We have to calculate how many adults (A) and children (C) were admitted.
We know that the total number of persons, which is the sum of adults and children, was 266, so we can write:
[tex]A+C=266[/tex]We also know that the fees collected were $1101. This is the sum of the adult tickets, which are price times the number of adults, and the children tickets, which are also price times the amount of children.
Then, we can write this as an equation:
[tex]2.25\cdot C+5.60\cdot A=1101[/tex]We have a system of linear equations with two equations and two unknowns.
We can solve it by substitution as:
[tex]A+C=266\Rightarrow A=266-C[/tex][tex]\begin{gathered} 2.25C+5.60A=1101 \\ 2.25C+5.60(266-C)=1101 \\ 2.25C+1489.6-5.60C=1101 \\ (2.25-5.60)C=1101-1489.6 \\ -3.35C=-388.6 \\ C=\frac{-388.6}{-3.35} \\ C=116 \end{gathered}[/tex]We can now use the first equation to calculate the number of adults:
[tex]A=266-C=266-116=150[/tex]Answer:
number of children = 116
number of adults = 150
In a game, two fair number cubes with faces numbered 1 through 6 are rolled. If the sum of the two numbers rolled is 12, the player wins c coupons. 11, the player wins 4 coupons. less than 11, the player loses 2 coupons. What value of c makes this game fair? A.10B.14 C.58 D.64
the probability to get a number less than 11 is 33/36, to get an 11 is 2/36 and to get an 12 is 1/36. if we want the game to be fair, the expected value should be 0, so we get
[tex]-2\cdot\frac{33}{36}+4\cdot\frac{2}{36}+\frac{c}{36}=0\rightarrow-66+8+c=0\rightarrow c=66-8=58[/tex]The lengths of two sides of an isosceles triangle are 5 and 9. The length of the third side could beA. 9, onlyB. none of theseC. either 5 or 9D. 5, only
Step 1: Theorem
In geometry, an isosceles triangle is a triangle that has two sides of equal length.
Step 2: Given data
Two sides are given with lengths 5 and 9.
Step 3:
The two equal lengths can be 5 and 5 or 9 and 9
Step 4:
The third length can be 5 or 9.
Final answer
is either 5 or 9.
Solve the following system of equations using elimination. A. (4, 2)B. (2, 16)C. (-2, 16)D. (16, -2)
Answer:
A. (4, 2)
Explanation:
Given the system of equations:
[tex]\begin{gathered} x+3y=10\cdots(1) \\ 6x+12y=48\cdots(2) \end{gathered}[/tex]In order to use the elimination method, multiply the first equation by 6 to make the coefficients of x the same.
[tex]\begin{gathered} 6x+18y=60\cdots(3) \\ 6x+12y=48\cdots(2) \end{gathered}[/tex]Subtract equation (2) from equation (3).
[tex]\begin{gathered} 6y=12 \\ \text{Divide both sides by 6} \\ y=\frac{12}{6} \\ y=2 \end{gathered}[/tex]Next, solve for x using any of the equations:
[tex]\begin{gathered} x+3y=10 \\ x+3(2)=10 \\ x=10-6 \\ x=4 \end{gathered}[/tex]The solution to the system of equations is (x,y)=(4,2).
Option A is correct.
Last year Brian opened an investment account with $5800. At the end of the year, the amount in the account had increased by 24.5%. How much is this increased in dollars? How much money was in his account at the end of last year?
Part a
How much is this increased in dollars?
Remember that
24.5%=24.5/100=0.245
so
Multiply the initial amount by the factor of 0.245, to obtain how much is increased
$5,800*0.245=$1,421
the answer part a is $1,421Part b
How much money was in his account at the end of last year?
Adds $5,800 and $1,421
$5,800+$1,421=$7,221
the answer part b is $7,221(a) Explain how the number of standard deviations could be found for any data set. Choose the correct answer below.(b) Find the number of standard deviations
The Empirical Rule states that:
• about 68% of values fall within one standard deviation of the mean,,
,• about 95% of the values fall within two standard deviations from the mean,
,• almost all of the values—about 99.7%—fall within three standard deviations from the mean.
