The probability that at least 285 rooms will be occupied is 0.0885
A popular resort hotel's reservation follows Normal distribution as size of sample is greater than 30 with mean np and standard deviation √npq
Given , Probability of cancelation : q = 7% = 0.07
Probability of no cancellation of room : p = 1 - q
p = 1 - 0.07
p = 0.93
here, Binomial distribution tends to normal
Sample size : n = 300
Mean = np
= 300 × 0.93
= 279
Standard deviation = [tex]\sqrt{npq}[/tex]
= [tex]\sqrt{(300)(0.93)(0.07)}[/tex]
= [tex]\sqrt{19.53}[/tex]
= 4.42
We have to find P(x ≥ 285)
subtracting 279 and dividing by 4.42 to each sides
P(x ≥ 285) = [tex]P(\frac{x - 278}{4.42} \geq \frac{285 - 278}{4.42} )[/tex]
= P(z ≥ 1.357) = 1 - P(z<1.357)
Using Z probability table ,
P(x ≥ 285) = 1 - (0.9115)
= 0.0885 is required probability
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where can I find L1 and L4 ? for missing alternate angles
< 1 = 113.1 degrees
< 4 = 66.9 degrees
Explanation:Alternate interior angles are equal
< 1 = < 3 = 113.1 degrees
< 2 = < 4 = 66.9 degrees
Elizabeth has
4 1/2 feet of material to make bookmarks. She will use 9 inches of material for each bookmark. How many bookmarks can Elizabeth make?
Salma runs 6 miles in 55 minutes. At the same rate, how many miles would she run in 44 minutes?
Answer:
The number of miles she would run in 44 minutes is;
[tex]4.8\text{ miles}[/tex]Explanation:
Given that;
Salma runs 6 miles in 55 minutes;
The rate at which she run is;
[tex]\text{rate =}\frac{\text{ distance}}{\text{time}}=\frac{6}{55}miles\text{ per minute}[/tex]At the same rate, the distance it will cover in 44 minutes is;
[tex]\begin{gathered} \text{time}=\frac{\text{distance}}{\text{rate}} \\ \text{distance}=\text{time}\times rate \\ \text{distance}=44\times\frac{6}{55} \\ \text{distance = 4.8 miles} \end{gathered}[/tex]The number of miles she would run in 44 minutes is;
[tex]4.8\text{ miles}[/tex]10x−1= 7 x + 26 7x+26
Answer:
x = - 27/179
Step-by-step explanation:
10x - 1 = 7x + 182x + 26
10x - 1 = 189x + 26
10x - 189x = 26 + 1
- 179x = 27
x = - 27/179
I just need to answer I'm trying to verify question
You have the following system of equations:
x + 3y = 1
y = 2x + 5
in order to solve the previous system, replace the expression y = 2x + 5, into the first equation and solve for x, as follow:
x + 3y = 1
x + 3(2x + 5) = 1 apply distribution property
x + 6x + 15 = 1 simplify lef side
7x + 15 = 1 subtrac 15 both sides
7x = 1 - 15
7x = -14 divide by 2 both sides
x = -14/2
x = -7
replace the previous value of x into the second equation to get y:
y = 2x + 5
y = 2(-7) + 5
y = -14 + 5
y = -9
Hence, the solution to the given system of equations is:
x = -7
y = -9
(-7 , -9)
9. Use the Distributive Property to solve the
equation 28-(3x+4)= 2(x+6) +x.
WITH SOLUTION please
Answer:
x=2
Step-by-step explanation:
T= 2
28 - (3æ+4) = 2(r + 6) + *
We need to use the distributive property for the
right side.
28 - 3z -4 = 2a + 12 + z
28 -3z -4 = (2) (æ) + (2)(6) + æ)
From here we need to subtract 3æ from both side.
-3æ + 24 -3 = 3æ + 12 – 3¢
3æ + 24 = 3z + 12
6z + 24 = 12
Transfer +24 on the right side. (P.S. don't forget to
change the sign)
62 = 12 - 24
6 = - 12
Finally, divide both sides by -6
6x/-6 = -13/-6
x=2
I hope I helped you
Select the correct answer.
Eric traveled to two cities on a single highway. The total distance one way was 200 miles. The distance from his original location to the first city was 40
miles less than the distance from the first city to the second city. Suppose that x represents the distance from the original location to the first city and y
represents the distance from the first city to the second city. The following system of equations represents the given situation
x + y = 200
x = y - 40
Which pair of coordinates represents the solution (in miles) to this system of equations?
