint events.
To know more about mutually exclusive event,
https://brainly.com/question/28565577?referrer=searchResults
#SPJ4