Answer:
−p3q2r−p3qr2−p2q3r−p2q2r2−p2qr3+pq3r2+pq2r3
Step-by-step explanation:
(p2qr+pq2r+pqr2)((−p)(q)+qr+−pr)
(p2qr)((−p)(q))+(p2qr)(qr)+(p2qr)(−pr)+(pq2r)((−p)(q))+(pq2r)(qr)+(pq2r)(−pr)+(pqr2)((−p)(q))+(pqr2)(qr)+(pqr2)(−pr)
−p3q2r+p2q2r2−p3qr2−p2q3r+pq3r2−p2q2r2−p2q2r2+pq2r3−p2qr3
−p3q2r−p3qr2−p2q3r−p2q2r2−p2qr3+pq3r2+pq2r3
[tex]\large\underline{\sf{Solution-}}[/tex]
Given that:
[tex]\sf\longmapsto(p^2qr+pq^2r+pqr^2)(-pq+qr-pr)[/tex]
Opening the brackets,
[tex]\sf\longmapsto p^2qr(-pq+qr-pr) + pq^2r(-pq+qr-pr) + pqr^2(-pq+qr-pr)[/tex]
Opening the next brackets,
[tex]\sf\longmapsto p^2qr(-pq)+ p^2qr(qr)- p^2qr(pr) + pq^2r(-pq)+ pq^2r(qr)- pq^2r(pr) + pqr^2(-pq)+ pqr^2(qr)- pqr^2(pr)[/tex]
So,
[tex]\sf\longmapsto -p^3q^2r+ p^2q^2r^2- p^3qr^2 - p^2q^3r+ pq^3r^2- p^2q^2r^2-p^2q^2r^2+ pq^2r^3- p^2qr^3[/tex]
[tex]\sf\longmapsto -p^3q^2r- p^3qr^2 - p^2q^3r+ pq^3r^2+ pq^2r^3- p^2qr^3+ p^2q^2r^2-2p^2q^2r^2 [/tex]
[tex]\sf\longmapsto -p^3q^2r- p^3qr^2 - p^2q^3r+ pq^3r^2+ pq^2r^3- p^2qr^3- p^2q^2r^2 [/tex]
Hence, the product is,
[tex]\longmapsto\bf -p^3q^2r- p^3qr^2 - p^2q^3r- p^2qr^3+ pq^3r^2+ pq^2r^3 - p^2q^2r^2 [/tex]
Which is the graph of the following equation?
|x| = 2
Answer:
A
Step-by-step explanation:
|x|= negative and positive with the lines
A normal population has a mean of 60 and a standard deviation of 12. You select a random sample of 9. Compute the probability the sample mean is : (a). Greater than 63. (b). Less than 56. (c). Between 56 and 63.
Using the normal distribution and the central limit theorem, it is found that there is a:
a) 0.2266 = 22.66% probability that the sample mean is greater than 63.
b) 0.1587 = 15.87% probability that the sample mean is less than 56.
c) 0.6147 = 61.47% probability that the sample mean is between 56 and 63.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In this problem:
Mean of 60, thus [tex]\mu = 60[/tex].Standard deviation of 12, thus [tex]\sigma = 12[/tex].Sample size of 9, thus [tex]n = 9, s = \frac{12}{\sqrt{9}} = 4[/tex].Item a:
This probability is 1 subtracted by the p-value of Z when X = 63, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{63 - 60}{4}[/tex]
[tex]Z = 0.75[/tex]
[tex]Z = 0.75[/tex] has a p-value of 0.7734.
1 - 0.7734 = 0.2266
0.2266 = 22.66% probability that the sample mean is greater than 63.
Item b:
This probability is the p-value of Z when X = 56, so:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{56 - 60}{4}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a p-value of 0.1587.
0.1587 = 15.87% probability that the sample mean is less than 56.
Item c:
This probability is the p-value of Z when X = 63 subtracted by the p-value of Z when X = 56.
These p-values were found in the previous items, so:
0.7734 - 0.1587 = 0.6147
0.6147 = 61.47% probability that the sample mean is between 56 and 63.
A similar problem is given at https://brainly.com/question/24663213
Emily is 4 times as old as Tiffany. In ten years time, Emily will be twice as old as Tiffany . Find their ages.
Emily is 4 times as old as Tiffany. In ten years time, Emily will be twice as old as Tiffany. Find their ages.
Solution:Let the age of Tiffany be x years.Then, the age of Emily = 4x years.After 10 years, the age of Tiffany will be (x+10) years.After 10 years, the age of Emily will be (4x+10) years.Therefore, by the problem
[tex]4x + 10 = 2(x + 10) \\ = 4x + 10 = 2x + 20 \\ = > 4x - 2x = 20 - 10 \\ = > 2x = 10 \\ = > x = \frac{10}{2} \\ = > x = 5[/tex]
So, Tiffany's present age = 5 years.Emily's present age = (4×5) years = 20 years.Answer:Emily's age is 20 years and Tiffany's age is 5 years.
Hope it helps!
I just need mental help at this point
Answer:
1:2
Step-by-step explanation:
QRS is double the size of TUV
1. How much of a difference is there, in interest, between an investment of $899 with simple interest of 5% and an investment of $499 with a simple interest of 9%, both for a six year term?
2. What balance will you have in your account, in 8 years, if you invest $4000 at 3.5% compounded quarterly?
3. Gina deposited $1500 in an account that pays 11% interest compounded monthly. What will the balance be in 5 years?
4. You invested $4,400 for 2 years at 7.3% compounded semianually. What is your total balance after 12 years?
5. You want to buy a new motorcycle so you borrow $14,200 for 5 years at an interest rate of 13% and it’s compounded daily. How much interest will you have paid after the 5 year term has ended?
HELppppppppppppppppp
9514 1404 393
Answer:
40 -8p -3w$4Step-by-step explanation:
Ms. Liu will have to pay 8p for p bags of popcorn, and 3w for w bottles of water. The amount she will have left will be these amounts subtracted from $40.
40 -8p -3w . . . . represents the money remaining
For p=3 and w=4, this evaluates to ...
40 -8(3) -3(4) = 40 -24 -12 = 4
Ms. Liu will have $4 left after her purchase.
5551-525152+62626626×552526
solve it.
Answer:
=34602838637675
Step-by-step explanation:
=−519601+(62626626)(552526)
=−519601+34602839157276
=34602838637675
Needs to show work.
1. Refer to the equation 2x − 6y = 12.
(a) Write the equation in Slope Intercept Form.
Answer:
y = 1/3x - 2
Step-by-step explanation:
2x − 6y = 12
-6y = -2x + 12
y = 1/3x - 2
step 1: find the factors of ac that add up to b. ac=6(−10)=−60 b=−11 the factors of −60 that add up to −11 are and . step 2: rewrite the trinomial with the x-term expanded, using the two factors from step 1. 6x2−11x−10 (6x2− )+( −10) step 3: group the first two and second two terms together, find the gcf and factor again. (2x−5)+ (2x−5
Answer:
For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=6⋅−10=−60 and whose sum is b=−11
.
6x2+4x−15x−10
Factor out the greatest common factor from each group.
2x(3x+2)−5(3x+2)
Factor the polynomial by factoring out the greatest common factor, 3x+2
.
(3x+2)(2x−5)
PLEASE HELP
answer both of the questions in the photo please
Answer:
-6
11
Step-by-step explanation:
-6n-5=31
-6n=36
n=-6
-28=-3n+5
3n=5+28
3n=33
n=11
Last year 300 people attended a play with ticket price of $8. The school estimates that 20 fewer people attend for each $1 increase in price. What ticket price would give the greatest income?
Answer:
$12
Step-by-step explanation:
If we stuck with the price of $8, then we end with an income of $2400
Increasing it by $1 will decrease attendance by 20
8 x 300 = 2400
9 x 280 = 2520
10 x 260 = 2600
11 x 240 = 2640
12 x 220 = 2640
13 x 200 = 2600
We're starting to go down, so let's stop there
The ticket price of $11 or $12 appears to give the most income
I would stick with $12 since your still getting more money from one ticket
The price of a ticket stick at $12 since you still get more money from one ticket.
What ticket price would give the greatest income?Last year 300 people attended a play with a ticket price of $8.
The school estimates that 20 fewer people attend for each $1 increase in price.
If we keep the price at $8, we'll end up with a $2400 profit.
Increasing it by $1 will result in a 20 percent drop in attendance.
8 × 300 = 2400
9 × 280 = 2520
10 × 260 = 2600
11 × 240 = 2640
12 × 220 = 2640
13 x 200 = 2600
Let's come to a halt here since we're starting to descend.
The $11 or $12 ticket price looks to generate the most revenue.
I'd continue with $12 because you'll still make more money with one ticket.
More about the greatest income link is given below.
https://brainly.com/question/9453332
#SPJ2
evaluate the expression (2.5)^3
please mark this answer as brainlist
The value of the expression is 15.625.
We have,
Expression:
(2.5)³
The base is 2.5 and the power is 3.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
This can be written as,
= 2.5 x 2.5 x 2.5
Convert the decimals into fractions.
= 25/10 x 25/10 x 25/10
Simplify the fractions.
= 15.625
Thus,
The value of the expression is 15.625.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ4
ar can drive 90 miles on 3 gallons of gas. How
many miles can be driven with 11 gallons of gas?
8) What is the area of a polygon with vertices
A(-2,4), B(4,4), C(7,0) and D(-5,0)?
(A) 48
(B) 42.5
(C) 36
(D) 24
Answer:
[C] 36.
Step-by-step explanation:
the given polygon is trapezoid, where its bases are AB and CD.
The required area can be calculated using the formula: A=0.5(AB+CD)*h, where h - height of the ABCD.
The lengths are: AB=6; CD=12; h=4, then the required area:
A=0.5(6+12)*4=36
30 points please answer (Must show work) Screenshot attached!!!
Answer:
1 thats it
Step-by-step explanation:
Answer:
the second, fourth
Step-by-step explanation:
Since they all have the same fraction, but different positive and negatives in each equation we can find out which ones are equal to the original equation by how many negatives each equation has.
The original equation has 2
first option only has 1, so we can eliminate that one
the second option has two, and they are the same equation as the original, only in reverse, so this one will be one of the answers.
the third only has one so we can get rid of that one.
the fourth has 2, even though it has a + it still makes 2/5 negative, so it is one of the answers as well.
and the fifth one is positive, and there are no negatives, so we can get rid of that one.
so the answers would be the second and fourth ones.
Find the equation of the linear function represented by the table y0 5 10 15 x 1 2 3 4
Answer:
y = 5x
Step-by-step explanation:
The first step is to find the slope. The table shows an increase of 5 on the x-axis and 1 on the y-axis. Our slope is 5/1 or 5
The y-intercept is 0 because when x=0, y=0. The value of y is the y-intercept.
help pls. i’ll give brainliest
Answer:
last 2 I think
Step-by-step explanation:
okokokokokipullup
The perimeter of a rectangle is equal to 54 units. The length of the rectangle is 2k units, and the width of the rectangle is k units
Which expression represents the perimeter, and what is the width of the rectangle?
The expression to represents the perimeter is,
54 = 2 (2k + k)
And, The width of the rectangle is, 9 units.
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
The perimeter of a rectangle is equal to 54 units.
And, The length of the rectangle is 2k units, and the width of the rectangle is k units.
Now, We know that;
Perimeter of rectangle = 2 (Length + Width)
Substitute the given values, we get;
Perimeter of rectangle = 2 (Length + Width)
54 = 2 (2k + k)
54 = 2 × 3k
54 = 6k
54/6 = k
k = 9
Hence, The width of the rectangle is, 9 units.
Learn more about the rectangle visit:
https://brainly.com/question/2607596
#SPJ2
Bro this my 10th time asking this pls. Someone help me giving brainlist :(
When converted to a household measurement, 9 kilograms is approximately equal to a
Answer:
D) 19.8 lbs
Explanation:
1kg in household measurement is equal to 35.274 ounces. 35.274*9=317.466 ounces.
1kg is also equal to 2.205 lbs. 9*2.205=19.8416
9 kg is also equal to 9000 grams, but grams are not a part of the household measurement system
a) 9000 grams. b) 9000 ounces. c) 19.8 ounces. d) 19.8 pounds.
This leaves us with 19.8 lbs
A family bought a total of 13 tickets to a magic show, some adult and some child. The family paid a total of $85
Adult tickets are $15 each and child tickets are $5 each.
Let x represent adult tickets and y represent child tickets.
Write an equation to model the total amount of money that they spent.
Answer:
250 $3 tickets and 100 $2 tickets were sold.
Step-by-step explanation:
The cost of tickets for a play is $3.00 for adults and $2.00 for children. 350 tickets were sold and $950 was collected. How many tickets of each type were sold?
Solution:
Step 1: Set up a table with quantity and value.
quantityvaluetotal$3 tickets$2 ticketstogether
Step 2: Fill in the table with information from the question.
The cost of tickets for a play is $3.00 for adults and $2.00 for children. 350 tickets were sold and $950 was collected. How many tickets of each type were sold?
Let x = number of $3 tickets
Let y = number of $2 tickets
Total = quantity × value
quantityvaluetotal$3 ticketsx33x$2 ticketsy22ytogether350950
Step 3: Add down each column to get the equations
x + y = 350 (equation 1)
3x + 2y = 950 (equation 2)
Use Substitution Method
Isolate variable x in equation 1
x = 350 – y (equation 3)
Substitute equation 3 into equation 2
3(350 – y) + 2y = 950
1050 – 3y + 2y = 950
3y – 2y = 1050 – 950
y = 100
Substitute y = 100 into equation 1
x + 100 = 350
x = 250
5 3/4 as an improper fraction
Answer:
23/4
Step-by-step explanation:
Answer:
A mixed number is an addition of its whole and fractional parts.
[tex]5 \frac{3}{4} [/tex]
Add:
[tex]5 \: and \: \frac{3}{4} [/tex]
To write 5 as a fraction with a common denominator, multiply by
[tex] \frac{4}{4} [/tex]
Combine:
[tex]5 \: and \: \frac{4}{4} [/tex]
Combine the numerators over the common denominator.
[tex] \frac{5.4 + 3}{4} [/tex]
Simplify the numerator.
Multiply 5 by 4.
Add 20 and 3.
[tex] \frac{23}{4} [/tex]
Step-by-step explanation:
Thanks!!!!!!
HELP HELP EASY
Use a calculator to approximate cos 43° and round to
four decimal places.
Answer:
0.731353701619170483287543608275622403378...
Step-by-step explanation:
cos((43 π)/180)
UwU
It's verified you can trust
0.7315Is what you needed
Six more than a number is 17
The unknown number given from the expression Six more than a number is 17 is 11
How to solve linear equation?let
The unknown number = x
x + 6 = 17
subtract 6 from both sidesx = 17 - 6
x = 11
check:
x + 6 = 17
11 + 6 = 17
Learn more about equation:
https://brainly.com/question/1214333
#SPJ1
What number is 28% of 45?
Answer:
12.6
Step-by-step explanation:
Hope it helps Brooo
Answer: 12.6
Step-by-step explanation:
28% × 45 = 12.6 => Divide 12.6 by 45And see if we get as a result: 28%
I hope this helps<33
Find the value of x.
calculate the formula of the triangle and then use pythagoras thereom to solve the values according to their sides
Don't forget to thank me later
2/3 : 2/6 as a unit rate
Answer:
3/1
Step-by-step explanation:
Calculator
What are the coordinates of the midpoint of CD where C(2,
6) and D(4, 10)?
O (3, 2)
0 (2, 3)
0 (3, – 8)
0 (-1, 2)
1
2
OCT
20
tv
Answer:
O (3, 2)
Step-by-step explanation:
use the vectors method
(2+4)/2. (-6+10)/2
(3, 2)
2
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
The numbers 7. 11, 12, 13, 14, 18, 21, 23, 27 and 29 are written on separate cards, and the cards are placed on a table with the numbers facing
down.
The probability of picking a card with an even number is?
Answer:
Answer=3/10
Step-by-step explanation:
even numbers=3
total cards=10
P=number of possible outcomes/total outcomes
=3/10
Answer:
you have a 3/10 probability of geting a even number bc
Step-by-step explanation:
there are ten numbers shown in the question and there are three even numbers out of ten so that is how you get you anewer
the cylinder has radius 4√3 and hight h. the total surface area of the cylinder is 56π√6. find the exact value of h giving the answer in the form a√2 + b√3 where a and b are both integers.
The area of the cylinder is a function of its height (h) and radius, ([tex]\mathbf{4\sqrt 3}[/tex])
The exact value of h is: [tex]\mathbf{7\sqrt 2- 4\sqrt 3}[/tex]
The given parameters are:
[tex]\mathbf{Area =56\pi\sqrt 6}[/tex]
[tex]\mathbf{r=4\sqrt 3}[/tex]
The surface area of a cylinder is calculated as:
[tex]\mathbf{Area = 2\pi rh + 2\pi r^2}[/tex]
Substitute values for Area
[tex]\mathbf{56\pi\sqrt 6= 2\pi rh + 2\pi r^2}[/tex]
Divide through by pi
[tex]\mathbf{56\sqrt 6= 2 rh + 2r^2}[/tex]
Substitute value for r
[tex]\mathbf{56\sqrt 6= 2 (4\sqrt 3)h + 2(4\sqrt 3)^2}[/tex]
[tex]\mathbf{56\sqrt 6= 8h\sqrt 3 + 2\times 48}[/tex]
[tex]\mathbf{56\sqrt 6= 8h\sqrt 3 + 96}[/tex]
Collect like terms
[tex]\mathbf{8h\sqrt 3 = 56\sqrt 6- 96}[/tex]
Make h the subject
[tex]\mathbf{h = \frac{56\sqrt 6}{8\sqrt 3}- \frac{96}{8\sqrt 3}}[/tex]
[tex]\mathbf{h = 7\sqrt 2- \frac{12}{\sqrt 3}}[/tex]
Rationalize
[tex]\mathbf{h = 7\sqrt 2- \frac{12\sqrt 3}{3}}[/tex]
[tex]\mathbf{h = 7\sqrt 2- 4\sqrt 3}[/tex]
Hence, the exact value of h is: [tex]\mathbf{7\sqrt 2- 4\sqrt 3}[/tex]
Read more about surface areas t:
https://brainly.com/question/25131428