O A.
(70, 130)
(80, 120)
(160, 120)
(100, 100)
B.
O c.
D.
E. (140, 60)
In linear equation, The solution to this system is (80, 120)
What is a linear equation example?
Ax+By=C is the typical form for linear equations involving two variables. A linear equation in standard form is, for instance, 2x+3y=5.Finding both intercepts of an equation in this format is rather simple (x and y).The following system of equations represents the given situation
x + y = 200
x = y - 40; substituting x from this equation to the first:
y - 40 + y = 200
2y = 240
y = 120
Corresponding value of x:
x = 120 - 40
x = 80
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3 to the power of 2 divided by 3
Answer:
3
Step-by-step explanation:
3 to the power of 2 is nine because 3 x 3 = 9
9 / 3 is 3
Answer:
3
Step-by-step explanation:
3²÷3¹
=3²-¹
=3¹
=3
or
3²÷3¹
=9÷3
=3
estimate 6 and five ninths times sixty eight and 1 third
To estimate this, let's first translate to figures.
We have:
[tex]\begin{gathered} \text{Five ninths = }\frac{5}{9} \\ \\ Sixty\text{ eight = 68} \\ \\ 1\text{ third = }\frac{1}{3} \end{gathered}[/tex]Let's estimate, we have:
[tex]undefined[/tex]The table shows our research activities of two students at an observatory how much does a student pay to use a telescope for 1 hour the supercomputer? for 1 hour?
Answer: Student 1 pays $23.5 to use a supercomputer and pays $14.1 to use a telescope
Step-by-step explanation:
Using cross multiply and divided method, we can find the unit rate or just dividing.
Student 1. 3 1
$70.5 x
70.5 x 1 = 70.5
70.5 ÷ 3 = $23.5
x = $23.5
5 1
70.5 x
70.5 x 1 =70.5
70.5 ÷ 5 = 14.1
x = $14.1
Student 1 pays $23.5 to use a supercomputer and pays $14.1 to use a telescope.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Using the cross multiply and divide method, we can find the unit rate or just divide.
Student 1. 3 1
$70.5 x
70.5 x 1 = 70.5
70.5 ÷ 3 = $23.5
x = $23.5
5 1
70.5 x
70.5 x 1 =70.5
70.5 ÷ 5 = 14.1
x = $14.1
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Emma is scrapbooking. She has 9 inches of paper and needs to cut it into 2/5 inch strips of paper. How many whole strips will she be able to make?
*
1 point
The number of strips Emma will be able to make 22.5 i.e. 22.
What is strips?The set of points in the plane between two parallel lines in the plane. The x,y coordinates plane of the points in the stripe satisfy the inequality C1 < . Ax + By < C2, where A, B, C1, C2 are certain constants and both A and B cannot be zero. The strip number is typically used in preparing the data for matching (or as a matching transformation within the matching processor). For text data that has numbers in the data but that you know are irrelevant, removing the numbers before matching is useful. As an abstract topological space, the Mobius strip can be embedded in three-dimensional Euclidean space in various ways. The twist is greater than 1 or the centerline is knotted.According to question
Total paper = Total strips × size of one
9 = n × 2/5
n = 22.5
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Don Williams wised his small motorboat to go 5 miles upstream to his favorite fishing spot. Against the current, the trip takes 5/6 hour. With the current the trip takes 1/2 hour. How fast can the boat travel in still water ? What is the speed of the current in still water the boat speed is __ mph. The speed of the current is ___ mph
let s = speed in still water
let c = rate of the current
then
(s-c) = effective speed up-stream
and
(s+c) = effective speed down-stream
Write a distance equation for each way; dist = time * speed
5/6*(s-c) = 5
1/2 *(s+c) = 5
Now we get rid of the fractions
5(s-c)=30
s + c = 10
5s - 5c = 30
s + c = 10
siplifying:
s - c = 6 (1)
s + c = 10 (2)
adding:
2s = 16, then s = 8
8 mph is the boat speed in still water
According with (2):
8 + c = 10, then c = 2
2 mph is the speed of the current
Given the following sequence of numbers find the recursive formula, and the appropriate sequence formula,(arithmetic or geometric) and find the next three numbers in the sequence.5, 9, 13, 17, 21,
We can say that it's an arithmetic sequence since it has a common rate of change or common difference of 4.
