The number of advance and same day tickets sold are 25 and 35 respectively.
How many tickect of each were sold?let
number of advance tickets sold = xNumber of same day tickets sold = yx + y = 65
25x + 30y = 1800
From (1)
x = 65 - y
Substitute x = 65 - y into (2)
25x + 30y = 1800
25(65 - y) + 30y = 1800
1625 - 25y + 30y = 1800
5y = 1800 - 1625
5y = 175
y = 175/5
y = 35
Substitute y = 35 into (1)
x + y = 65
x + 35 = 65
x = 65 - 35
x = 25
Therefore, Simultaneous equation is used to determine the number of advance and same day tickets sold.
25 advance tickets and 35 same day tickets were sold.
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Which quadrant includes every points with a positive x-coordinate and a negative y-coordinateA) Quadrant IB) Quadrant IIC) Quadrant IIID) Quadrant IV
Hello!
Let's write some information about each quadrant:
Quadrant I:
x > 0 and y > 0
Quadrant II:
x < 0 and y > 0
Quadrant III:
x < 0 and y < 0
Quadrant IV:
x > 0 and y < 0
Answer:Alternative D) Quadrant IV
Tutorial ExerciseSimplify.✓98 + 8Step 1Simplify each term.V 98 + V8 = 172.2 + 237X V2 + V222= 7✓ 2 + 2V 2Submit Skip (you cannot come back)Need Help?Watch it
Expanding the expressions,
[tex]\sqrt[]{49\cdot2}\text{ +}\sqrt[]{2\cdot2\cdot2}[/tex][tex]\sqrt[]{7^2\cdot2}\text{ + }\sqrt[]{2^3}[/tex][tex]\sqrt[]{7^2}\text{ }\times\sqrt[]{2}\text{ +}\sqrt[]{2^2}\text{ }\times\sqrt[]{2}[/tex][tex]\begin{gathered} 7\times\sqrt[]{2}\text{ +2}\times\sqrt[]{2} \\ 7\sqrt[]{2}\text{ + 2}\sqrt[]{2} \\ =9\sqrt[]{2} \end{gathered}[/tex]Hence, in the boxes where you have the term missed, the correct answer to put there is:
[tex]\sqrt[]{7^2\text{ }}\text{not }\sqrt[]{7}[/tex]I need the correct answer i have 1 more chance at the question and i must complete 100% mastery to get credit for my homework
Given:
The equation is
[tex]2x^{\frac{5}{3}}-18x=0[/tex]Required:
Find the non-zero solution to the equation.
Explanation:
The given equation is
[tex]2x^{\frac{5}{3}}-18x=0[/tex]Rewrite the equation as:
[tex]2x^{\frac{5}{3}}=18x[/tex]Divide both sides by 2.
[tex]x^{\frac{5}{3}}=9x[/tex]Take cube on both sides.
[tex]\begin{gathered} (x^{\frac{5}{3}})^3=(9x)^3 \\ x^5=729x^3 \\ x^5-729x^3=0 \end{gathered}[/tex]Take out common x
[tex]x^3[/tex][tex]x^3(x^2-729)=0[/tex]Find the factor by using the formula
[tex]a^2-b^2=(a-b)(a+b)[/tex][tex]\begin{gathered} x^3(x-27)(x+27)=0 \\ x=0,27,-27 \end{gathered}[/tex]Final Answer:
Thus the non-zero solutions to the given equation are x =27, -27.
Find the mean, variance, and standard deviation for the data set. 19,11,21,9,15
Given:
The dataset : 19, 11, 21, 9, 15
Mean
The sum of the values divided by the number of values.
[tex]\begin{gathered} mean\text{ = }\frac{\sum_^x}{n} \\ =\text{ }\frac{19\text{ + 11 + 21 +}9\text{ + 15}}{5} \\ =\text{ }\frac{75}{5} \\ =\text{ 15} \end{gathered}[/tex]The mean is 15
Variance
Variance is a measure of dispersion, meaning it is a measure of how far a set of numbers is spread out from their average value.