According to this, to have at least 99.0% of the data inside our interval, we must select approximately k = 3 standard deviations.
Answer• A. Use the Empirical Rule
,• k = 3
I just need the answer
Answer
(x - 3) and (x - 8)
Explanation:
The root of the equation is 3 and 8
(x - 3) = 0 or (x - 8) = 0
(x - 3) (x - 8) = 0
Therefore, the zero of the quadratic function are (x - 3) and (x - 8)
Using the formula for area of a rectangle, A = lw, solvefor the length, l.
ANSWER
[tex]l=\frac{A}{w}[/tex]EXPLANATION
We want to solve for the length, l, in the formula for the area of a rectangle:
[tex]A=lw[/tex]We simply want to make the length the subject of the formula. To do this, divide both sides of the formula by w:
[tex]\begin{gathered} \frac{A}{w}=\frac{lw}{w} \\ \Rightarrow l=\frac{A}{w} \end{gathered}[/tex]That is the answer.
Write the equation 16x2 + 25y2 − 32x + 50y + 16 = 0 in vertex form.
Solution
We have the following equation given:
[tex]16x^2+25y^2-32x+50y+16=0[/tex]We can complte the squares and we have this:
[tex]16(x^2-2x)+25(y^2+2y)+16=0[/tex][tex]16(x^2-2x+1)+25(y^2+2y+1)+16=16+25[/tex]And then if we simplify we got:
[tex]16(x-1)^2+25(y+1)^2=25[/tex][tex]\frac{(x+1)^2}{(\frac{5}{4})^2}+\frac{(y+1)^2}{1}=1[/tex]A box contains 3 red balls 2 blue balls and 5 white balls a ball is selected and it’s color noted a second ball is selected an it’s color noted find the probability of each of these. 1. P(selecting 2 blue balls) with replacement between the first and second draw2. P(selecting 2 white balls) without replacement between the first and second drawAnswer the questions below show all your work and make sure your answer is in lowest fraction form.
1.
On the first draw, 2 out of the 10 balls are blue. Therefore, the probability of choosing a blue ball is:
[tex]\frac{2}{10}\rightarrow\frac{1}{5}[/tex]On the second draw, 2 out of the 10 balls are blue, because the drawn blue ball is replaced. Therefore, the probability of choosing a second blue ball is:
[tex]\frac{2}{10}\rightarrow\frac{1}{5}[/tex]The probability of choosing 2 blue balls in a row, with replacement between the first and second draw, is:
[tex]\frac{1}{5}\cdot\frac{1}{5}=\frac{1}{25}[/tex]Or 4%
ANSWER 1:
[tex]\frac{1}{25}[/tex]2.
On the first draw, 5 out of the 10 balls are white. Therefore, the probability of choosing a white ball is:
[tex]\frac{5}{10}\rightarrow\frac{1}{2}[/tex]On the second draw, 4 out of the 9 remaining balls are white. Remember that the white ball drawn isn't replaced.
Therefore, the probability of choosing a second white ball is:
[tex]\frac{4}{9}[/tex]Thereby, the probability of choosing 2 white balls in a row, without replacement between the first and second draw, is:
[tex]\frac{1}{2}\cdot\frac{4}{9}=\frac{4}{18}\rightarrow\frac{2}{9}[/tex]Or about 22%
ANSWER 2:
[tex]\frac{2}{9}[/tex]2. You have a fruit punch recipe that calls for 1 pint of juice per person. You want to make enough for 121people. The expressionp can be used to convert pints to gallons.8a) What is the expression used to calculate? gallonsb) What does the variable p represent? pintsc) Use the expression to determine how many gallons of juice you will need for 12 people.Show your work here:
Given:
[tex]\frac{1}{8}p[/tex]The expression can be used to convert pints to gallons.
Where:
1 pint of juice = 1 person
Given that you want to make enough for 12 people, lets' answer the following.
(a) What is the expression used to calculate?
