Answer:
x= -2
y= -1
z= -3
Step-by-step explanation:
x-y= -1 (1)
x+z= -5 (2)
y-z= 2 (3)
(1)+(3)==> x-z= 1 (4)
(4)+(2)==> 2x= -4 ==> x= -2
we replace x by its value in equation (2):
-2+z= -5 ==> z= -3
we replace z by its value in equation (3):
y-(-3)= 2 ==> y+3=2 ==> y= -1
guys help me I really need your help
Answer:
a x^2/2 is a polynomial because the power of x is 2 which is a positive whole number but 2/x^2 is not a polynomial because the power of x is -2 which is negative whole number.
b.in
[tex] \sqrt{2 x} [/tex]
the power if x will be
[tex]x {}^{ \frac{1}{2} } [/tex]
which is not a whole number so it is not a polynomial.
but in
[tex] \sqrt{2} x[/tex]
the power if x is a positive whole number.so it is a polynomial.
c.the greatest power of variable of the term is called degree of polynomial
A popular brand of pen is available in 13 colors and 2 writing tips. How many different choices of pens do you have with this brand?
There are ___ different choices of pens with this brand.
Answer:
7
Step-by-step explanation:
i had it
Find the domain of the function.
f (x) =2/5x+4
Answer:
(-∞,∞)
Step-by-step explanation:
Answer:
The domain of the function is (-∞, ∞)
hope this helps!
Each marble bag sold by Debra's Marble Company contains 8 yellow marbles for every 4 blue marbles. If a bag has 56 yellow marbles, how many blue marbles does it contain?
Answer:
28 blue marbles
Step-by-step explanation:
yellow: blue
8 4
To get to 56 yellow marbles multiply by 7
yellow: blue
8*7 4*7
56 28
There will be 28 blue marbles
Factor the following expressions completely. Show and check all work on your own paper.
x^2+169
Factor the following expressions completely. Show and check all work on your own paper.
5x^2-50x+125
Factor the following expressions completely. Show and check all work on your own paper.
100x^2-25y2
Answer:
See the expressions and the answers below
Step-by-step explanation:
Given data
The first expression is given as
x^2+169 .-> we can not factorize the expression anymore
The second expression
5x^2-50x+125
5(x^2-10x+25)
The third expression
100x^2-25y2
25(4x^2-y^2)
What is the smallest positive three-digit number that is a multiple of 4 and whose digits' sum is 23?
Answer:
the number is 788......
PLEASE HELP ME
An expression is shown below:
6x^2y − 3xy − 24xy^2 + 12y^2
Part A: Rewrite the expression by factoring out the greatest common factor. (4 points)
Part B: Factor the entire expression completely. Show the steps of your work. (6 points)
9514 1404 393
Answer:
(3y)(2x^2 -1x -8xy +4y)(3y)(x -4y)(2x -1)Step-by-step explanation:
Part A: All of the coefficients have a common factor of 3. All of the variable products have a common factor of y, so the greatest common factor of all terms is 3y. The expression can be written as ...
(3y)(2x^2 -1x -8xy +4y)
__
Part B: The remaining factor can be factored pairwise:
3y(x(2x -1) -4y(2x -1)) = 3y(x -4y)(2x -1)
Four students each ran 100 m in a 400-m relay race. The team’s total was 49.44 seconds. Find the average time of each runner.
the average time of each runner is 12.36
Answer:
12.36 seconds
Step-by-step explanation:
Total time = 49.44 seconds
Students = 4
Average = 49.44/4 = 12.36 seconds
Answered by GAUTHMATH
Find the first five terms of the sequence..
Answer:
The Next fiver tems are - 2, -2,-8,-12,-16
Step-by-step explanation:
Answer:
2,-6,2,-6,2
Step-by-step explanation:
a1 = 2
an = -an-1 -4
Let n =2
a2 = -a1 -4 = -2-4 = -6
Let n=3
a3 = -a2 -4 = - (-6) -4 = +6 -4 = 2
Let n = 4
a4 = -a3 -4 = -2 -4 = -6
Let n=5
a5 = -a4 -4 = -(-6) -4 = +6-4 = 2
a Merchant of New York bought some goods from Nepal worth Rs 55680 if 1 dollar = rs 72.50 and £1= Rs 128 if by sending money through London he saves 19.80 Dollars find the rate of exchange between new York and London?