[tex]\begin{gathered} variance\text{ = }\frac{\sum^(x-x*)^2}{n-1} \\ =\text{ }\frac{(19-15)^2\text{ + \lparen11-15\rparen}^2+(21-15)^2\text{ +}(9-15)^2\text{ + \lparen15-15\rparen}^2\text{ }}{5-1} \\ =\text{ 26} \end{gathered}[/tex]The variance is 26
Standard deviation
The standard deviation is square root of the variance
[tex]\begin{gathered} \sigma\text{ = }\sqrt{26} \\ =\text{ 5.099} \\ \approx\text{ 5.10} \end{gathered}[/tex]The standard deviation is 5.10
Let Ln denote the left-endpoint sum using n subintervals. Compute the indicated left sum for the given function on the indicated interval. (Round your answer to four decimal places.) L4 for f(x) = 1/x-1on [3, 4] L4 =
The indicated left sum for the given function on the indicated interval, the value L4 for f(x) = 1/x-1on [3, 4] L4 = 0.7595.
Let Ln denote the left-endpoint sum using n sub intervals.
We are given that
[tex]f(x) = \frac{1}{x-1}[/tex] [3,4]
We have to find L4
It means n = 4
x = [tex]\frac{b-a}{n} = \frac{4-3}{4} = \frac{1}{4}[/tex] = 0.25
Now, intervals are
[3, 3.25], [3.25, 3.50], [3.5, 3.75], [3.75, 4]
Now,
[tex]L_{4} = f(x_{0}) \triangle x+f(x_{1})\triangle x +f(x_{2})\triangle x+f(x_{3})\triangle x\\ \\ L_{4} = \frac{1}{3-1} (0.25)+\frac{1}{3.25-1}(0.25)+\frac{1}{3.5-1}(0.25)+\frac{1}{3.75-1}(0.25)\\ \\ L_{4} = 0.7595[/tex]
Hence the answer is the indicated left sum for the given function on the indicated interval, the value L4 for f(x) = 1/x-1on [3, 4] L4 = 0.7595.
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In a bakery, the ratio of fruit scones to cheese scones is 3:4.
a) Given that there are 24 cheese scones, how many fruit scones are there?
b)
If 6 fruit scones were sold, what would be the new ratio of fruit scones to cheese scones?
Answer:
a) 18 and b)1:2
Step-by-step explanation:
for a i divided 24 by 4 (24:4) and got 6 the i multiplied 3 by 6 and got 18. also you could do a proportion and fruit scones would be x so you have to calculate x. if you don't know how to do proportions you can ask me i can explain.
for b since i got the count was 18:24. i took away those six from 18 and got with the ratio 12:24. i divided both sides by twelve and got 1:2
Answer:
a) 18 fruit scones
b) 6:8
Step-by-step explanation:
a) The ratio is 3:4 given that there 3 fruit scones to 4 cheese scones so if there are 24 cheese scones, 24/4=6, 3*6=18 so there 18 fruit scones.
b) The ratio is 3:4 given that there 3 fruit scones to 4 cheese scones so if there are 6 fruit scones, 6/3=2, 2*4=8 so there are 8 cheese scones. The new ratio would be 6:8
15)The demand equation for a certain product is given by the formulap = 32-10.0001x+1where x is the number of units sold in a month and p is the price perunit. If the price is set at $14.75 for the month, how many units will be sold?
The demand equation is given to be:
[tex]p=32-\sqrt{0.0001x+1}[/tex]where p is the price and x is the number of units sold.
If the price per unit is $14.75, the number of units will be calculated as follows:
[tex]\begin{gathered} p=14.75 \\ \therefore \\ 14.75=32-\sqrt{0.0001x+1} \end{gathered}[/tex]Subtracting 32 from both sides, we have:
[tex]\begin{gathered} -\sqrt{0.0001x+1}=14.75-32 \\ -\sqrt{0.0001x+1}=-17.25 \end{gathered}[/tex]Multiply both sides by -1:
[tex]\sqrt{0.0001x+1}=17.25[/tex]Square both sides:
[tex]\begin{gathered} 0.0001x+1=17.25^2 \\ 0.0001x+1=297.5625 \end{gathered}[/tex]Subtract 1 from both sides:
[tex]\begin{gathered} 0.0001x=297.5625-1 \\ 0.0001x=296.5626 \end{gathered}[/tex]Divide both sides by 0.0001:
[tex]\begin{gathered} x=\frac{296.5625}{0.0001} \\ x=2965625 \end{gathered}[/tex]The number of units sold will be 2,965,625 units.