The given expression is used to calculate the number of gallons. This is because it converts pints to gallons.
Therefore, the expression is used to calculate the number of gallons.
(b) What does the variable p represent.
The variable, p, represents the amount of pints used.
Therefore, the variable p represents pints.
(c) Use the expression to determine how many gallons of juice you will need for 12 people.
Where:
1 person = 1p
12 people = 12p
Now, substitute 12 for p and evaluate:
[tex]\begin{gathered} \frac{1}{8}p \\ \\ =\frac{1}{8}\ast12 \\ \\ =\frac{12}{8} \\ \\ =1.5 \end{gathered}[/tex]Therefore, you will need to make 1.5 gallons of juice for 12 people.
ANSWERS:
• (a) gallons
,• (b) pints
,• (c) 1.5 gallons
The diagonales of this rhombus are 20 millimeters and 7 millimeters.
The rule of the area of the rhombus using its 2 diagonals is
[tex]A=\frac{d1\times d2}{2}[/tex]Since the diagonals of the given rhombus are 20 mm and 7 mm
Then d1 = 20 and d2 = 7
Substitute them in the rule above
[tex]\begin{gathered} A=\frac{20\times7}{2} \\ A=\frac{140}{2} \\ A=70mm^2 \end{gathered}[/tex]The area of the rhombus is 70 square millimeters
What does the value of f(x)=(1+1/x)^x approach as x approaches infinity?
In order to determine the value of f(x) as x approaches to oo, replace larger values of x into the function and identify the tendency of f(x), as follow:
x = 1000
[tex]f(1000)=(1+\frac{1}{1000})^{1000}\approx2.7169[/tex]x = 1000000
[tex]f(1000000)=(1+\frac{1}{1000000})^{1000000}\approx2.7182[/tex]x=1000000000
[tex]f(1000000000)=(1+\frac{1}{1000000000})^{1000000000}\approx2.7182[/tex]As you can notice, as x approaches to oo, f(x) approaches to 2.7182..., which is the value of constant e.
answer: e
The price p (in dollars) and the quantity x sold of a certain product obey the demand equation p = -8x + 600. What quantity x maximizes revenue (R= xp)? What is the maximum revenue? What price should the company charge to maximize revenue?
Given:
Demand equation is
[tex]\text{ p}=-8x+600.[/tex]where p is the price(in dollars) and x is the quantity of the product.
Required:
We have to find the quantity x that is, the value of x for which revenue is maximized, the maximum revenue, and the price should the company charge to maximize the revenue.
Explanation:
The formula for the revenue function is
[tex]\begin{gathered} R(x)=x\times\text{ p} \\ \Rightarrow R(x)=x(-8x+600) \end{gathered}[/tex][tex]\Rightarrow R(x)=-8x^2+600x.[/tex]Comparing this equation with
[tex]y=ax^2+bx+c[/tex]we get
[tex]a=-8\text{ and }b=600.[/tex]The value of x for maximum revenue is
[tex]x=\frac{-b}{2a}=\frac{-600}{2(-8)}=\frac{-600}{-16}=37.5[/tex]So we take the value of x approximately 38 because it cannot be decimal or fraction.
Therefore, the maximum revenue is
[tex]\begin{gathered} -8\times(38)+600\times(38) \\ =-304+22800 \end{gathered}[/tex][tex]=22496[/tex]To maximize the revenue company should charge
[tex]\begin{gathered} \text{ p}=-8\times38+600 \\ \Rightarrow\text{ p}=-304+600 \end{gathered}[/tex][tex]\Rightarrow p=296[/tex]Final answer:
Hence the final answer is:
The quantity x maximizes revenue is
[tex]38.[/tex]The maximum revenue is
[tex]22496.[/tex]The price should the company charge to maximize revenue is
[tex]296.[/tex]
It’s a bit easy but I just need to know the answer
The given function is,
[tex]g(x)=x^3+2[/tex]The parent function is,
[tex]f(x)=x^3[/tex]The graph of the function and the parent function can be drawn as,
Where red graph is the parent function f(x) and the blue graph is given by the function g(x).