Answer:
$1.85 = £1
Step-by-step explanation:
55680/72.50 = 786
55680/128 = 435
435x = (786 + 19.80)
x = 805.8/435
x = 1.85
Answer:
£1 = $1.72
Step-by-step explanation:
55680/72.50=768
55680/128=435
768.00 - 19.80 = 748.20
x = 748.20 / 435
x = $1.72
Integrate the following. ∫[tex]84dx[/tex]
Answer:
[tex]\displaystyle \int {84} \, dx = 84x + C[/tex]
General Formulas and Concepts:
Calculus
Integration
IntegralsDefinite/Indefinite IntegralsIntegration Constant CIntegration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \int {84} \, dx[/tex]
Step 2: Integrate
[Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int {84} \, dx = 84\int {} \, dx[/tex][Integral] Reverse Power Rule: [tex]\displaystyle \int {84} \, dx = 84x + C[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integrations
When a teacher in a private school points out to her high school principal that since there are empty seats in all classrooms, the cost of additional students is really zero, she is using the
Answer:
The answer is "Principal of marginal analysis".
Step-by-step explanation:
To determine unless the benefits of even an aggressive resource would outweigh its costs, and therefore increase utility, individuals and businesses can use a valuation model to compare the risks versus the benefits of more activities, like whether to create or consuming more. It's the amount during which net value is greater than or equal to marginal cost that's the optimal quantity in this situation. The amount where the marginal social cost curve and consumer surplus line connect.
How many minutes in 4 hours
Answer: 240 minutes
Step-by-step explanation:
Concept:
Here, we need to know the idea of unit conversion.
Unit conversion is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors.
1 hour = 60 minutes
Solve:
1 hour = 60 minutes
4 hours = 4 × 60 = 240 minutes
Hope this helps!! :)
Please let me know if you have any questions
Please help! Thank you.
Answer:
B at -1 minus we go to - ∞
at -1 plus we to + ∞
Step-by-step explanation:
x^2 -x
g(x) = ---------
x+1
Factor out x
x(x-1)
g(x) = ---------
x+1
As x is to the left of -1
x is negative (x-1) is negative
x+1 will be slightly negative
g(-1 minus) = -*-/ - = - and we know that the denominator is very close to zero we are close to infinity so we go to - ∞
As x is to the right of -1
x is negative (x-1) is negative
x+1 will be slightly positive
g(-1 plus) = -*-/ + = + and we know that the denominator is very close to zero we are close to infinity so we go to ∞
The chi-square test statistic is χ2 = 18.68 and the P-value is between 0.0025 and 0.005. What conclusion should the researcher make? Use α = 0.05.
We don't know what the exact p-value is, but we are told that it's as large as 0.005 which is smaller than alpha = 0.05
Since the p-value is smaller than alpha, this means we reject the null hypothesis.
The way you can remember this is "if the p-value is low, then the null must go". By "low", I mean "smaller than alpha".
Recall that the p-value is the probability of observing that specific test statistic, or larger. So the chances of chi-squared being 18.68 or larger is a probability between 0.0025 and 0.005; there's a very small chance of this happening. The p-value is based entirely on the assumption that the null is correct. But if the null is correct, then the chances of landing on this are very small. We have a contradiction that basically leads to us concluding the null must not be the case. It's not 100% guaranteed of course, but it's fairly strong evidence.
In short, the p-value being smaller than alpha = 0.05 means we reject the null.
In order to accept the null, the p-value must be 0.05 or larger.
You play a game where you roll a single die. You pay $1 to play, and the payouts are $0.50 if you roll an
even number, $2 if you roll a 1, and $1 if you roll a 3 or 5. What are the odds for winning money if you play this game? Show your work and Explain.
Let W be the random variable representing your winnings from playing the game. Then
[tex]P(W=w)=\begin{cases}\text{prob. of rolling an even number}=\frac12&\text{if }w=\$0.50-\$1=-\$0.50\\\text{prob. of rolling a 1}=\frac16&\text{if }w=\$2-\$1=\$1\\\text{prob. of rolling 3 or 5}=\frac13&\text{if }w=\$1-\$1=\$0\\0&\text{otherwise}\end{cases}[/tex]
In short, you have a 1/6 chance of profiting from the game, and a 5/6 chance of losing money. So the odds of winning are (1/6)/(5/6) = 1/5 or 1 to 5.
Solve the following equation for
g
g. Be sure to take into account whether a letter is capitalized or not.
Answer:
q/N = g
Step-by-step explanation:
q = Ng
Divide each side by N
q/N = Ng/N
q/N = g
WILL GIVE BRAINLIEST!!!!!!! A boy had 20 cents. He bought x pencils for 3 cents each. If y equals the number of pennies left, write an equation showing the dependence of y on x. What is the domain of the function?But it says that x is a whole number for the domain. PLS HELP.
Answer:
Hey there!!
The total number of cents - 20
Cost for each pencil - 3 cents
Number of pencils bought - ' x '
y = number of pennies left
What is the domain ?
Show how y is dependent on x ..
Let's get this into an equation :
... The total cost for x pencils bought = 3x
... Number of pennies left = 20 - 3x
... y = number of pennies left
... y = 20 - 3x
Notice : If the x value changes, the y value changes too
... If x = 1 , then , y = 17; If x = 2 , then , y = 14
Hence, we could say y is dependent upon x
Domain = ?
... Remember - The total number of pennies = 20 ; hence, the total cost cannot go above 20 cents.
Hence, we will have to work with inequalities
The equation :
... 20 ≥ 3x
Divide 3 on both sides
20 / 3 ≥ x
x ≥ 6.667
Let's take this as 6
Hence , the domain will be :
D : { 1 , 2 , 3 , 4 , 5 , 6 }
Hope my answer helps!
The table gives Josh's probabilities of scoring in various ranges on a par-70 course in a given round, find the probability of the event. par or above х Below 60 60 64 65 69 70 74 75 79 80 84 85 89 90 94 95 99 100 or above P(x) 003 007 016 0 28 020 0.12 007 003 003 0.01
The probability of the event. par or above is 0.74
Using the table in the question as reference, we are to calculate the probability of an event par or above.
This probability is represented as: P(par or above)
The par value from the question is:
[tex]par = 70[/tex]
So, the required probability is:
[tex]P(par\ or\ above) = P(x \ge 70)[/tex]
This mean that we consider scores that are 70 and above
So, the formula to use is:
[tex]P(par\ or\ above) = P(70-74) + P(75 -79) +..... + P(100\ or\ above)[/tex]
Using the data from the question, the equation becomes
[tex]P(par\ or\ above) = 0.28+ 0.20 +0.12+ 0.07+ 0.03+ 0.03+ 0.01[/tex]
[tex]P(par\ or\ above) = 0.74[/tex]
Read more at:
https://brainly.com/question/16693319
Answer:
The probability of Josh scoring par or above is 0.75.
Step-by-step explanation:
Find where par is on the table (70-74). Since it is par or above, you would take the probabilities of par and all numbers higher than par. Add them together, and you have your answer.
(.29) + (.21) + (.11) + (.08) + (.02) + (.03) + (.01) = 0.75
**I attached a screenshot of the table and the correct answer
good luck! <3
Which shows the image of rectangle ABCD after the rotation () (W)?
13
VA
1
V
Answer:
Graph (1)
Step-by-step explanation:
Given rule for the rotation of a figure is,
A(x, y) → A'(-y, x)
This rule defines the rotation of point A by 90° counterclockwise about the origin.
Coordinates of point A → (-2, 0)
Coordinates of point C → (-1, 0)
Following the rule of rotation,
A(x, y) → A'(-y, x)
A(-2, 0) → A'(0, -2)
C(-1, 4) → C'(-4, -1)
Now search the image points from the graphs attached,
Graph (1) will be the answer.
In a random sample of seven aerospace engineers, the sample mean monthly income is $6824 and the sample standard deviation is $340. Construct a 95% confidence interval for the population mean. Assume that the monthly incomes are normally distributed.
Answer:
The 95% confidence interval for the population mean is ($6510, $7138).
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom,which is the sample size subtracted by 1. So
df = 7 - 1 = 6
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 6 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.4469.
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.4469\frac{340}{\sqrt{7}} = 314[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 6824 - 314 = $6510.
The upper end of the interval is the sample mean added to M. So it is 6824 + 314 = $7138.
The 95% confidence interval for the population mean is ($6510, $7138).
Which matrix equation represents the system of equations?