Arithmetic sequences are represented by the following formula:
Recursive formula:
[tex]\begin{gathered} a_n=a_{n-1}+d \\ \text{Explicit formula:} \\ a_n=a_1+(n-1)d \\ \text{The next three numbers would be: }a_6,a_7,a_8 \end{gathered}[/tex]an= nth term
a1= 1st term
n= number of terms
d= common difference
[tex]\begin{gathered} a_6=5+(6-1)\cdot4 \\ a_6=25 \\ a_7=5+(7-1)\cdot4 \\ a_7=29_{} \\ a_8=5+(8-1)\cdot4_{} \\ a_8=33 \end{gathered}[/tex]Julia works for a company selling light bulbs. She sells fluorescent light bulbs for $5 a piece and incandescent light bulbs for $2. To meet her quota, she needs to sell over 100 light bulbs and make at least $350.If the solution region is the amount of light bulbs Julia needs to sell to meet her quota, which graph's shaded area represents the solution region?
Given:
Julia works for a company selling light bulbs. She sells fluorescent light bulbs for $5 a piece and incandescent light bulbs for $2.
Let the number of the fluorescent light bulbs = y
And the number of the incandescent light bulbs = x
To meet her quota, she needs to sell over 100 light bulbs and make at least $350.
So, we can write the following system of inequalities:
[tex]\begin{gathered} x+y>100 \\ 2x+5y\ge350 \end{gathered}[/tex]Now, we will graph the system of the inequalities to find the area of the solution
The graph will be as follows:
So, the answer will be the graph that is on the upper right-side.
Graph x
Please look at picture! thank you!
Answer:
16
Step-by-step explanation:
write the equation for a3
a3 = a2 + 3(3) -> eq1
now find what is a2, write equation for a2
a2 = a1 + 3(2) -> eq2
you know a1=1, replace that into eq2
a2 = 1 + 3(2) = 1 + 6 = 7
replace a2 into eq1
a3 = 7 +3(3) = 7 + 9 = 16
need help as soon as possible !!!!!!
The value of the variable x: 40
Angles of the polygon are :
3x = 120(2x + 10) = 90(2x + 5) = 85(2x - 15) = 65What is Polygon?An Indian blockchain scalability platform is called Polygon. It addresses Ethereum's problems with excessive costs, a subpar user experience, and a meager number of transactions per second. Creating a framework for Proof of Stake transactions is one approach taken to overcome these problems.Calculate the measure of angles as follows:
3x(2x + 10)(2x + 5)And
(2x - 15)Since we have,
Sum of angle measure = 360°
Thus: 3x + (2x + 5) + (2x + 10) + (2x - 15) = 360Opening the brackets:
3x + 2x + 5 + 2x + 10 + 2x - 15 = 360Adding the like terms:
9x + 15 - 15 = 3609x = 360x = 360/9x = 40Hence, The measure of the variable is 40.
And the angle measures are:
3 x 40 = 120°(2(40) + 5) = 80 + 5 = 85°(2(40)+ 10) = 80 + 10 = 90°(2(40) - 15) = 80 - 15 = 65°Therefore, the value of the variable x: 40
Angles of the polygon are :
3x = 120(2x + 10) = 90(2x + 5) = 85(2x - 15) = 65To learn more about Polygon click on the link
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The figure below shows a circle with center J, diameter LT, secant TO, andtangents EB and IP. Which of the angles must be right angles? Select all thatapply.
Answer:
Explanation:
The angles that are right angles are the ones that measure 90 degrees.
These are:
angles formed at L
angles formed at E
Answer:
Explanation:
The angles that are right angles are the ones that measure 90 degrees.
These are:
angles formed at L
angles formed at E
x²+2x for x=-3 please hurry
Answer:
3
Step-by-step explanation:
x²+2x and x=-3
= (-3)² +2(-3)
= 9-6
=3
Perform the following food service calculation.
Meat served: chicken with a bone
Pounds of chicken available: 48 lbs.
How many guests can be served?
The number of guests that can be served is 12
How to determine the number of guests?From the question, we have the following parameters that can be used in our computation:
Meat served: 4 lbs chicken with a bone
Pounds of meat available: 48 lbs.
The number of guests needed is calculated using the following equation
Number of guests = Pounds of meat available/Meat served
Substitute the known values in the above equation, so, we have the following representation
Number of guests = 48/4
Evaluate the quotient
Number of guests = 12
Hence, 12 guests can be served with the available meat
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Possible question
Perform the following food service calculation.