From the graph it is evident that the g(x) is the translation of the graph f(x) by 2 units up.
Thus, "2 units" and "up" are the correct options.
Kevin rented a truck for one day. There was a base fee of $16.95, and there was an additional charge of 94 cents for each mile driven. Kevin had to pay$296.13 when he returned the truck. For how many miles did he drive the truck?
Answer:
He did drive the truck for 297 miles.
Step-by-step explanation:
The cost of driving x miles is modeled by a linear function in the following format:
C(x) = ax + b
In which a is the cost per mile and b is the flat cost.
There was a base fee of $16.95, and there was an additional charge of 94 cents for each mile driven.
This means that b = 16.95, a = 0.94. So
C(x) = 0.94x + 16.95
Kevin had to pay $296.13 when he returned the truck. For how many miles did he drive the truck?
We have to find x for which C(x) = 296.13. So
C(x) = 0.94x + 16.95
296.13 = 0.94x + 16.95
0.94x = 296.13 - 16.95
0.94x = 279.18
x = 279.18/0.94
x = 297
He did drive the truck for 297 miles.
Evaluatef(2x^5 - 7x^3 + 6)dx
Given the following integral:
[tex]\int(2x^5-7x^3+6)dx[/tex]To integrate the polynomial, the exponent will be increased by 1 then we divide by the new exponent.
The solution will be as follows:
[tex]\begin{gathered} \int(2x^5-7x^3+6)dx=\frac{2}{6}x^6-\frac{7}{4}x^4+6x+C \\ \end{gathered}[/tex]So, the answer will be:
[tex]\frac{1}{3}x^6-\frac{7}{4}x^4+6x+C[/tex]3. While surfing the Internet, you find a site that claims to offer "the mostpopular and the cheapest DVDs anywhere." Unfortunately, the website isn'tclear about the how much they charge for each DVD, but it does give you thefollowing information:Number of DVDs Ordered1 is $15 Two DVD - $24 and Three DVD $33(includes S&H)$15 $24 $33a. Plot the points and connect them to form a line.b. What is the slope of the line containing the data points?c. What does the slope represent in this problem?d. What is the y-intercept of the line that contains the data points?
Data:
You have two variables: number of DVDs and cost. The cost is the dependient variable as depend of the number of DVDs. Then in a x-y plane you put in the x-axis the number of DVDs and in the y-axis the cost:
The slope can be find with the next formula:
[tex]m=\frac{(y_2-y_1)}{(x_2-x_2)}[/tex]You use two points:
[tex]m=\frac{24-15}{2-1}=\frac{9}{1}=9[/tex]The slope is 9The slope represents the change on the cost in relation with the number of DVDs.The y-intercept can be find using the general formula of the slope inercept lineal equation:
[tex]y=mx+b[/tex]Where m is the slope and b the y-intercept.
You know the value of m, and use a given point to find the y-intercpt:
Point (1,15)
[tex]15=9(1)+b[/tex][tex]15-9=b[/tex][tex]6=b[/tex]The y-intercept is: 6 and represents the value of the variable in the y-axis when x=0
3Concession Stand SalesSoda Water No Drink TotalHot Dog 5046 158Pizza 120 58182No Food 3010Total 200 1404004How many people purchased no food and nodrink?200601020
Concession Stand Sales Soda
Water No Drink Total
Hot Dog 50
46 158
Pizza 120 58
182
No Food 30
10
Total 200 140
400
4
How many people purchased no food and no
drink?
200
60
10
20
A group of friends shook hands with each other at a party. Peter did notshake hands with everyone at the party because he was late and somefriends had already left. There were a total of 25 handshakes. How many friends were still at the party when Peter arrived?
When "n" number of people then number of people is:
[tex]\text{handshakes}=\frac{n(n-1)}{2}[/tex]If the handshakes is 25 then:
[tex]25=\frac{n(n-1)}{2}[/tex][tex]\begin{gathered} 25\times2=n(n-1) \\ 50=n^2-n \\ n^2-n-50=0 \\ \end{gathered}[/tex]Solve the equation:
[tex]\begin{gathered} n=\frac{-(-1)\pm\sqrt[]{1-4(1)(-50)}}{2} \\ n=\frac{1\pm\sqrt[]{1+200}}{2} \\ n\approx7 \end{gathered}[/tex]So 7 friends still at the party.
Write 0.611111111111 as a fraction PLEASE EXPLAIN STEP BY STEP!
We have to write N=0.6111... as a fraction.
This is a periodic number.
We start by transforming the number as:
[tex]10\cdot N=10\cdot0.6111\ldots=6.111\ldots=6+0.111\ldots[/tex]Now we take the periodic part we have (x=0.111...) and express it like this:
[tex]10x=10\cdot0.111\ldots=1.111\ldots=1+0.111\ldots=1+x[/tex]Then, we have:
[tex]\begin{gathered} 10x=1+x \\ 10x-x=1 \\ 9x=1 \\ x=\frac{1}{9} \end{gathered}[/tex]We use 10 to have the non-periodic part as an integer and the periodic part as a decimal.
Now we know that our periodic part of the number is equal to 1/9.
So we come back to N and complete:
[tex]\begin{gathered} 10N=6+0.111\ldots=6+\frac{1}{9} \\ N=\frac{1}{10}(6+\frac{1}{9})=\frac{1}{10}(\frac{6\cdot9}{9}+\frac{1}{9})=\frac{1}{10}\cdot\frac{54+1}{9}=\frac{1}{10}\cdot\frac{55}{9}=\frac{55}{90} \end{gathered}[/tex]Then, 0.6111... as a fraction is 55/90.
Identify the mathematical properties Liam uses to justify each step
Given the following expression:
[tex]\text{ 2x(x + 3) = 6x + 4}[/tex]Let's determine the mathematical properties being used as we simplify,
Step 1: Distributive Property
[tex]\text{ 2x(x + 3) = 6x + 4}[/tex][tex]\text{ (2x)(x)+ (2x)(3) = 6x + 4}[/tex][tex]\text{ 2x}^2\text{ + 6x = 6x + 4}[/tex]Step 2: Subtraction Property of Equality.
[tex]\text{ 2x}^2\text{ + 6x = 6x + 4}[/tex][tex]\text{ 2x}^2\text{ + 6x - 6x = 6x -6x + 4}[/tex][tex]\text{ 2x}^2\text{ = 4}[/tex]Step 3: Division Propert
14.9x+1/3 (-12-27x)-33.2 , x=-3simplify the expression using the properties of operations.
14.9x+1/3 (-12-27x)-33.2
Using PEDMAS;
First, let's open the parenthesis
14.9x - 4 - 9x - 33.2
Rearrange
14.9x - 9x -4 -33.2
5.9x - 37.2
But from the question x= -3
Substitute x=-3 in the above;
5.9(-3) - 37.2
-17.7 - 37.2
-54.9
Can you help with a compound equality
In general, a compound inequality consists of two inequalities joined by the word "and" or the word "or". Let's focus on the "or" case:
Example.We aim to find a set of numbers satisfying at least one of the equations. The idea is to solve each equation independently as you showed me:
We've obtained two simplified inequalities. The next step is to understand each of them as sets and join them by a union of sets ("capital u"). Let's begin with the inequality on the left. It represents all numbers "dominated" by 2 and 2 is not included (for it's strict). Then, in terms of sets, it looks like
[tex](-\infty,2)\text{.}[/tex]The right parenthesis means that 2 is not included, and "minus infinite" expresses the idea of all numbers below.
Let's analyze the second inequality. In this case, we aren't interested in the numbers below but the numbers above 2, where 2 is included. In terms of sets, it looks like
[tex]\lbrack2,\infty)\text{.}[/tex]The bracket means that 2 is included. The infinite on the right captures the idea of "all numbers above". The answer to the compound inequality is the union of both sets:
[tex](-\infty,2)\cup\lbrack2,\infty)\text{.}[/tex]Surprisingly, the solution is all numbers!
