The sum of two numbers is 130 and their difference is 34 Let x be the first number and y be the second
number Set up a system of equations and use the elimination method to find the numbers. You must
show your work
10. A theater sold 800 tickets for Friday night's performance, One child ticket costs $4.50 and one adult
ticket costs $6.00. The total amount collected was $4.500. How many of each type of ticket were sold?
11. The postal service offers flat-rate shipping for priority mail in special boxes. Malia shipped 4 small
boxes and 2 medium boxes, which cost her $54 to ship. Meanwhile, Stephen shipped 1 small box and
2 medium boxes, and paid $33. How much does it cost to ship these two sizes of boxes?
Answers
Step-by-step explanation:
9)=
By the question:-
x + y = 130-i
x - y = 34-ii
Now,
Add i and ii,
x + y + x -y = 164
or, 2x = 164
so, x = 82
Now,
x -y = 34
or, 82 - y = 34
so, y = 48
The numbers are 82 and 48.
10) =
Let adults ticket be x and childs ticket be y.
x + y = 800
x = 800 - y - eqn i
4.5x + 6y = 4500
Substituting x's value from eqn i,
4.5(800-y) + 6y = 4500
or, 3600 - 4.5y + 6y = 4500
or, 1.5y = 900
so, y = 600
Now,
x + y = 800
or, x + 600 = 800
so, x = 200
Hence, 600 adult tickets were sold and 200 child tickets were sold.
11)=
Let cost of one small box be x and one medium box be y.
So,
4x + 2y = 54-eqn i
x + 2y = 33-eqn ii
subtracting eqn i from ii,
x + 2y - 4x - 2y = - 21
or, -3x = - 21
so, x = 7
Now,
x + 2y = 33
or, 2y = 33 - 7
or, y = 26/2
so, y = 13
So, cost of one small box is $7 and medium box is $13.
Related Questions
I need help with this Question.
Answers
The number of quarts in 12 L is 12.684 qt.
Given that, 12 L to qt.
What is metric conversion?Metric Conversion refers to the conversion of the given units to desired units for any quantity to be measured.
Here,
There are 1.057 quarts in a liter, and there are 0.946 liters in a quart.
Now, 12 L=12×1.057
= 12.684 qt
Therefore, the number of quarts in 12 L is 12.684 qt.
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Select the values that make the inequality
Answers
The answer is -4, -1, 1, 3, 3.9, 3.99, 3.999.
Given,
In the question:
To see the figure:
To select the values that makes the inequality s ≤ 4 true.
Number table are given in figure.
To see the figure and analysis.
Now, According to the question;
To make the inequality s ≤ 4 true.
The selected value must be less than 4 {Properties of Inequality}
The values are sorted from small to large:
So, The answer is -4, -1, 1, 3, 3.9, 3.99, 3.999.
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Pixel A is located 80 km from the Jacksonville radar. How many seconds did it take for the radar pulse to travel to the target at Pixel A and return to the radar? (It will be a very small answer!)
C= 3 × 10^8 m s−1
R= 80,000
R= CT/2
Answers
[tex]C=3\times 10^8~\frac{m}{s}\hspace{5em}R=80000\implies R=8\times 10^4 \\\\[-0.35em] ~\dotfill\\\\ R=\cfrac{CT}{2}\implies 2R=CT\implies \cfrac{2R}{C}=T\implies \cfrac{2(8\times 10^4)}{3\times 10^8}=T \\\\\\ \cfrac{16\times 10^4}{3\times 10^8}=T \implies \cfrac{16}{3}\times\cfrac{10^4}{10^8}=T\implies \cfrac{16}{3}\times\cfrac{1}{10^8\cdot 10^{-4}}=T \\\\\\ \cfrac{16}{3}\times\cfrac{1}{10^{8-4}}=T \implies \cfrac{16}{3\times 10^4}=T\implies \cfrac{16}{30000}=T\implies \cfrac{1}{1875}=T[/tex]
Neema bought appliances costing $3725 at a store charging 5% add-on interest. She made a $700 down payment and agreed to monthly payments over four years. Find the total cost, for the appliances plus
interest.
The total cost for the appliances plus interest is $
(Type an integer or decimal.)
Answers
The total cost for the appliances plus interest is 4330.
What is an interest rate?
The amount a lender charges a borrower is called an interest rate, and it is expressed as a percentage of the principal or the loaned amount. Typically, a loan's interest rate is expressed as an annual percentage rate, or APR.
Here, we
Cost of the appliance = $3725
Neema paid $700 so amount financed = $3725 - $700 = $3025
Interest rate on the loan = 3025*0.05*4 = $605
Total cost of the appliance = $3725 + 605 = $4330
Hence, the total cost for the appliances plus interest is 4330.
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Examine the worked examples. Then, answer the questions.
Alessa's car uses 2 gallons of gas to drive 45 miles.How many miles can
Alessa's car drive using 15 gallons of
Answers
Answer:
Alessa's car would be able to drive 337.5 miles with 15 gallons of gas.
Find the value of the expression:
3x^0 for x=2.6
Answers
Answer:
1
Step-by-step explanation:
We don't even need to calculate 3 x 2.6 considering any number raised to the power of zero equals 1.
3x ≥5 or -3/5x-3>7 solve the compound inequality
Answers
By using the concept of linear inequation, the required solution is
[tex]x > \frac{5}{3} \ or \ x < -\frac{50}{3}[/tex]
What is linear inequation?
Inequation shows the comparision between two algebraic expressions by connecting the two algebraic expressions by [tex]> , < . \geq, \leq[/tex]
A one degree inequation is known as linear inequation.
Here the given linear inequation is
[tex]3x \geq 5 \ or \ \frac{-3}{5}x -3 > 7[/tex]
Now
[tex]3x \geq 5 \ or \ \frac{-3}{5}x -3 > 7\\\\x \geq \frac{5}{3} \ or \ \frac{-3}{5} x > 7 + 3\\\\x \geq \frac{5}{3} \ or \ \frac{-3}{5}x > 10\\\\x > \frac{5}{3} \ or \ x < \frac{10 \times 5}{-3}\\\\x > \frac{5}{3} \ or \ x < -\frac{50}{3}[/tex]
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A bag of fertilizer covers 3000 square feet of lawn. Find how many bags of fertilizer should be purchased to cover a rectangular lawn 290 feet by 170 feet. To cover the lawn bags of fertilizer are required
Answers
Answer: The correct answer is 17 bags of fertilizer to cover the lawn
Step-by-step explanation:
1 bag of fertilizer covers 3000 SF of lawn
How many bags are needed for an area of 290 feet x 170 feet
Calculate the Square Feet:
290 x 170 = 49,300 SF
Divide space (SF) by bag coverage (SF):
49,300 / 3,000 = 16.43 bags of fertilizer
Round up answer to 17 bags of fertilizer
Essay for operation of sets
Answers
What is Set Theory Formula?
The set formula is given in general as n(A∪B) = n(A) + n(B) - n(A⋂B), where A and B are two sets and n(A∪B) shows the number of elements present in either A or B and n(A⋂B) shows the number of elements present in both A and B.
In a set theory, there are three major types of operations performed on sets, such as: Union of sets (∪) Intersection of sets (∩) Difference of sets (–)
Set Operations include Set Union, Set Intersection, Set Difference, Complement of Set, and Cartesian Product of Set
Set Union
The union of sets A and B (denoted by A ∪ B) is the set of elements that are in A, in B, or in both A and B. Hence, A ∪ B = { x | x ∈ A OR x ∈ B }.
n(A∪B) = n(A) + n(B) − n(A∩B)
Set Intersection
The intersection of sets A and B (denoted by A ∩ B) is the set of elements which are in both A and B. Hence, A ∩ B = { x | x ∈ A AND x ∈ B }.
n(A∩B) = n(A)+n(B)−n(A∪B)
Set Difference
The set difference of sets A and B (denoted by A - B) is the set of elements that are only in A but not in B. Hence, A - B = { x | x ∈ A AND x ∉ B }.
Complement of a Set
The complement of a set A (denoted by A’) is the set of elements which are not in set A. Hence, A' = { x | x ∉ A }. More specifically, A'= (U - A) where U is a universal set that contains all objects.
The complement of a universal set is an empty set U′ = ϕ. The complement of an empty set is a universal set ϕ′ = U.
Cartesian Product / Cross Product
The Cartesian product of n number of sets A1, A2, ... An denoted as
A1 × A2 ... × An can be defined as all possible ordered pairs
De-Morgan's Law - The De Morgan's law states that for any two sets A and B, we have (A ∪ B)' = A' ∩ B' and (A ∩ B)' = A' ∪ B'
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Tina has 5345 beads . She has 3687 fewer beads than her sister . How many beads does her sister have ?
Answers
Answer:
Her sister has 9032 beads
Step-by-step explanation:
All you have to do is Tina's beads plus the extra number of beads that her sister has
5345 + 3687 = 9032
Solve the following 2(x + 3) = x - 4
Answers
Answer:
x = - 10
Step-by-step explanation:
2(x + 3) = x - 4
==> distribute the 2
2x + 6 = x - 4
==> subtract 6 from both sides
2x = x - 10
==> subtract x from both sides
x = - 10
Which equation below represents the Exponent Property of Logs?
Answers
The only equation given that represents the Exponent Property of Logs is; Option A: log(A^r) = r*log(A)
How to find the exponent property of logarithm?The exponent property of logarithm says that the log of a power is the exponent times the logarithm of the base of the power. For example;
logₐ(MN) = logₐM + logₐN
logₐ(M/N) = logₐM - logₐN
logₐ(3²) = 2logₐ3
The first example above shows the product rule of logarithms
The second example shows the quotient rule of logarithms
The third rule shows the power rule
Now, looking at the options, the only one that shows the correct pattern of exponent property of logarithm is;
Option A: log(A^r) = r*log(A)
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Hank rents 9 cases of plates.He has 250 guests attending the banquet. There are 30 plates in each case. Did Hank rent enough plates? Explain
Answers
Answer:
yup
Step-by-step explanation:
so to find the amount of plates he has we :
30*9 = 270
How many guests :
250
Hank has 20 extra plates,
hope this helps :)
How will the mode be affected if the outlier is removed from the data set below? 58, 60, 53, 54, 60, 35, 58, 60
will the mode decrease?
will the mode not change?
is there not enough information?
will the mode increase?
Answers
The mode will not change.
Given data,
58,60,53,54,60,35,58,60
Outlier is the value in a set of data that much higher or lower than other values in data.
from given data, outlier is 35.
Mode is the value in a set of data that occurs more frequently in set of data.
from given data, 60 occurs more frequently.
Hence, 60 is the mode of data.
If outlier is removed from the data set then it will not affect the mode of the data
Thus, the mode will not change.
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Which equation represents this statement?
3 times the sum of 4 and a number is 18.
O 3 +4n = 18
O 3n+ 4 = 18
O 3.4+ n = 18
O 3 (n+4)= 18
Answers
The equation represents the statement "3 times the sum of 4 and a number is 18 " is option (D) 3(n+4) = 18
The statement is
3 times the sum of 4 and a number is 18
The equation is the the mathematical statement the represents the relationship between two expression or variables with an equal sign.
Consider the unknown number = n
Sum of 4 and the number = n + 4
3 times the sum of 4 and the number = 3(n + 4)
3 times the sum of 4 and a number is 18
3(n + 4) = 18
Hence, the equation represents the statement "3 times the sum of 4 and a number is 18 " is option (D) 3(n+4) = 18
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Fill in the blank, rounding the result to exactly three significant digits when necessary
81 m = ___ ft
Answers
3. One batch of pancakes needs 1 1/4 cups of pancake mix. One box has 9 cups of pancake mix How many batches of pancakes can be made with one box of pancake mix?
Answers
A company that most adults would erase all of their personal data online if they could. In order to test this claim, a GFI Software Survey of 565 randomly selected adults showed that 59% of them would erase all of their personal information online if they could.
A. State the null and alternative hypotheses (in symbols).
B. Explain what a Type 1 and a Type 2 error would be in this case.
C. State the conclusion if the null hypothesis is rejected.
D. State the conclusion if the null hypothesis is not rejected.
Answers
a) The null and alternative hypothesis are given as follows:
Null: [tex]H_0: p \leq 0.5[/tex]Alternative: [tex]H_1: p > 0.5[/tex]b) The errors are given as follows:
Type I: A sample which gives enough evidence that most people would erase the data, if in reality they wouldn't.Type II: A sample in which the proportion of people that would erase their data isn't significantly above 50%, when in fact it is.c) The conclusion of a rejected null hypothesis is: There is enough evidence that most adults would erase their data if they could.
d) The conclusion of a not rejected null hypothesis is: There is not enough evidence that most adults would erase their data if they could.
What are the hypothesis tested?At the null hypothesis, it is tested if there is not enough evidence that most adults would erase all of their personal data online if they could, that is, if the proportion is not greater than 50%, hence:
[tex]H_0: p \leq 0.5[/tex]
At the alternative hypothesis, it is tested if there is enough evidence that they would erase the information, that is, if the proportion is greater than 50%, hence:
[tex]H_1: p > 0.5[/tex]
A rejected null hypothesis means that the alternative hypothesis is accepted, that is, there is enough evidence that most adults would erase their data if they could.
A not rejected null hypothesis, conversely, means that there is not enough evidence that most adults would erase their data if they could.
What are type I and type II errors?Type I errors are when a true null hypothesis is rejected. Hence, the context of this problem, it would mean a sample which gives enough evidence that most people would erase the data, if in reality they wouldn't.
Type II errors are when a false null hypothesis is not rejected. Hence, the context of this problem, it would mean a sample in which the proportion of people that would erase their data isn't significantly above 50%, when in fact it is.
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help me 10 pnts thanks so much
Answers
The expression 3.2^2 - 1 and 10 - 0.33 * 2 should be joined by less than to form an inequality
What is inequality?Inequality refers to a way of representing relationships between variables at the left hand side of equation to the variables to the right hand side of an equation.
The signs used in inequality are of 4 types namely
less thangreater thanless than or equal togreater than or equal toThe given expression is solved as follows
3.2^2 - 1
= 10.24 - 1
= 9.24
10 - 0.33 * 2
= 10 - 0.66
= 9.34
The two expressions can be joined as below
9.24 < 9.34
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find the smallest value of an expression
(without using a calculator)
[tex]\bf\sqrt{(x-8)^2+(y+4)^2} +|y+3x|[/tex]
Answers
Step-by-step explanation:
to eliminate the always positive absolute value at the end let's set y = -3x
that makes the absolute value term = 0 in all cases.
then we have
sqrt((x - 8)² + (-3x + 4)²)
the x-value that makes this a minimum result also makes
(x - 8)² + (-3x + 4)²
a minimum.
x² - 16x + 64 + 9x² - 24x + 16
10x² - 40x + 80
the x that makes this a minimum, also makes
x² - 4x + 8
a minimum.
we get the extreme value as zero of the first derivative :
0 = 2x - 4
4 = 2x
x = 2
so, we get the minimum of all these expressions for x = 2.
as y = -3x, we get y = -3×2 = -6.
the minimum value for the expression is with
x = 2
y = -6
so, the minimum value is
sqrt((2 - 8)² + (-6 + 4)²) + |-6 + 3×2| =
= sqrt((-6)² + (-2)²) + |-6 + 6| =
= sqrt(36 + 4) + 0 =
= sqrt(40) = 6.32455532...
what the area and pelase explain give brainly points
Answers
Answer: 10 squares
Step-by-step explanation:
The answer for the area is 10 squares but I’m not sure that’s what they’re asking for.
can anyone help with this
Answers
Answer:
bla blablablablabla
Step-by-step explanation:
blablablablablabla
what is:
s . s + 0.5s . s
if s=8.2
Answers
Answer:
100.86
Step-by-step explanation:
8.2*8.2+0.5(8.2)*8.2
manuel wishes to purchase 25cent and 30 cent stamps. he decides to buy 10 fewer 30 cent stamps. How many of each can he buy for no more than $19.00
Answers
Using the simplification, Manuel buy 15 stamps of 25 cents and 5 stamps of 30 cent.
In the given question,
Manuel wishes to purchase 25 cent and 30 cent stamps.
He decides to buy 10 fewer 30 cent stamps.
We have to find how many of each can he buy for no more than $19.00.
Let he buy x stamps of 25 cent.
He want to buy 10 fewer 30 cent stamps.
So he buy x−10 stamps of 30 cent.
But he have to buy total stamps of $19.
So the equation is
x+x−10 = 19
Simplifying
2x−10=19
Add 10 on both side
2x−10+10=19+10
2x=29
Divide by 2 on both side
2/2 x =29/2
x=14.5
x≈15
Hence, he buy 15 stamps of 25 cent.
Now finding the number of 30 cent.
he buy x−10 stamps of 30 cent.
So 15−10=5.
So he buy 5 stamps of 30 cent.
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Pam has worked for the same employer for 5 years. Her current salary is $73,500
which is 122.5% of her starting salary. What was Pam's starting salary?
Answers
What was Pam's starting salary?
Pam's current salary for 5 years = $73.500
Her salary went up for 122.5% in 5 years.
a = her starting salary
First, we will make an equation of this problem.
Let's use a as the symbol of her starting salary
equation that we are going to use
73500 = 122.5% x a
Next, we move a to the left and we want to divide 73500 with 122.5%
a = 73500 / (122.5/100)
Next, we want to divide 73500 with 1.225 since we've done dividing 122.5 with 100
a = 73500 / 1.225
a = 60000
Finally, we got the answer of Pam's starting salary was $60.000
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Amanda has 5 office assistants. If A is the event that at least 4 of them are men and B is the event that at least 4 of them are women, are A and B mutually exclusive?
Choose the correct answer below.
O No
Yes
Answers
A and B are mutually exclusive events
The correct answer is yes
What are mutually exclusive events?
Two events are mutually exclusive in statistics and probability theory if they cannot happen simultaneously. A coin toss is the most basic illustration of two events that cannot coexist. The result of tossing a coin can be either heads or tails, but neither outcome can happen at the same time.
We are given that Amanda has 5 office assistants.
Events A is the event that at least 4 of them are men. this means that there is at most 1 female assistant
Events B is the event that at least 4 of them are women. this means that there is at most 1 male assistant.
Now one of the conditions is possible but both at the same time is not possible
Hence the both events are mutually exclusive.
The correct answer is yes
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What line is perpendicular to the line y= -1/2x + 8
Answers
Answer: y=2x+8
Step-by-step explanation:
you take the reverse of the slope being 2 including the negative.
Current Year Previous Year
Occupied Rooms 1,512 1,458
Total Rooms 1,800 1,800
Answers
The proportions of the total rooms that were occupied each year are:
The current year is 84%.The previous year is 81%.What is the proportion?Proportion is the fractional value of a variable when compared to the whole.
Proportions show the ratio or relative relationship between two or more values set as equal.
Like ratios, proportions are depicted in fractions, decimals, or percentages to show how two values compare.
Current Year Previous Year
Occupied Rooms 1,512 1,458
Total Rooms 1,800 1,800
Proportion of occupied rooms = 84% 81%
(1,512/1,800 x 100) (1,458/1,800 x 100)
Thus, on average, room occupancy for the two years is 82.5%, and proportionately for each year, it is 84% for the current year, while the previous year recorded 81%.
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Question Completion:What proportion of the total rooms were occupied each year?
Amount Desired at End of Period
$17,600.00
Length of Time
7
1. Period Used
2. Rate Used
23. PV factor used
3 4. PV of amount desired at end of period
Rate
2%
Compounded
Quarterly
Required:
Complete the following using the information above and the present value Table 12.3
or the present value table in the Business Math Handbook or the present value
formula to answer the following:
Note: Use cells A2 to D3 from the given information to complete this question.
Answers
A percentage is a number or ratio expressed as a fraction of . It is often denoted using the percent sign, "%" and PV factor used is 0.62026 .
Hence,
The amount desired at end of a period is $9400.
The length of time is 4 years .
The rate is 2%.
Compounded is monthly.
The period used is 48.
The rate used is 1%.
The PV factor used is 0.62026 .
The PV of the amount desired at the end of the period is $5830.45
What is the percentage?
A percentage is a number or ratio expressed as a fraction of . It is often denoted using the percent sign, "%".
Here from the question,
PV factor = (1 + i) ----(1)
where, i = 12/12 % , i =1
and
n = 4(12)
n = 48
Substituting the values in the equation , we get
PV factor = (1 + 0.01)^ -48
PV factor = 0.62026
Hence,
the amount desired at end of a period is $9400.
The length of time is 4 years.
The rate is %.
Compounded is monthly.
The period used is 48 .
The rate used is 1%.
The PV factor used is 0.62026.
The PV of the amount desired at the end of the period is $5830.45
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You might need: Calculator
Solve for a.
Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.
4x +49x+8
Answers
Explanation:
Collect like terms by adding their coefficients (4+49)x +8
Add the numbers 53x+8
Hope this helps:)