2. Booker's father sells computer software and earns a 4.25% commission on every software package he sells. How much commission would he earn on a software package that sold for $15,725? Round to the nearest cent. (Example 1)
To solve the exercise you can use a rule of three, like this:
[tex]\begin{gathered} \text{\$}15,725\rightarrow100\text{\%} \\ \text{\$}x\rightarrow4.25\text{\%} \\ x=\frac{4.25\text{\%}\cdot\text{ \$15,725}}{100\text{\%}} \\ x=\text{ \$}\frac{4.25\cdot\text{15,725}}{100} \\ x=\text{ \$}\frac{68831.25}{100} \\ x=\text{ \$668.31} \end{gathered}[/tex]Therefore, the commission earned will be $668.31.
What is 100 times 95 times 38
Answer: 361000
Step-by-step explanation:
Riddle this: i am a four digit number my thousands digit is 1 more than 0. my hundreds digit is odd, but less than 3.my tens digit is even, but more than 7. my ones digit is 5. who am i? am i an even or odd number?
Answer:
Step-by-step explanation:
you are 1185 and you are an odd number.
Solve by using Substitution: 3x-y=13 2x +2y = -10
multiply: 1/6 (-3/7) answer in simplest form
1/6 (-3/7)
[tex]\frac{1}{6}\cdot\frac{-3}{7}=\frac{-3}{6\cdot7}=\frac{-3}{2\cdot\text{ 3 }\cdot\text{ 7}}=\frac{-1}{2\cdot7}=\frac{-1}{14}[/tex]Answer:
-1 /14
[tex]\frac{-1}{14}[/tex]6x2−2x=0
The 1st x is to the 2nd power
Answer:
x = 0 x = 1/3
3) Sketch a graph, labelling and scaling the axes, of the line y = 2x – 3.
y = 2x - 3
Put x = 0 and solve
y = 2(0) - 3
y = 3
We have a point (0, 3)
Put y = 0 and solve for x
0 = 2x - 3
2x = 3
x = 3/2
x = 1.5
The second point is (1.5, 0)
Below is the graph
Question 13A neighborhood association surveyed its residents regarding marital status and living situation. The results are in the table. What is the probabilitythat a resident is married given that the person owns their home?TotalOwns a Home150Rents a Home17032080250330173SingleMarriedDivorcedWidowedTotal53373201205059087910O050을拉茲结印0
This question is a conditional probability question
P(B|A) means Event B given Event A
In other words, event A has already happened, now what is the chance of event B?
From the given question
let
B = the event that a resident is married.
A = the event that the person owns their home.
So
Thus
[tex]P(B\text{/A)=}\frac{80}{320}=\frac{1}{4}[/tex]Donna makes $10.50 each hour she works at her job how much money does she make for 15.75 hours of work round your answer to the nearest cent
To solve this problem, multiply Donna's earnings per hour by the number of hours of work. This is $10.50 times 15.75.
[tex]10.50\cdot15.75=165.375\approx165.38[/tex]She makes $165.38 for 15.75 hours of work.
11. a $58 video game is on sale for a 14% discount. what is the price with the discount
As given by the question
There are given that the price of the video games is $58.
Now,
According to the question, there are given that 14% discount on their game price
So,
The price with discount is:
[tex]58\times\frac{14}{100}=8.12[/tex]Then,
[tex]58-8.12=49.88[/tex]Hence, the price with the discount is $49.88
Use the diagram below in the following given information to prove the opposite size of a parallelogram are congruent
Given:
ABCD is a parallelogram.