Evaluate each expression if x= -3, y= 8, and z= -416. y-(-5)18. -8 ÷ y
Given:
x = -3, y = 8, and z = -4
Let's solve the following:
• 17. xz
Substitute -3 for x and -4 for z.
We have:
[tex]\begin{gathered} xz=(-3)\text{ }\ast\text{ (-4) = 12} \\ \\ xz\text{ = 12} \end{gathered}[/tex]• 19. x + 11
Substitute -3 for x and evaluate.
We have:
[tex]\begin{gathered} x\text{ + 11 = -3 + 11 = 8} \\ \\ x+11=8 \end{gathered}[/tex]• 16. y - (-5)
Substitute 8 for y and evaluate.
We have:
[tex]\begin{gathered} y\text{ - (-5) = 8 - (-5) = 8 + 5 = 13} \\ \\ y\text{ - (-5) = 13} \end{gathered}[/tex]• 18. ,-8 ÷ y
Substitute 8 for y and evaluate
We have:
[tex]-8\div y=-8\div8\text{ = }-1[/tex]ANSWER:
xz = 12
x + 11 = 8
y - (-5) = 13
-8 ÷ y = -1
the measure of two consecutive angles in a parallelogram are in a 13:7 ratio. What is the measure of the acute angle in the parallelogram
In a parallelogram, consecutive angles are supplementary angles.
Let a and b be two consecutive angles in a parallelogram, so that their ratio is 13:7. Then:
[tex]\frac{a}{b}=\frac{13}{7}[/tex]Since they are supplementary angles, then:
[tex]a+b=180[/tex]Isolate a from the first equation and substitute the expression for a in the second equation:
[tex]\begin{gathered} a=\frac{13}{7}b \\ \frac{13}{7}b+b=180 \\ \Rightarrow\frac{20}{7}b=180 \\ \Rightarrow b=\frac{7}{20}\times180 \\ \Rightarrow b=63 \end{gathered}[/tex]The value of a can be calculated from any of the equations from the value of b, and turns out to be equal to 117.
From the angles 117° and 63°, the acute angle is 63°.
Therefore, the measure of the acute angle in the parallelogram, is:
[tex]63^{\circ}[/tex]a surveyor standing 58 M from the base of a building measures the angle to the top of the building and finds it to be 39 degrees. the surveyor then measures the angle to the top of the radio tower on the building and find that it is 48°. how tall is the radio tower .
First, let's calculate the height to the top of the building:
Thereby,
[tex]\begin{gathered} \tan 39=\frac{B}{58}\rightarrow B=58\tan 39 \\ \Rightarrow B=46.97m \end{gathered}[/tex]Now, let's calculate the height to the top of the radio tower:
This way,
[tex]\begin{gathered} \tan 48=\frac{T}{58}\rightarrow T=58\tan 48 \\ \Rightarrow T=64.42 \end{gathered}[/tex]Substracting both heights, we'll get that:
[tex]64.42-46.97=17.45[/tex]The radio tower is 17.45 m tall.
17. How many solutions does thesystem of equations have?4x + 5y = 65y + 4x = 8A one solutionB) two solutionsC infinitely many solutionsno solution
we have the following:
[tex]\begin{gathered} 4x+5y=6 \\ 5y+4x=8 \end{gathered}[/tex]solving:
[tex]\begin{gathered} 4x+5y=6 \\ x=\frac{6-5y}{4} \end{gathered}[/tex]replacing:
[tex]\begin{gathered} 5y+4\cdot\frac{6-5y}{4}=8 \\ 5y+6-5y=8 \\ 6=8 \end{gathered}[/tex]therefore, the system no solutions
The probability that a customer will order a nonalcoholic beverage is .48b. Find the probability that in a sample of 12 customers, at least 5 will order a nonalcoholic beverage. (Round your answer to 4decimal places.)
Given:
probability of ordering non-alcoholic beverage = 0.48
probability of not ordering non-alcoholic beverage = 1 - 0.48 = 0.52
FInd: the probability that in a sample of 12 customers, at least 5 will order a nonalcoholic beverage.
