Answer:
a. The sum of an odd and an even integer is odd: 3 + 2 = 5
b. The sum of two odd integers is an even integer: 3 + 5 = 8
c. The square of an odd integer is an odd integer: 3² = 9
d. . The product of two odd integers is an odd integer.: 3 x 5 = 15
Step-by-step explanation:
Proving the following statements using a direct proof;
a. The sum of an odd and an even integer is odd:
let the odd integer = 3
let the even integer = 2
3 + 2 = 5
5 is an odd integer, proved
b. The sum of two odd integers is an even integer.
let the first odd integer = 3
let the second odd integer = 5
3 + 5 = 8
8 is an even integer, proved
c. The square of an odd integer is an odd integer. .
let the odd integer = 3
3² = 9
9 is an odd integer, proved
d. The product of two odd integers is an odd integer.
let the first odd integer = 3
let the second odd integer = 5
3 x 5 = 15
15 is an odd integer, proved
Answer:
a. The sum of an odd and an even integer is odd: 3 + 2 = 5
b. The sum of two odd integers is an even integer: 3 + 5 = 8
c. The square of an odd integer is an odd integer: 3² = 9
d. . The product of two odd integers is an odd integer.: 3 x 5 = 15
Step-by-step explanation:
Proving the following statements using a direct proof;
a. The sum of an odd and an even integer is odd:
let the odd integer = 3
let the even integer = 2
3 + 2 = 5
5 is an odd integer, proved
b. The sum of two odd integers is an even integer.
let the first odd integer = 3
let the second odd integer = 5
3 + 5 = 8
8 is an even integer, proved
c. The square of an odd integer is an odd integer. .
let the odd integer = 3
3² = 9
9 is an odd integer, proved
d. The product of two odd integers is an odd integer.
let the first odd integer = 3
let the second odd integer = 5
3 x 5 = 15
15 is an odd integer, proved
Help ASAP!!!.
Simplify the expression:
2x + 1 + 7x
3/4x-4=5/6
Rewrite so it doesn’t have any fraction
HELP ME ASAP!!! I WILL MARK BRAINLIEST!!
PLEASE MIDDLE SCHOOL MATH NEED HELP!!!! THIS IS URGENT 13 POINTS TO FULL ANSWER!!!
I bought 7 1/3 pounds of apples from Store A and 9 2/6 pounds of apples from Store B. I made apple sauce using 2 1/2 pounds of apples, how many pounds do I have left?
Answer:
14 1/6
Step-by-step explanation:
7(1/3)+ 9(2/6)= 16(2/3)
16(2/3)
16(2/3)-2(1/2)= 14(1/6)
Answer:
14 1/6
Step-by-step explanation:
7 + 9 =16
convert 2/6 = 1/3
1/3 +1/3=2/3+16=
16 2/3 -2 1/2=
a bottle of hand lotion is on sale for $2.25. if this price represents a 50% discount from the original price, what is the original price to the nearest cent?
Answer:
4.50
Step-by-step explanation:
2.25 plus 2.25 aka half
Please answer these giving brainliest to the first right person. 20 points.
Answer:
31.x>2
32.x<-2
33.x<5
34.x>0
Step-by-step explanation:
if you rolled two dice, what is the probability that you would roll a sum of 2
Answer:
2.78%
Step-by-step explanation:
Theres only one number combination you could get for the sum of 2 ( 1 and 1) but there is 36 different outcomes on the 2 dice that you could get for all the numbers.
1/36=.02777.. =.0278 but since its a percentage you move it over 2x to the right from the decimal point which would give you 2.78%
Line s has a slope of -7/2 line t is perpendicular to a. What is slope of line t
Answer: 2/7
Step-by-step explanation:The slope of perpendicular lines are opposite reciprocals
If 30% of the pupils in a school are boys, what percentage of the pupils are girls?
Answer:
70%
Step-by-step explanation:
An ordered pair that satisfies all the equations in a linear system of equations is called a(n) __________ of the linear system.
Answer:solution
Step-by-step explanation:
An ordered pair that satisfies all the equations in a linear system of equations is called a: solution of the linear system.
A linear function is a function that has a positive relationship between its variables.
Hence, an increase in one variable (input variable) causes an increase in the other variable (output variable) because the variables are directly proportional.
Mathematically, the graph of a linear function is a straight-line and its slope is always constant.
On a related note, a linear system of equation is an algebraic equation of the first order with two variables and each of its term having an exponent of one.
Generally, a system of linear equations in two variables must have at least two solution.
In conclusion, a solution of the linear system is an ordered pair that satisfies all the equations in a linear system of equations.
Read more: https://brainly.com/question/24085666
PLZ HURRY IT'S URGENT!!