Meat served: 4 lbs chicken with a bone
Pounds of meat available: 27 lbs.
How many guests can be served?
a stationary shop had an equal number of pens and notepads at first. after selling 1250 pens and 380 notepads, there were 4 times as many notepads as pens left. how many pens did the stationary shop have at first
The stationary shop had 90 pens with them initially.
Let,
The number of pens initially at the stationary shop=x
The number of pens and the number of notepads are said to be equal. Therefore, The number of notepads initially at the stationary shop=x
After selling,
The number of pens = x-1250
The number of notepads = x-380
The number of pens was four times the number of the number of notepads. Modelling the linear equation for the situation:
x-1250=4(x-380)
x-1250=4x-1520
x=4x-270
-3x=-270
x=90
The stationary shop had 90 pens initially.
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#11 i
Solve 7w-9=13 - 4w.
W =
Answer:
w=2
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
7w−9=13−4w
7w+−9=13+−4w
7w−9=−4w+13
Step 2: Add 4w to both sides.
7w−9+4w=−4w+13+4w
11w−9=13
Step 3: Add 9 to both sides.
11w−9+9=13+9
11w=22
Step 4: Divide both sides by 11.
11w/11=22/11
w=2
Write an equation in point-slope form for the line that has a slope of 1/5 and contains the point (2,−9).
The equation is y+9=(1/5)(x-2).
What is a slope form?It is used to find the equation of the straight line which is inclined at a given angle to the x-axis and passes through a given point. The three major forms of linear equations are point-slope form, standard form, and slope-intercept form. The equation of the slope form is y-y₁ = m(x - x₁)
The formula for the point-slope is,
y-y₁ = m(x - x₁)
y₁ is the y-coordinate of the point in the line, x₁ is the x-coordinate of the point in the line and m is the slope.
y₁ = -9
m = 1/5
x₁ = 2
Substituting the above values in the above equation, we get
y-(-9) = (1/5)(x-2)
By simplifying the above equation, we get
y+9 = (1/5)(x-2)
Therefore, the equation is y + 9 = (1/5)(x-2).
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May I please get help with this where I have tried multiple times but still cannot find the right answers for them
Given a point with coordinates (x, y), to rotate 90º counterclockwise, the rule is:
[tex](x,y)\Rightarrow(-y,x)[/tex]In thisc ase, we have the point:
[tex](2,-1)[/tex]Applying the rule:
[tex](2,-1)\Rightarrow(1,2)[/tex]Jason has three more than four times the amount of money Jeff has together they have $72 how much money does each person have
hello
determine the amount each of them have, let's write an equation to represent thier total amount
let x represent the amount Jason have
let y represent the amount Jeff has
now, we know that Jason has 3 more than 4 times the amount Jeff has
x = 4y + 3 .... equation 1
x + y = 72 .... equation 2
from equation 2,
make x the subject of formula
[tex]\begin{gathered} x+y=72 \\ x=72-y \end{gathered}[/tex]x = 72 - y .....equation 3
put equation 3 into equation 1
x = 4y + 3
72 - y = 4y + 3
solve for y
[tex]\begin{gathered} 72-y=4y+3 \\ \text{collect like terms} \\ 4y+y=72-3 \\ 5y=69 \\ y=\frac{69}{5} \\ y=13.8 \end{gathered}[/tex]we know y = 13.8
we can simply substitute the value into equation 2 and solve for x
[tex]\begin{gathered} x+y=72 \\ y=13.8 \\ x+13.8=72 \\ x=72-13.8 \\ x=58.2 \end{gathered}[/tex]therefore, Jason has $58.2 and Jeff has $13.8
Which equations represent a linear function? Select two. a. y = x-1 b. y = – 4.5 C. 3x – 4y = 2 d. 5x2 = 10y e. y = 1/2x2 +6
Explanation
a linear function must have
dependent and independent variables, ( y and x in this case)and the exponent of the independent vairable must be 1, so
Step 1
Check
a)
[tex]a)\text{ y=x-1}[/tex]this is a linear function
b)
[tex]y=4.5[/tex]this is not a functin, this expression has not x
c)