To prove:
[tex]AD\cong BC\text{ and AB}\cong CD[/tex]Proof:
[tex]\begin{gathered} \text{ABCD is a parallelogram}\ldots\ldots\text{ given.} \\ DC\parallel AB\text{ and AD}\parallel BC\ldots\ldots..by\text{ definition of parallelogram} \\ \angle\text{DCA congruent to }\angle\text{BAC; }\angle BCA\text{ congruent to }\angle DAC\ldots\ldots\text{.}AI\text{ angles theorem} \\ AC\cong AC\ldots.\text{ reflexive property} \\ \Delta ADC\cong\Delta CBA\ldots.by\text{ ASA} \\ AD\cong BC\text{ and AB}\cong CD\ldots\ldots by\text{ CPCTC} \end{gathered}[/tex]
Hence proved.
Arsenia has 80 movie posters and 40 band posters. She plans to sell 24 movie posters. She says that if she
also sells 24 band posters, the ratio of movie posters to band posters stays the same. Is that true? Why or
why not? Complete the explanation.
No. Arsenia's statement is not true because if it was true then before and after selling the posters, the ratio have to be same which is 2:1.
Given,
Arsenia has 80 movie posters and 40 band posters
She plans to sell 24 movie posters and 24 band posters.
Number of remaining movie posters =80-24=56
Number of remaining band posters=40-24=16
Ratio of movie posters and band posters before selling,
[tex]80:40=2:1[/tex]
Ratio of movie posters and band posters after selling,
[tex]56:16=7:2[/tex]
Thus, Arsenia's statement is not true because if it was true then before and after selling the posters, the ratio have to be same which is 2:1
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Solve for X: 3. (7x - 1) 125 Submit Question
Answer:
From the given figure;
[tex](7x-1)^0=125^0[/tex]Reason: Alternate angle.
Solving for x;
[tex]\begin{gathered} 7x-1=125 \\ 7x=125+1 \\ 7x=126 \\ x=\frac{126}{7} \\ x=18 \end{gathered}[/tex]Therefore, the value of x is;
[tex]x=18[/tex]1_<2x-4
1.-5
2.-1
3.7
Which of the following values are solutions to the inequality
Answer:
VB B.
Step-by-step explanation:
B.
Some of the children at a nursery arrive by car.
. 40% of the children at the nursery are boys.
70% of the boys at the nursery arrive by car.
• 60% of the girls at the nursery arrive by car.
What is the probability that a child chosen at random from the nursery arrives by car?
Answer:
Will assume that there are 100 kids.
100 x 40% =40 of them are boys
40 x 70% = 28 boys arrive by car.
100 - 40 = 60 - Number of girls in Nursery.
60 x 60% = 36 of them arrive by car.
28 boys + 36 girls = 64 - kids that arrive by car.
64 / 100 = 64% - probability of a randomly picked kid that he/she arrived by car.
If a spring is stretched 10cm by a weight of 8kg how much will it be stretched by 3kg
The amount of string that can be stretched by 3 kg weight is 5/ 4× 3
= 15 / 4 = 3.75 cm
Given ; The string is attached to a weigh whose weight is 8 kg
the length of the string which is being stretched is 10 cm
The amount of string that can be stretched by 3 kg weight can be calculated by unitary method
According to the unitary method ;
the string when attached to a 1 kg weight the length will be = 10 / 8 = 5 /4
Thus the amount of string that can be stretched by 3 kg weight is 5/ 4× 3
= 15 / 4 = 3.75 cm
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a movie theater is having a special. if a group of four pays $7.25 each for the tickets, each person can get popcorn and a drink for $5.75. use the expression 4(5.75 + 7.25) to find the total cost for 4 friends.
The total cost for the 4 friends will be $52.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
A group of four pays $7.25 each for the tickets, each person can get popcorn and a drink for $5.75.
Now,
Since, a group of four pays $7.25 each for the tickets, each person can get popcorn and a drink for $5.75.
Hence, We can formulate;
The total cost = 4 (5.75 + 7.25)
= 23 + 29
= 52
Thus, The total cost for the 4 friends will be $52.
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Kim places $1,250 into a bank account that pays 4.25% simple interest. if she does not add or remove any money from the account, how much interest will she earn after 60 months (anwers must be written as money-rounded to the hundred to the place)
The rule of the simple interest is
[tex]I=P\times R\times T[/tex]P is the initial amount
R is the rate in decimal
T is the time in years
Since Kim places $1250, then
P = 1250
Since the rate is 4.25%, then
[tex]R=\frac{4.25}{100}=0.0425[/tex]Since the time is 60 months, divide it by 12 to change it to years
[tex]\begin{gathered} T=\frac{60}{12} \\ T=5 \end{gathered}[/tex]Substitute them in the rule above
[tex]\begin{gathered} I=1250\times0.0425\times5 \\ I=265.625 \end{gathered}[/tex]Round it to the nearest hundredth
I = $265.63
A cheeseburger it’s twice the price of a slice of pizza and order of three cheeseburgers and four slices of pizza is $15 right in the Quetion for for the green information
Answer: 45+x = 45x
Step-by-step explanation:
A recording company obtains the blank cds used to produce its labels from three compact disk manufacturers: i, ii, and iii. The quality control department of the company has determined that 3% of the compact disks produced by manufacturer i are defective, 4% of those produced by manufacturer ii are defective, and 2% of those produced by manufacturer iii are defective. Manufacturers i, ii, and iii supply 36%, 52%, and 12%, respectively, of the compact disks used by the company. What is the probability that a randomly selected label produced by the company will contain a defective compact disk?.
The probability that a randomly selected label produced by the company will contain a defective compact disk is 0.034.
How to calculate the probability?In this, it should be noted that there are 3 possible cases in the chosen disc can be from any of the manufacturing companies, so the total probability will be the sum of probabilities of getting a faulty disc from companies 1-3.
The probability from company 1 will be;
= 0.03*0.36
The probability from company 2 will be:
= 0.04*0.52
The probability from company 3 will be:
= 0.02*0.12
The total probability will now be:= (0.36*0.03)+(0.04*0.52)+(0.02*0.12)
= 0.0108 + 0.0208 + 0.0024
= 0.034
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Simplify the expression 2n/6n+4 times 3n+2/3n-2
Answer:11n^3/9-2n^2/3+44n/3-8Step-by-step explanation:
Step-by-step explanation:
Given parallelogram ABCD, diagonals AC and BD intersect at point E. AE=2x, BE=y+10, CE=x+2 and DE=4y−8. Find the length of BD.A. 18B. 32C. 16D. 6
For the given parallelogram, the diagonals AC and BD intersect at point E. That means;
[tex]\begin{gathered} BE=DE \\ \text{Also,} \\ AE=CE \end{gathered}[/tex]Substitute for the given values and we'll have;
[tex]\begin{gathered} BE=DE \\ y+10=4y-8 \\ \text{Collect all like terms and you'll have;} \\ y-4y=-8-10 \\ -3y=-18 \end{gathered}[/tex]Divide both sides by -3 and you'll have;
[tex]\begin{gathered} \frac{-3y}{-3}=\frac{-18}{-3} \\ y=6 \end{gathered}[/tex]Note that line segment BD is made up of;
[tex]\begin{gathered} BD=BE+DE \\ BD=(y+10)+(4y-8)_{} \\ BD=y+10+4y-8 \\ BD=4y+y+10-8 \\ BD=5y+2 \\ \text{When y=6, we now have} \\ BD=5(6)+2 \\ BD=30+2 \\ \text{BD}=32 \end{gathered}[/tex]Therefore, the answer is option B
13+v+2v=v+3+4combine like termsmove letters to the leftwhat's left?add or subtract constantwhat's left?divide coefficientanswer
13+v+2v=v+3+4
Combine like terms
13+3v=v+7
Move letters to the left
13+3v-v =7
13+2v=7
Subtract constant
2v=7-13
2v=-6
divide both side by 2
2v/2 = -6/2
v = -3