Answer:
B. [tex]\left[\begin{array}{ccc}-1&2\\0&1\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right] =\left[\begin{array}{ccc}0\\-2\\\end{array}\right][/tex]
Step-by-step explanation:
Given the systems of equations
-x + 2y = 0
y = -2
This can also be written as:
-x + 2y = 0
0x + y = -2
We are to write in this form AX = b
A is a 2by2 matrix with coefficients of x nd y
X is a column matrix containing the unknown
b is a column matrix with the values at the right hand sides (0 and -2)
Writing in matrix form;
[tex]\left[\begin{array}{ccc}-1&2\\0&1\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right] =\left[\begin{array}{ccc}0\\-2\\\end{array}\right][/tex]
A certain test preparation course is designed to help students improve their scores on the LSAT exam. A mock exam is given at the beginning and end of the course to determine the effectiveness of the course. The following measurements are the net change in 5 students' scores on the exam after completing the course: 16, 21, 22, 12, 22
Using these data, construct a 90% confidence interval for the average net change in a student's score after completing the course. Assume the population is approximately normal. Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
Answer:
The critical value used is [tex]T_c = 2.132[/tex]
The 90% confidence interval for the average net change in a student's score after completing the course is (14.357, 22.843).
Step-by-step explanation:
Before building the confidence interval, we need to find the sample mean and the sample standard deviation.
Sample mean:
[tex]\overline{x} = \frac{16+21+22+12+22}{5} = 18.6[/tex]
Sample standard deviation:
[tex]s = \sqrt{\frac{(16-18.6)^2+(21-18.6)^2+(22-18.6)^2+(12-18.6)^2+(22-18.6)^2}{4}} = 4.45[/tex]
Confidence interval:
We have the standard deviation for the sample, so the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom,which is the sample size subtracted by 1. So
df = 5 - 1 = 4
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 4 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 2.132. The critical value used is [tex]T_c = 2.132[/tex]
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.132\frac{4.45}{\sqrt{5}} = 4.243[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 18.6 - 4.243 = 14.357
The upper end of the interval is the sample mean added to M. So it is 18.6 + 4.243 = 22.843.
The 90% confidence interval for the average net change in a student's score after completing the course is (14.357, 22.843).
Pls help
Q.2 Choose the correct alternative for each question.
1. 400 is successor of ______.
A. 399 B.401 C. 398 D. 402
(1 Marks each)
2. The product of a non-zero whole number and its predecessor is always_________.
A. an odd number B. an even numberC. 0 D. a prime number
KHALSA LITTLE FLOWER SCHOOL | GRADE 6 | Mathematics 1
3. The predecessor of 1 million is ___________.
A. 99999 B. 1000001 C. 2000000 D. 999999
4. Whole numbers are closed under ________.
A. addition and subtraction B. addition and multiplication C. addition and division D. subtraction and division
5. The only whole number which does not have a predecessor is ________. A.2 B.0 C.3 D.1
6. ________ million make 1 crore.
A. 100 B. 10 C. 1000 D. 10,000
7. 3856 is rounded off to the nearest tens as ______.
A. 3850 B. 3860 C. 3800 D. 3000 8. In Roman numerals, the symbol ______ can be repeated.
A. D B. V C. X D. L
9. The Roman numeral for 91 is _______.
A. IXLL B. CXI C. IXC D. XCI
10. The Roman numeral LV stands for _______.
A. 65 B. 45 C. 55 D. 105
Answer:
Step-by-step explanation:
1-399
2 C
3-A 99999
4a
5b
7 b
8 C
9D
10c
the line parallel to 5x-3y=15 and containing (5,7)
what is the equation of the line?
Answer:
3y=5x-4
Step-by-step explanation:
As the lines are parallel, the slope will be 5/3. The equation of line will be y=(5/3)*x-4/3. 3y=5x-4
Which of the following is equivalent to 5 + 5x > 8(x-1) ?
-3x > -12
3x 13
3x < 6
-4X > -12
5+5x>8(x-1)
5+5x>8x-8
5x-8x>-8+5
-3x>-3
5 + 5x > 8(x-1) is equivalent to -3x > -13.
How to estimate the equivalent function to 5 + 5x > 8(x-1) ?Let, the expression be 5 + 5x > 8(x-1)
By applying Multiplicative Distribution Law, we get
5 + 5x > 8x - 8
Rearrange unknown terms to the left side of the equation, then
5x - 8x > -8 - 5
Combine like terms, we get
-3x > -8 - 5
Calculate the sum or difference
-3x > -13
Divide both sides of the inequality by the coefficient of the variable, then we get
[tex]$x < \frac{-13}{-3}$[/tex]
Determine the sign for multiplication or division:
[tex]$x < \frac{13}{3}$[/tex]
Therefore, the correct answer is -3x > -13.
Complete question:
Which of the following is equivalent to 5 + 5x > 8(x - 1)?
-3x > -12
3x < 13
3x < 6
-4x > -12
To learn more about algebraic expression
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Andre owns a computer backup service. He charges his customers $2.50 for each backup CD. His expenses include $875 for the CD recording equipment and $0.35 for each blank CD. Which equation could Andre use to calculate his profit p for the recording of n CDs?
Answer:
[tex]p =2.15n - 875[/tex]
Step-by-step explanation:
Given
[tex]CD_s= n[/tex]
[tex]Charges = 2.50[/tex] per CD
Expenses
[tex]E_1 = 875[/tex]
[tex]E_2 = 0.35[/tex] per CD
Required
The profit (p)
First, calculate the total income on n CDs
[tex]Total = Charges * n[/tex]
[tex]Total = 2.50 * n[/tex]
[tex]Total = 2.50n[/tex]
Next, the expenses on n CDs
[tex]Expenses = E_1 + E_2 * n[/tex]
[tex]Expenses = 875 + 0.35 * n[/tex]
[tex]Expenses = 875 + 0.35n[/tex]
The profit (p) is:
[tex]p = Total - Expenses[/tex]
[tex]p =2.50n - (875 + 0.35n)[/tex]
Open bracket
[tex]p =2.50n - 875 - 0.35n[/tex]
Collect like terms
[tex]p =2.50n - 0.35n - 875[/tex]
[tex]p =2.15n - 875[/tex]
A man purchased a magazine at the airport for $2.69. The tax on the purchase was $0.13. What is the tax rate at the airport? The tax rate is %. (Round to the nearest percent as needed.)
We need to find the percent, let's start but making the equation.
The price is 2.69
The tax cost is 0.13
So what percent of 2.69 is = 0.13.
Equation: X/100 x 2.69 = 0.13
Multiply each side by 100 so we can get x alone with the price: 2.69x = 13
Now to get x alone, we must divide both sides by 2.69: x = 4.8
Finally, we just round 4.8 to the nearest whole number, which is 5 (5 or above give it a shove, 4 or below let it go, we have 8 so we give it a shove). This means that the answer will be 5%.
I hope this helps! :)
I need help please
Don’t skip the questions if you know the answer please I need the answers as soon as possible!!
y=x²-10x-7
a>0 so we will be looking for minimum
x=-b/2a=10/2=5
y=25-50-7=-32
Answer: (5;32)
y=-4x²-8x+1
а<0 so we will be looking for maximum
х=-b/2a=8/-8=-1
у=4+8+1=13
Maximum point (-1;13)
It is claimed that the average child has no time to go to school. For the child spends 8 hours per day,or one third of his/her time sleeping. Based on a 365 day year, that’s 121.67days sleeping. Also the child spends three hours per day eating. That’s a total of 45 days in the year spent eating. Also the child spends 90 days taking summer vacation. Also the child spends 21 days on Christmas and Easter holiday. Finally, the child has each Saturday and Sunday off. That’s a total of 104 days. In short, we (rounding to whole days accounted for 122+45+90+21+104=382 days of the year taken up by ordinary child inlike activities. This is already more than the 365 days that are known to comprise a year. We conclude that there is certainly no time for the child to attend school. What is wrong with this reasoning?
Answer:
See below.
Step-by-step explanation:
Sleeping:
8/24 * 365 = 121.76 days
Eating:
3/24 * 365 = 45.63 days
Total sleeping and eating: 167 days
Summer Vacation & Holidays:
90 + 21 = 111 days
Saturdays and Sundays: 52 + 52 = 104 days
Vacation + Holidays Saturdays + Sundays = 111 + 104 = 215 days
It may be true that all days of vacation, holiday, Saturdays, and Sundays combined are a total of 215 days, but these 215 days cannot be added to the 167 days above because these 215 days include time for sleeping and eating which was already included in the sleeping and eating times for the entire year. The mistake in the reasoning is counting twice the time of sleeping and eating on the 215 days in which there is no school.