[tex]3x-4y=2[/tex]this functin has x and y, and the exponent of x is 1, so, this is a linear function
d)
[tex]5x^2=10y[/tex]this function has x and y, but the exponent is 2, so this is not a linear function
e)
[tex]y=\frac{1}{2}x^2+6[/tex]this function has x and y, but the exponent is 2, so this is not a linear function
i hope this helps you
19) Given that f(x)x² - 8x+ 15x² - 25find the horizontal and vertical asymptotes using the limits of the function.A) No Vertical or Horizontal asymptotesB) No Vertical asymptotesHorizontal asymptote aty - 1Vertical asymptote at x = 5Horizontal asymptote at y = 1D) Vertical asymptote at x = -5Horizontal asymptote at y = 1
EXPLANATION
Since we have the function:
[tex]f(x)=\frac{x^2-8x+15}{x^2}[/tex]Vertical asymptotes:
[tex]For\:rational\:functions,\:the\:vertical\:asymptotes\:are\:the\:undefined\:points,\:also\:known\:as\:the\:zeros\:of\:the\:denominator,\:of\:the\:simplified\:function.[/tex]Taking the denominator and comparing to zero:
[tex]x+5=0[/tex]The following points are undefined:
[tex]x=-5[/tex]Therefore, the vertical asymptote is at x=-5
Horizontal asymptotes:
[tex]\mathrm{If\:denominator's\:degree\:>\:numerator's\:degree,\:the\:horizontal\:asymptote\:is\:the\:x-axis:}\:y=0.[/tex][tex]If\:numerator's\:degree\:=\:1\:+\:denominator's\:degree,\:the\:asymptote\:is\:a\:slant\:asymptote\:of\:the\:form:\:y=mx+b.[/tex][tex]If\:the\:degrees\:are\:equal,\:the\:asymptote\:is:\:y=\frac{numerator's\:leading\:coefficient}{denominator's\:leading\:coefficient}[/tex][tex]\mathrm{If\:numerator's\:degree\:>\:1\:+\:denominator's\:degree,\:there\:is\:no\:horizontal\:asymptote.}[/tex][tex]\mathrm{The\:degree\:of\:the\:numerator}=1.\:\mathrm{The\:degree\:of\:the\:denominator}=1[/tex][tex]\mathrm{The\:degrees\:are\:equal,\:the\:asymptote\:is:}\:y=\frac{\mathrm{numerator's\:leading\:coefficient}}{\mathrm{denominator's\:leading\:coefficient}}[/tex][tex]\mathrm{Numerator's\:leading\:coefficient}=1,\:\mathrm{Denominator's\:leading\:coefficient}=1[/tex][tex]y=\frac{1}{1}[/tex][tex]\mathrm{The\:horizontal\:asymptote\:is:}[/tex][tex]y=1[/tex]In conclusion:
[tex]\mathrm{Vertical}\text{ asymptotes}:\:x=-5,\:\mathrm{Horizontal}\text{ asymptotes}:\:y=1[/tex]Factor the trinomial completely.3x2 - 13x - 10
3x2 - 13x - 10
multiplying the first and third terms we have
-30x2
The factors of -30 that will be added to get - 13 are -15 and 2
so we split the expression further
= 3x2 - 15x + 2x - 10
= 3x (x - 5) + 2 (x - 5)
= (x -5)(3x + 2)
Given below is a number written in factored form. Use this representation to determine the following. Factored Form 7.7.7.7.7.7 Enter the number in exponential form. Enter the number in standard form.
Given number in factored form 7.7.7.7.7.7 can be represented in the following way :
Exponential form : 7⁶
Standard form. : 11.7649 × 10⁴
As given in the question,
Given number in factored form is equal to 7.7.7.7.7.7
Represent the given factored form number into exponential form and standard form is written as :
Exponential form is given by :
7.7.7.7.7.7
= 7¹⁺¹⁺¹⁺¹⁺¹⁺¹
= 7⁶
Standard form is given by :
7.7.7.7.7.7
= 117649
= 11.7649 × 10⁴
Therefore, given number in factored form 7.7.7.7.7.7 can be represented in the following way :
Exponential form : 7⁶
Standard form. : 11.7649 × 10⁴
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Choose the graph of this equation. y = 2.5x
Answer:
1
Step-by-step explanation:
Jordan types at a constant rate of 40 words per minute. The number of words typed, y, is a function of the number of minutes spent typing Part A Which equation models this situation? 95 CV 40and how many words can he type in 7.5 minutes
To write the equation that represents the situatio, as y is in function of x, you multiply the rate by the number of minutes (x):
[tex]y=40x[/tex]In 7.5 minutes he can type:
[tex]y=40(7.5)=300[/tex]