What is the slope of the line?
x=−8
options:
undefined
-8
1
0
Answer:
im pretty sure it's -8
Answer:
undefined
Step-by-step explanation:
the line goes straight down
A regional office of the Internal Revenue Service randomly distributes returns to be audited to the pool of auditors. Over the thousands of returns audited last year, the average amount of extra taxes collected was $356 per audited return. One of the auditors, Jeffrey Jones, is suspected of being too lenient with persons whose returns are being audited. For a simple random sample of 30 of the returns audited by Mr. Jones last year, an average of $340 in extra taxes was collected.
Required:
Assuming a normal population of extra taxes collected with a standard deviation of $90, do the suspicions against Mr. Jones appear to be justified?
Answer:
The decision rule is
Fail to reject the null hypothesis
The conclusion is
There is sufficient evidence to conclude that the justification against Mr. Jones appears not to be justified
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = \$ 356[/tex]
The sample size is n = 30
The sample mean is [tex]\= x = \$340[/tex]
The standard deviation is [tex]\sigma = \$ 90[/tex]
The null hypothesis is [tex]H_o : \mu = \$ 35 6[/tex]
The alternative hypothesis is [tex]H_a : \mu \ne \$ 35 6[/tex]
Let assume the significance level is [tex]\alpha = 0.05[/tex]
Generally the test statistic is mathematically represented as
[tex]t = \frac{\= x - \mu }{\frac{\sigma }{\sqrt{n} } }[/tex]
=> [tex]t = \frac{ 340 - 356 }{\frac{90 }{\sqrt{30} } }[/tex]
=> [tex]t =-0.9737 [/tex]
Generally the sample size from the question is small that it is not greater than 30 hence we use t-test
Now the degree of freedom is mathematically represented as
[tex]df = n- 1[/tex]
=> [tex]df = 30- 1[/tex]
=> [tex]df= 29[/tex]
Generally the p-value is mathematically represented as
[tex]p-value = 2 P (t > -0.9737 )[/tex]
Generally from the t-distribution table , the probability of -0.9737 at a degree of freedom of [tex]df= 29[/tex] for a two -tailed test is
[tex]P (t > -0.9737 ) = 0.33825793[/tex]
Hence p-value is
[tex]p-value = 2*0.33825793[/tex]
[tex]p-value = 0.676 [/tex]
From the value we obtained we see that [tex]p-value > \alpha[/tex] hence
The decision rule is
Fail to reject the null hypothesis
The conclusion is
There is sufficient evidence to conclude that the justification against Mr. Jones appears not to be justified
The average of 4,-8,6,14,-3 is
Answer: The average is 2.6
Step-by-step explanation:
The average is the same as the mean so to find the mean of the numbers add them up and divide it by the number of values.
(4) + (-8) + (6) + ( 14) + (-3) = 13
13/5 = 2.6
For each of these intervals, list all its elements or explain 2.1 Sets 131 why it is empty. a) [a,a] c) (a, a] e) (a,b), where a > b b) [a,a) d) (a, a) f) [a,b],wherea>b
Answer: b
Step-by-step explanation:
You decide to purchase a bond for $500. It pays 5% simple interest per year and matures in 5 years. How much interest will you earn once the bond matures? Round your answer to the nearest dollar.
Do NOT round until you have calculated your final answer.
Answer:
$625
Step-by-step explanation:
You start with $500
The interest per year is 5% or 500 x 0.05 = $25
If it matures 5 years and each year has an increase of $25 then
Year 1 - $525
Year 2 - $550
Year 3 - $575
Year 4 - $600
Year 5 - $625
Answer:
Step-by-step explanation:
We express the interest rate r in decimal form, so we have r=5%=5100=0.05. The principal is P=500 and the time in years is t=5. So, the interest is I=Prt=(500)(0.05)(5)=$125. The interest earned is $125.
The students can make 6 tickets from each sheet of paper. How many sheets of paper. How many sheets of paper are needed for 125 tickets?
Answer:
21 sheets of paper
Step-by-step explanation:
If its basically 6 tickets to a piece of paper then you just divide 125 tickets by 6 and get 20.833.... Then your round to the nearest sheet which is 21.
Hope this helps!
Answer:
Approx. 21 sheets of paper
Step-by-step explanation:
1 sheet of paper is used to make 6 tickets
6 tickets = 1 sheet
If 1 sheet is used to make 6 tickets. The number of sheets used to make 125 tickets will more.
if
6 tickets = 1 sheet
125 tickets = (125÷6) × 1
= 20.83333333333
Mr. Javier purchased a number of pencils for ₱180 and sold all except 6 at a profit of ₱2 per pencil. With the total amount received, he could buy 30 more items than before. Find the number of items he bought and the cost of each in pesos
Answer:
36 pencils
[tex]Cost = 0.2[/tex]
Step-by-step explanation:
Given
Cost Price = 180
Represent the number of items by x
This implies that the cost of each item is [tex]\frac{x}{180}[/tex]
[tex]Selling\ Price = Cost + Profit[/tex]
[tex]Selling\ Price = \frac{x}{180} + 2[/tex]
Since all but 6 items were sold, the total selling price is:
[tex]Total = (x - 6)(\frac{x}{180} + 2)[/tex]
This amount can be used to buy 30 more items.
So, we have:
[tex](x - 6)(\frac{x}{180} + 2) = x + 30[/tex]
Multiply both sides by 180
[tex]180 * (x - 6)(\frac{x}{180} + 2) =180(x + 30)[/tex]
[tex](x - 6)(x + 360) = 180x + 5400[/tex]
Expand brackets
[tex]x\² + 360x - 6x - 2160 = 180x + 5400[/tex]
[tex]x\² + 354x - 2160 = 180x + 5400[/tex]
Equate to 0
[tex]x\² + 354x - 180x - 2160 - 5400 = 0[/tex]
[tex]x\² + 174x - 7560 = 0[/tex]
Expand
[tex]x\² + 210x - 36x - 7560 = 0[/tex]
[tex]x(x + 210) - 36(x + 210) = 0[/tex]
[tex](x - 36)(x + 210) = 0[/tex]
[tex]x - 36 = 0[/tex] or [tex]x + 210 = 0[/tex]
[tex]x = 36[/tex] or [tex]x = -210[/tex]
Since, number of items can't be negative, we have to discard x = -210.
Hence:
[tex]x = 36[/tex]
We can then conclude that, Mr. Javier purchased 36 pencils
Recall that
[tex]Cost = \frac{x}{180}[/tex]
[tex]Cost = \frac{36}{180}[/tex]
[tex]Cost = 0.2[/tex]
Parker invests $1000 for 5 years at a simple rate of 10%.
A. How much interest will Parker earn after 5 years?
B. What will be the total amount that Parker will have after 5 years?
Answer:
SI=PTR/100
= 1000×5×10/100
=$500
Parker will receive $500 as interest.
Amount=$500+$1000
=$1500
Parker will have $1500 altogether.
If A and B are independent events, which equation must be true?
Α.
P(B/A) = P(A)
B.
P(B/A) = P(B)
C.
P(B/A) = P(A) P(B)
D.
P(B/A) = P(A) + P(B)
Answer:
B. P(B/A)=P(B)
what are the slopes of the two different lines? are they undefined?
Answer:
m = (y2 -- y1) / (x2 -- x1)
Step-by-step explanation:
Find the product of (18k+ 2m)(m + k)
Answer:
18k^2+2m^2+20km
Step-by-step explanation:
Vickie bought 54 tickets for a ride at an amusement park.each ride cost 3 tickets and Vickie has been on x rides so far.which expression to the number of tickets that Vickie has left?
Answer: 18
Steps: 54/3=18
1 8
3/54
-3
24
-24
0
dai is comparing how many trading cards he has with friends Maura
Answer:
ok
Step-by-step explanation:
Solve for x and y in the equation.
xy=80 and log x - 2 log y =1
9514 1404 393
Answer:
(x, y) = (40, 2)
Step-by-step explanation:
Taking the antilog of the second equation, we have ...
x/y^2 = 10
x = 10y^2
Substituting this into the first equation gives ...
(10y^2)y = 80
y^3 = 8 . . . . . . . . divide by 10
y = 2 . . . . . . . . . . cube root
x = 10·2^2 = 40
The solution is (x, y) = (40, 2).
Greatest common factor of 81
Answer:
81
Step-by-step explanation:
I just looked it up :)
Answer:
27
Step-by-step explanation:
Please help! Number 7 and 8 don't forget to put the graph points thank you!
Answer:
Step-by-step explanation:
7- is (0,1)(1,3)
8- is(-3,0)(-3,0)
Multiply 3/5 by 10/21 Express your answer in simplest form
Answer:
2/7
Step-by-step explanation:
Answer:
3/5 * 10/21= 2/7
What is the product of-3 and-13? Enter your answer as a mixed number, in simplified fom, in the box
Answer:
39
Step-by-step explanation:
-3x(-13) = 39.
If this question was asking for something different I apologize.
what is the population of A politician is interested in the proportion of voters in his district who think he is doing a good job. Define the following in terms of the study. Give examples where appropriate.
Answer:
lovely peachlings
Step-by-step explanation:
an object is thrown upward at a speed of 74 feet per second by a machine from a height of 18 feet off the ground. The height h of the object after t seconds can be found using the equation h=-16t^2+74t+18
Answer:
First part:
Set h(t) = 73 and solve for t.
-16t2 + 64t + 16 = 73
-16t2 + 64t - 57 = 0
Solve this quadratic equation for t. You should get 2 positive solutions. The lower value is the time to reach 73 on the way up, and the higher value is the time to reach 73 again, on the way down.
Second part:
Set h(t) = 0 and solve the resulting quadratic equation for t. You should get a negative solution (which you can discard), and a positive solution. The latter is your answer.
Step-by-step explanation: