Answer:
(4x^4 + 3y) * (16x^8 - 12x^4 y + 9y^2)
Step-by-step explanation:
rewrite 64x^12 as (4x^4)^3
(4x^4)^3 + 27y^3
rewrite 27y^3 as (3y)^3
a^3+b^3=(a+b)(a^2 - ab + b^2)
(4x^4 + 3y) ((4x^4)^2 - (4x^4 * (3y) + (3y)^2)
[tex]\\ \rm\Rrightarrow 64x^{12}+27y^3[/tex]
[tex]\\ \rm\Rrightarrow 4^3x^3x^6x^3+3^3y^3[/tex]
[tex]\\ \rm\Rrightarrow (4xxxx)^3+(3y)^3[/tex]
[tex]\\ \rm\Rrightarrow (4x^3)^3+(3y)^3[/tex]
a^3+b^3=(a+b)(a^2+ab+b^2)[tex]\\ \rm\Rrightarrow (4x^3+3y)(16x^6+12x^3y+9y^2)[/tex]
Maria and John decide to shop for furnishings for the new house. They choose items that amount to $5600.00. The store has 2 fixed installment simple interest loan options for purchasing:
Option 1: 20% down payment and financing at 5% simple interest per year for 3 years.
Option 2: no down payment and financing at 5.25% simple interest for 4 years.
Answer each of the following questions separately, showing all your work to reach each answer.
A. Which option will result in smaller finance charge (interest)? What will that finance charge/interest be?
B. Which option will result in the smaller monthly payment on this fixed installment loan? What will that monthly payment be?
C. They decide to defer any purchases and invest a $5600 bonus that Maria will be getting from work in a savings account. The APR is 21.6% compounded monthly. How much interest will they earn in 4 years?
D. They decide to defer any purchases and loan the $5600 bonus to a needy relative at 1.5% simple interest per year. How long will the term of the loan need to be if they want to earn $500 in interest (assuming the loan is not paid off early).
Answer:
A. The option that results in the smaller finance charge/interest is option 1
B. The option that will result in the smaller monthly payment is option 1
C. The interest they will earn in 4 years, I = $6,643.972
D. The time it will take for them to earn an interest of $500 by loaning $5,600 at 1.5% is approximately 5.95 years
Step-by-step explanation:
A. The simple interest, I, formula is given as follows;
[tex]I = \dfrac{P \times R \times T }{100}[/tex]
Where;
P = The principal
R = The rate
T =The time given for the loan
For Option 1 the first option, we have;
Down payment = 0.2 × $5600.00 = $1,120.00
Principal = $5600.00 - $1,120.00 = $4,480.00
[tex]\therefore I = \dfrac{\$ 4480\times 5 \times 3 }{100} = \$672[/tex]
For Option 2. the second option, we have;
P = $5600.00
[tex]\therefore I = \dfrac{\$ 5600 \times 5.25 \times 3 }{100} = \$1176[/tex]
The option that results in the smaller finance charge is option 1
B. For option 1, the total amount = Principal + Interest
∴ The total amount remaining = $4480 + $672 = $5,152
The monthly payment = A/N
Where;
A = The total amount yet to be paid out of the loan = $5,152
N = The number of time periods = 3 × 12 = 36 months
The monthly payment = $5,152/36 = [tex]\$ 143.\overline{111}[/tex]
For option 2, the total amount = Principal + Interest
∴ The total amount remaining = $5,600 + $1176 = $6776
The monthly payment = A/N
Where;
A = The total amount yet to be paid out of the loan = $6,776
N = The number of time periods = 3 × 12 = 36 months
The monthly payment = $6,776/36 = [tex]\$ 188.\overline{222}[/tex]
Therefore, the option that will result in the smaller monthly payment is option 1
C. For a compound interest on a principal of $5,600 invested for 4 years in a savings account that gives an interest rate 21.6% per annum, we have;
[tex]A = P \times \left(1 + \dfrac{r}{n} \right)^{(n\times t)}[/tex]
We have, using the annual rate, rather than calculating for the monthly rate;
[tex]A = 5600 \times \left(1 + 0.216 \right)^{4} \approx 12243.972[/tex]
Therefore, the amount they will have in 4 years ≈ $ 12,243.972
The interest they will earn in 4 years, I = A - P ≈ $ 12,243.972 - $5,600 = $6,643.972
The interest they will earn in 4 years, I = $6,643.972
D. To earn an interest of $500 at an interest rate of 1.5%, we have;
[tex]500 = \dfrac{5600 \times 1.5 \times T}{100} = 84 \times T[/tex]
From which we have;
[tex]T = \dfrac{500}{84} = \dfrac{125}{21} = 5\frac{20}{21} \approx 5.95[/tex]
Therefore, the time it will take for them to earn an interest of $500 by loaning $5,600 at 1.5% is approximately 5.95 years.
-8(y+5)+2y=2 please help me with this
36.24 divided by 9.06 is equal to
Answer:
4
Step-by-step explanation:
4/7 x 9/20 will give brainliest
Answer:
9/35 or 0.2571428
Answer:
9/35 (Already Simplified)
Step-by-step explanation:
For fraction multiplication, multiply the numerators and then multiply the denominators to get
4×97×20=36140
This fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 36 and 140 using
GCF(36,140) = 4
36÷4140÷4=935
Therefore:
47×920=935
Solution by Formulas
Apply the fractions formula for multiplication, to
47×920
and solve
4×97×20
=36140
Reduce by dividing both the numerator and denominator by the Greatest Common Factor GCF(36,140) = 4
36÷4140÷4=935
Therefore:
4/7×9/20=9/35
Desperate need for help!
Maths!
Will award brainliest!
Step-by-step explanation:
fg(x) =
[tex] {(x - 4)}^{2} + 3(x - 4)[/tex]
=
[tex] {x}^{2} + 16 - 8x + 3x - 12[/tex]
=
[tex] {x}^{2} - 5x + 4[/tex]
Determine the slope of line (AB) and the slope of line (CD). Determine whether line (AB) and line (CD) are parallel, perpendicular, or just intersecting (neither). Points A and B line on the line y = 2/3x + 4. Points C and D line on the line 6x + 4y = 16.
Answer:
The slopes are perpendicular
Step-by-step explanation:
Points A and B line on the line y = 2/3x + 4.
This line is in the form
y = mx+b where m is the slope
The slope is 2/3
Points C and D line on the line 6x + 4y = 16.
Solve for y
6x+4y = 16
4y = -6x +16
Divide by 4
4y/4 = -6/4x + 16/4
y = -3/2 x +4
The slope is -3/2
The slopes multiply to -1
2/3 * -3/2 = -1
so they are perpendicular
Plz help!!
Point H is the circumcenter of triangle DEF.
Which must be true? Select two options.
Point H is the center of the circle that passes through points D, E, and F.
Point H is the center of the circle that passes through points L, M, and N.
Line segment H E is-congruent-to line segment H D
Line segment L H is-congruent-to line segment N H
Line segment F L is-congruent-to line segment F N
Answer:
a & c
Step-by-step explanation:
edge
Answer:
A. Point H is the center of the circle that passes through points D, E, and F
C. HC≈HD
-6 - (-8) + 6 =
What is the value?
Answer:
The answer is 8
Step-by-step explanation:
use order of operations.
*remember that there is an understood -1 in -(-8). this can also be written as -1(-8)*
[tex]-6-(-8)+6\\-6+8+6\\2+6\\8[/tex]
hope this helps!
-3/5 divided by - 3/4 PLEASE HURRY make it in simplest form please
Answer: Exact Form: 4 /5
Decimal Form: 0.8
Step-by-step explanation:
Answer:
Step-by-step explanation:
Cancel -3
[tex]\frac{1}{5x4}[/tex]
Simplify 5 x 4 to 20.
[tex]\frac{1}{20}[/tex]
Decimal Form: 0.05
I need help fast! This is polynomials help
Answer:
incorrectcorrectincorrectStep-by-step explanation:
A + B = (-4x^2 +2x -5) +(3x^2 +6) = x^2(-4+3) +x(2) +(-5+6) = -x^2 +2x +1
The given sum is Incorrect.
__
A - C = (-4x^2 +2x -5) -(-5x -4) = -4x^2 +x(2+5) +(-5+4) = -4x^2 +7x -1
The given difference is Correct.
__
B + C = (3x^2 +6) +(-5x -4) = 3x^2 -6x +2
The given sum is Incorrect.
if h(x) 1/4x-4. what is h(10)
Answer:
-1.5
Step-by-step explanation:
Substitute the given value into the function and evaluate.
Complete the equation for the standard form of the line that has an x-intercept of 3 and a y-intercept of 5
Answer:
5x+3y=-15
Step-by-step explanation:
Find area of triangle. Picture included.
Answer:
5040
your welcome
Answer:
A=35
hope this helps
can you also please mark me as brainliest?
What is the meaning of the expression (94+33)-3
124
i added 94+33 then substracted 3 hope it helps you
what is (3 x 10) + (4 x 1) + (5 x 1/10) + (5 x 1/100) + (6 x 1/1000)
Answer:
34.556
Step-by-step explanation:
Hope this helps!
Photos and videos have become an important part of the online social experience, with more than half of Internet users posting photos or videos online that they have taken themselves. Let A be the event an Internet user posts photos that they have taken themselves, and B be the event an Internet user posts videos that they have taken themselves. A research center finds that P(A) = 0.47, P(B) = 0.28,and P(A or B) = 0.52.
Required:
What is the conditional probability that an Internet user posts photos that they have taken themselves, given that they post videos that they have taken themselves?
Answer:
0.82
Step-by-step explanation:
Given:
A be the event that an Internet user posts photos taken by themselves.
B be the event that an Internet user posts photos taken by themselves.
P(A) = 0.47
P(A) = 0.28
P(A or B) = [tex]P(A\cup B)[/tex] = 0.52
To find:
Conditional probability that an Internet user posts photos given that they post videos.
OR
P(A/B) = ?
Solution:
Formula to be used to find the required conditional probability:
[tex]P(A/B) = \dfrac{P(A \cap B)}{P(B)}[/tex]
For this, [tex]P(A \cap B)[/tex] is required.
Formula
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
[tex]0.52=0.47+0.28-P(A\cap B)\\\Rightarrow P(A\cap B)=0.23[/tex]
Now, the required conditional probability is:
[tex]P(A/B) = \dfrac{P(A \cap B)}{P(B)}\\\Rightarrow P(A/B) = \dfrac{0.23}{0.28}\\\Rightarrow \bold{P(A/B)} = 0.82}[/tex]
So, the answer is 0.82.
a random sample of 21 students from U and 21 students at A&T for surveyed their music listening habits. Their responses (IN HOURS, each square represents 0.5 hour) were record and displayed using the following histograms. The one on the left is from U and the one on the right is for A&T students. Which data set (the U students or the SHSAT students) has a larger standard deviation? Explain!
The numbers are a bit blurry so I can't determine the numeric standard deviation for each set. However, we can see that the histogram on the left has an outlier, which will increase the standard deviation compared to the data set that doesn't have an outlier. Therefore it is likely data set U has a larger standard deviation.
Two random variables x and y are independent if the value of x does not affect the value of y. If the variables are not independent, they are dependent. A new random variable can be formed by finding the sum or difference of random variables. If a random variable x has mean μx and a random variable y has mean μy then the means of the sum and difference of the variables are given by the following equations. μx+y=μx+μy μx−y=μx−μy The distribution of a test's scores for college-bound male seniors has a mean of 1528 and a standard deviation of 319. The distribution of a test's scores for college-bound female seniors has a mean of 1498 and a standard deviation of 304. One male and one female are randomly selected. Assume their scores are independent.What is the average sum of their scores? What is the average difference of their scores?
Answer: [tex]\mu_{x+y} =[/tex] 3026
[tex]\mu_{x-y}=[/tex] 30
Step-by-step explanation: Average sum of the female and male's test score is the sum of expected value of each gender:
[tex]\mu_{x+y}=\mu_{x}+\mu_{y}[/tex]
Assuming x represents the random male selected and y represents the random female selected:
[tex]\mu_{x+y}=1528+1498[/tex]
[tex]\mu_{x+y}=[/tex] 3026
The average sum of their scores is 3026.
Average difference is the difference between the expected value (mean) of each gender:
[tex]\mu_{x-y}=\mu_{x}-\mu_{y}[/tex]
[tex]\mu_{x-y}=[/tex] 1528 - 1498
[tex]\mu_{x-y}=[/tex] 30
The average difference of their scores is 30.
Which of the following represents the shaded area as a fraction, a decimal, and a percent of the whole?
Answer:
3
Step-by-step explanation:
I will give you brainliest if you answer this
The predicted high temperature for yesterday was 55 ℉. The actual high temperature was 47 ℉. Calculate the percent error.
A bag of equally sized rhinestones weighs 16 ounces. Each rhinestone weighs 0.016 ounce. If you have 2 bags of rhinestones, how many rhinestones do you have?
(a) SINGLE person (including head of household)
If the amount of wagon (after
subtracting withholding allowancos) The amount of income tax
to withholdie
Not over $42
SO
Over
But not over
of excess over
$42
-$214 50.00 plus 10%
$42
5214 -5750 517 20 plus 15%
-5214
S739
-51,732 505.95 plus 25%
-S739
$1,732 -53,565 5344.20 plus 20%
-51.732
$3,586 -57,703 $85772 plus 33%
$3,586
57.700 -57,735 $2,222.93 plus 35% -57,703
S7735
52,234.13 plus 30.8% ---37,735
Paul, a successful executive chef at an exclusive restaurant, earns $2,250 each week. Based on the table, calculate the income tax
withheld each week from Paul's paycheck.
A)
$344.20
B)
$473.70
$489.24
D)
597420
I need lots of help please help omggg
Answer:
/
Step-by-step explanation:
Answer:
expanded form: (500,000 +20,000) + (3,000 + 600 + 40)
standard form: 523,604
expanded form: (4,000,000,000 + 10,000) + (7,000 + 90) + (40 + 7)
standard form: 4,017,947
Step-by-step explanation:
Hope this helps have a nice day
plz give me brainliest :)
how many even integer numbers are between 12/5 and 56/5
Answer:
4
Step-by-step explanation:
12/5=2.4
56/5=11.2
so the even integers between them are
4,6,8, and 10
4 inegers
There are four even integers number that lies between 12/5 and 56/5. Then the numbers are 4, 6, 8, and 10.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
The decimal number is the sum of a whole number and part of the fraction number. The fraction number is greater than zero but less than one.
If the integer number is divisible by 2, then the number will be known as even number.
The two integers are 12/5 and 56/5.
Convert the numbers into decimal form.
2.4 and 11.2
There are 4 even integers that are 4, 6, 8, and 10.
There are four even integers number that lies between 12/5 and 56/5. Then the numbers are 4, 6, 8, and 10.
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ2
Marlene decided to buy 2 bags of apples weighting 3 1/4 pounds each, instead of buying 3 bags weighting 2 2/5 pounds each. Did she end up with more apples or fewer apples but buying bigger bags
Answer:
c onedge
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
Name the remainder for the quotient and describe or show how you found the remainder.
(x^3 - x^2 - 17x -15) ÷ (x-5)
Answer:
Step-by-step explanation:
The expression x^3 - x^2 - 17x -15) ÷ (x-5) shows that x+5 is one of the factor if the polynomial function. According to factor theorem, we will equate the factor to zero and find x;
x+5 = 0
x = -5
Next is to generate the remainder.
Substitute x = -5 into the polynomial function
P(x) = x^3 - x^2 - 17x -15
P(-5) = (-5)^3 - (-5)^2 - 17(-5) -15
P(-5) = -125-25+85-15
P(-5) = -150+70
P(-5) = -80
Hence the remainder is -80
Answer:
Qoutient=x^2+4x+3
Remainder=0
In George's school, 0.386 of the students participated in an event. If there are one thousand students in George's school, how many participated in the event?
Which relation is a function? It would be epic if you answer today lol
Answer:
Step-by-step explanation:
Pretty sure it's the third picture where it makes a U shape, since it passes the vertical line test.
Determine the degree of the polynomial -57
Answer:
linear polynomial
Step-by-step explanation:
as no degree is given
Find (f +g) (x) when
f(x) = x +3 and g(x) = x - 3
a) 2x+6
b) 2x
c) 2x-6
d) 6
PLEASE I NEED HELP SO MUCH I DONT UNDERSTAND (repost cause the x showed up as 2)