Solution:
Recall the binomial probability formula.
[tex]P(x)=nCr\times p^r\times q^{n-r}[/tex]where
p = probability of success: 0.48
q = probability of failure: 0.52
n = the number of samples: 12
r = number of success (at least 5 which means not 1, 2, 3, or 4.
To determine the probability of having at least 5, let's calculate when r = 0, r = 1, r = 2, r = 3, and r = 4.
Let's start with r = 0 and solve.
[tex]P(0)=_{12}C_0\times0.48^0\times0.52^{12}[/tex][tex]\begin{gathered} P(0)=1\times1\times0.000390877 \\ P(0)=0.000390877 \end{gathered}[/tex]At r = 1,
[tex]P(1)=_{12}C_1\times0.48^1\times0.52^{11}[/tex][tex]\begin{gathered} P(1)=12\times0.48^\times0.000751686 \\ P(1)=0.0043297 \end{gathered}[/tex]Now, let's solve for r = 2.
[tex]P(2)=_{12}C_2\times.48^2\times.52^{10}[/tex][tex]\begin{gathered} P(2)=66\times.2304\times.00144555 \\ P(2)=0.02198 \end{gathered}[/tex]Moving on to r = 3.
[tex]P(3)=_{12}C_3\times0.48^3\times0.52^9[/tex][tex]\begin{gathered} P(3)=220\times0.110592\times0.0027799 \\ P(3)=0.067636 \end{gathered}[/tex]Then, lastly at r = 4.
[tex]P(4)=_{12}C_4\times0.48^4\times0.52^8[/tex][tex]\begin{gathered} P(4)=495\times0.05308\times0.00534597 \\ P(4)=0.14047 \end{gathered}[/tex]Let's now add the probability of getting r = 0, r = 1, r = 2, r =3, and r = 4 customers ordering a nonalcoholic beverage.
[tex]P(0)+P(1)+P(2)+P(3)+P(4)[/tex][tex]0.0043297+0.02198+0.067636+0.14047=0.2344157[/tex][tex]0.000390877+0.0043297+0.02198+0.067636+0.14047=0.2348[/tex]0.2348 is the probability of at most 4 customers ordering a non-alcoholic beverage.
Since the question is the probability of at least 5 customers ordering a non-alcoholic beverage which is the opposite of the at most 4 customers, then, let's subtract its probability from 1.
[tex]1-0.2348=0.7652[/tex]Therefore, the probability that in a sample of 12 customers, at least 5 will order a nonalcoholic beverage is approximately 0.7652.
Math scores for two classes are shown in the box plot below. A. What is the median score of class AB. What is the interquartile range of class B?See question and box plot in attached photo.
Let's put more details in the given question to better understand the problem:
Let's now answer the questions:
A. What is the median score of class A?
Based on the given box plot, the median score of Class A is 73.
The answer is 73.
B. What is the interquartile range of class B?
For us to get the interquartile range, we will be using the following formula:
[tex]\text{ Interquartile range = Q}_3\text{ - Q}_1[/tex]In the given box plot for Class B, the following are observed:
Q3 = 87
Q1 = 79
Therefore, the interquartile range will be:
[tex]\text{ Interquartile range = 87 - 79 = 8}[/tex]The interquartile range of Class B is 8.
The answer is 8.
Consider the following statistical series number of children per household:1) Establish a table with the modalities, numbers, absolute and relative frequencies2)Represent the distribution by a stick diagram from the ni (numbers), then the fi(fréquency)
1) The values to consider to make the table are the number of children.
The frequencies are the number of times each value occurs.
To find the relative frequencies, we have to divide each frequency by the total amount of households surveyed.
value frequency relative frequency
0 30 0.1 = 30/300
1 45 0.15= 45/300
2 15 0.05 = 15/300
3 60 0.2 = 60/300
4 90 0.3 = 90/300
5 60 0.2 = 60/300
total = 300
2) The stick diagram is: