Answer:
[tex]\frac{a^2^0b^5}{c^5d^3^0}[/tex]
Step-by-step explanation:
When one raises a value to an exponent, one can multiply the current value of the exponent by the number it is raised to. This is the case because raising a value to an exponent is another way of representing that value times itself the number of times that the exponent indicates. Remember, if no exponent is written, then the exponent is (1).
One can apply this here by multiplying every exponent in this problem by (5) since the fraction is raised to the power (5).
[tex](\frac{a^4b}{cd^6})^5[/tex]
[tex]=\frac{(a^4^*^5)(b^1^*^5)}{(c^1^*^5)(d^6^*^5)}[/tex]
Simplify,
[tex]=\frac{a^2^0b^5}{c^5d^3^0}[/tex]
I'm so confused, please help!
A family wants to purchase a house that costs $120,000. They plan to take out a $100,000 mortgage on the house and put $20,000 as a down payment. The bank informs them that with a 15-year mortgage their monthly payment would be $745.86 and with a 30-year mortgage their monthly payment would be $546.01. Determine the amount they would save on the cost of the house if they selected the 15-year mortgage rather than the 30-year mortgage.
9514 1404 393
Answer:
$62,308.80
Step-by-step explanation:
The total amount paid on the 15-year mortgage is ...
($745.86/mo)×(12 mo/yr)×(15 yr) = $132,254.80
The total amount paid on the 30-year mortgage is ...
(546.01/mo)×(12 mo/yr)×(30 yr) = $196,563.60
__
The amount saved by selecting the 15-year mortgage is the difference of these amounts:
$196,563.60 -132,254.80 = $62,308.80
_____
Additional comment
This problem statement has several numbers in it that are irrelevant to the question being asked. This is why you need to read and understand the given information, and also understand the question being asked.
Here, the total cost of the house will include the mortgage cost and the down payment. The down payment is the same in either case, so does not factor in when we subtract one total cost from the other. Any difference in cost is due only to the difference in loan cost.
I really need help! Please find the area of the polygon?
Answer:can you help me
write a letter to your friend about important of reading books?
Answer:
Area = 189 m^2
Step-by-step explanation:
This is a trapezium with height h=9m, base, b = 24, top, t = 18.
The area is given by
A = (base+top)*height/2
= (24+18)*9/2
= 189 m^2
a patient is advised to supplement her diet with 3g of calcium per day. The calcium tablets she purchases 300mg per tablet. How many tablets should the patient take per day?
Answer:
Number of tablet needed = 1 tablet
Step-by-step explanation:
Given:
Amount of calcium per day needed = 3 gram
Amount of calcium in a tablet = 300 mg
Find:
Number of tablet needed
Computation:
Number of tablet needed = Amount of calcium per day needed / Amount of calcium in a tablet
Number of tablet needed = 3gram / 300 milligram
Number of tablet needed = 300 milligram / 300 milligram
Number of tablet needed = 1 tablet
Calculate a positive co-terminal angle for θ=40°
Answer:
400
Step-by-step explanation:
angles that are coterminal with the angle 400? => 4000 and 7600 are two positive coterminal angles.
What is the percent change from 40 to 55? Show calculations and final answer. Round to the nearest percent.
Answer:
73%
Step-by-step explanation:
40/55 x 100
= 72.72727273
Rounded = 73%
Hope this helps!
Given the Graph, identify the slope
Answer: The slope is -5/3 or -1.4
Algebra
[tex]s = \frac{y2 - y1}{x2 - x1} [/tex]
[tex]s = \frac{5}{3} [/tex]
Ty
7
What is the slope of a line that is perpendicular to the line
shown on the graph?
6
5
O-2
4
3+
2
2
0 -
0 2 / 2
o
1
O 2
1
2 3
4 5 6 7 X
7 6 5 4 3 2 - 21.
-2-
--3-
6
Answer:
-1/2
Step-by-step explanation:
Perpendicular lines have negative reciprocal slopes.
The solution is, -1/2 is the slope of a line that is perpendicular to the line
shown on the graph.
What is slope?In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).
here, we have,
we have to,
find the slope of the line shown using
the formula, m = y1- y2 / x1- x2
from the given graph we get,
Let
P1(0,1)
P2(1,3)
now we get,
replacing
m = 2/1
= 2
so, here, m1 = 2
two lines are perpendicular when
m1 * m2 = -1
as, we know that,
Perpendicular lines have negative reciprocal slopes.
so, we get ,
m2 = -1/2
Hence, The solution is, -1/2 is the slope of a line that is perpendicular to the line
shown on the graph.
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QUESTION 5 of 10: You have a choice of a $2,000 rebate on a $13,000 vehicle or 18% off. Which is better?
O a) Rebate
Ob) 18% off
Submit
C2021 Knowledge Matters, Inc.
Lesson
Estimated time: 60 minutes
Answer:
18% off
Step-by-step explanation:
i just took the test
7.find the equation of a circle with one of the diameters x+2y+8=0and passing through the intersection of a circle x²+y²+2=0 and x²+y²-3y=0.
ans:
[tex]\bold=4x²+4y²+22x+21y=0.}[/tex]
Answer:
See belowStep-by-step explanation:
Find the intersection of circles
x² + y² + 2x = 0 and x² + y² - 3y = 0Subtract the equations to find:
2x = -3y ⇒ y = -2/3xBy substitution find the points:
(0, 0) and (-1.385, 0.923)Find midpoint between these two points:
x = (0- 1.385)/2 = -0.6925 , y = (0 + 0.923)/2 = 0.4615Find perpendicular bisector passing through this point:
y - 0.4615 = 3/2(x + 0.6925)y = 1.5x + 0.4615 + 1.5(0.6925)y = 1.5x + 1.50025Find intersection of the lines, it is the center:
y = 1.5x + 1.50025x + 2y + 8 = 0Solving we get:
x = -2,75, y = -2.625Find radius, the distance from center to point (0, 0) and get equation of circle:
(x + 2.75)² + (y + 2.625)² = (0 + 2.75)² + (0 + 2.625)²x² + 5.5x + y² + 5.25y = 04x² + 22x + y² + 21y = 04x² + 4y² + 22x + 21y = 0Answer:
Answer is in the picture
The area of a rectangle is 28 m', and the length of the rectangle is 1 m more than twice the width. Find the dimensions of the rectangle.
Answer:
8m ×3.5m
Step-by-step explanation:
Area of rectangle= length ×width
Let the length and width of the rectangle be L and W meters respectively.
Area of rectangle= LW
LW= 28 -----(1)
L= 2W +1 -----(2)
Subst. (2) into (1):
(2W +1)(W)= 28
Expand:
2W² +W= 28
-28 on both sides:
2W² +W -28= 0
Factorise:
(W +4)(2W -7)= 0
W +4=0 or 2W -7=0
W= -4 (reject) or W= 3.5
Substitute W= 3.5 into (2):
L= 2(3.5) +1
L= 7 +1
L= 8
∴ The dimensions of the rectangle is 8m ×3.5m.
What is the radius of the quarter if the area is about 452.16 square millimeters ? Use 3.14 for pi. Do not label. Do not round.
Answer:
Step-by-step explanation:
Im not sure but i think
452.16/3.14.= 3.14r^2/3.14
144(square root sign) = squarw root sign r^2)
12=r
Solve the system of equations given below. y - 15 =3x and -2 + 5y = -3
Answer:
y-15=3x balakaksnzujsbhzbskndh
Answer:
x = - 6 , y = - 3
Step-by-step explanation:
y - 15 = 3x => y = 3x + 15 ------- ( 1 )
-2x + 5y = - 3 --------- ( 2 )
Substitute ( 1 ) in ( 2 ) :
-2x + 5 ( 3x + 15) = - 3
-2x + 15x + 75 = - 3
13x = - 3 - 75
13x = - 78
x = - 6
Substitute x in ( 1 ) :
y = 3x + 15
= 3 ( - 6 ) + 15
= - 18 + 15
y = - 3
Find the unknown side length, x. Write your answer in simplest radical form.
A. 15
B. 5 square root of 10
C. 2 square root of 70
D. 4 square root of 37
Answer:
C .2 square root of 70 skaskaskaska
Y is directly proportional to
the square of (x - 1). y=63
when x=4. find the value of y
when x=6.
Answer:
y = 100
Step-by-step explanation:
y [tex]\alpha[/tex] [tex](x -1)^{2}[/tex]
y = c ([tex]x^{2}[/tex] - 2x + 1)
When y = 63, x = 4;
63 = c ([tex]4^{2}[/tex] - 2(4) + 1)
= 9c
63 = 9c
c = [tex]\frac{63}{9}[/tex]
c = 7
Thus,
y = 4([tex]x^{2}[/tex] - 2x + 1)
The value of y when x = 6 can be determined as;
y = 4([tex]6^{2}[/tex] - 2(6) + 1)
= 4(25)
y = 100
Therefore, y = 100
A company that produces fine crystal knows from experience that 15% of its goblets havecosmetic flaws, while the remaining 85% are flawless.(a) (8 points) If eight goblets are selected at random, what is the probability that exactly twohave flaws
Answer:
The probability that exactly two have flaws is P (x=2) = 0.2376
Step-by-step explanation:
Here
Success= p= 0.15
Failure = q= 0.85
total number= n= 8
Number chosen = x= 2
Applying the binomial distribution
P (x=x) = nCx p^x(q)^n-x
P (x=2) = 8C2 0.15 ²(0.85)^8
P (x=2) = 0.2376
The success is chosen about which we want to find the probability. Here we want to find the probability that exactly two have flaws so success would be having flaws therefore p = 0.15
Prove that: log b (p2 - q2) – log b (p + q) = log b (p – q)
Answer:
Step-by-step explanation:
The formulas used to solve :
[tex][ log_b(\frac{x}{y}) = log_bx - log_by][/tex]
[tex](p^2 - q^2) = (p+q)(p-q)[/tex]
[tex]log_b(p^2 - q^2) - log _b(p + q) = log_b(p-q)\\\\log_b(\frac{(p^2 -q^2)}{(p+q)}) = log_b(p-q)\\\\log_b(\frac{(p+q)(p-q)}{(p+q)}) = log_b(p-q)\\\\log_b(p-q) = log_b(p-q)\\\\[/tex]
Hence proved.
Solve for x. Round to the nearest tenth, if necessary.
Answer:
x = 8.8
Step-by-step explanation:
take 20 degree as reference angle .the,
hypotenuse = OQ = x (hypotenuse is always opposite of 90 degree)
perpendicular(opposite) = PQ 3 (opposite of reference angle is perpendicular or also called as opposite)
base(adjacent) = OP (side which lies on the same line where 90 degree and reference angle)
using sin rule
sin 20 = opposite / hypotenuse
0.34 = 3 / x
x = 3/0.34
x = 8.82
x = 8.8
PLEASEEEE HELPPPPP IM BEGGING SOMEONE HELPPP PLEASEEEEEEEEE PLEASEEEEEEEE
Answer:
x = -1
y = 6
Step-by-step explanation:
We can multiply the second equation by two, so we can have opposite y terms:
2 (3x - 2y = -15)
6x - 4y = -30
Now, we can add the equations, and the y terms can cancel out:
7x + 4y = 17
+ 6x - 4y = -30
13x = -13
x = -1
Now, we can plug in x:
3(-1) - 2y = -15
-3 - 2y = -15
-2y = -12
y = 6
A company is considering to choose between two investment projects with the
following details.
Project A : Costs RM7 million in upfront costs and will generate RM3 million in
annual income for five years starting three years from now.
Project B : Costs RM2.5 million upfront and RM2 million in each of the next
three years. This project generates no annual income but will be sold
six years from now for a sales price of RM16 million.
By using Net Present Value approach, with a discount rate of 8%, determine
which project should be choosen by the company.
Answer: Project A should be chosen as it has the highest NPV.
Step-by-step explanation:
Project A
Present value of inflows:
First find the present value of inflows 3 years from today. Bear in mind that the inflow is constant so this is an annuity:
= 3 million * Present value interest factor of annuity, 8%, 5 years
= 3 million * 3.9927
= RM11,978,100
Discount this value to the present:
= 11,978,100 / (1 + 8%)³
= RM9,508,602
Net Present value = Present value of inflows - Investment
= 9,508,601 - 7,000,000
= RM2,508,601
Project B:
Find present value of costs:
= 2,500,000 + (2 million * Present value interest factor of annuity, 3 years, 8%)
= 2,500,000 + (2,000,000 * 2.5771)
= 2,500,000 + 5,154,200
= RM7,654,200
Net present value = (16,000,000 / (1 + 8%)⁶) - 7,654,200
= RM2,428,514
Project A should be chosen as it has the highest NPV.
On four consecutive days, a concert pianist practiced for
3 1/2 hours,
6 1/3hours,
4 1/4 hours, and
5 1/6hours. Find the pianist's total practice time.
Answer:
19 hours and 15 minutes
Step-by-step explanation:
if you add it up all together it equals to 19.25 hours but you would convert it into 19 hours and 15 minutes
The pianist's total practice time is 19 3/12 hours.
Given that, on four consecutive days, a concert pianist practised for 3 1/2 hours, 6 1/3hours, 4 1/4 hours, and 5 1/6hours.
We need to find the pianist's total practice time.
How to add fractions?Mixed fractions with unlike denominators are a group of those mixed fractions that do not have the same denominator. Let us learn how to add mixed fractions with unlike denominators with the help of the following steps.
Step 1: The whole numbers of both the fractions are added first.
Step 2: If the denominators are different, so we have to find the Least Common Multiple (LCM) of the denominators.
Step 3: With the help of the LCM, we will write their respective equivalent fractions so that they become like fractions.
Step 4: Now, we have both the fractions with the same denominators, that is, they have been converted to like fractions.
Step 5: Add the like fractions now and then simplify.
Total=3 1/2+6 1/3+4 1/4+5 1/6
=(3+6+4+5) (1/2+1/3+1/4+1/6)
=18 (1/2+1/3+1/4+1/6)
LCM of denominators 2, 3, 4 and 6 is 12.
Now, 18 (6/12+4/12+3/12+2/12)
=18 15/12
=19 3/12
Therefore, the pianist's total practice time is 19 3/12 hours.
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Your checking account is in debt $20. You use this account to make a $10 purchase. Then, you deposit $38 into the account. What is the balance of the checking account?
Answer: 8
Step-by-step explanation
Answer:
$8
Step-by-step explanation:
If we just keep track of the money in the account, we can solve this pretty quickly. If the balance is -20, and we subtract another 10 from it, it gives us -30. $38 is then deposited into the account, giving us a balance of $8.
[tex]-20-10+38=8[/tex]
i need to find the area of a rectangle using the formula A=b*h the height is 810 cm the base is 10 meters...i know i need to convert, but how do i set up the equation to gigute/work this this out?
Answer:
81000[tex]cm^{2}[/tex] or 8.1[tex]m^{2}[/tex]
Step-by-step explanation:
1m = 100cm
10m = 1000cm
a= b*h
a= 1000cm * 810cm
= 810000[tex]cm^{2}[/tex]
1[tex]m^{2}[/tex] = 10000[tex]cm^{2}[/tex]
810000[tex]cm^{2}[/tex] = 8.1[tex]m^{2}[/tex]
What is the slope of the line that is parallel to the y-axis and passes through the point (–1, 5)?
–1
0
5
undefined
Undefined.
All lines that are parallel to the y-axis have an undefined slope.
Answer:
This is an Undefined Slope
Of their first 18 games of the season, the
Chicago Cubs lost 4 games and won the
others. What percent of the games have
they won?
The percentage of the games the club has won is P = 77.78 %
What is Percentage?A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %
The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.
Percentage change is the difference between the measured value and the true value , as a percentage of the true value
Percentage change =( (| Measured Value - True Value |) / True Value ) x 100
Given data ,
Let the total number of games = 18
The number of games they lost = 4
So , the number of games they won = 14 games
Now , the percentage of games they won = ( 14 / 18 ) x 100
On simplifying the equation , we get
A = 0.7778 x 100
A = 77.78 %
Hence , the percentage is 77.78 %
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Suppose the manager of a shoe store wants to determine the current percentage of customers who are males. How many customers should the manager survey in order to be 80% confident that the estimated (sample) proportion is within 9 percentage points of the true population proportion of customers who are males?
Answer:Sử dụCustomer Datang
Step-by-step explanation:
Please help i’ll rate brainliest too
Answer:
- 4
Step-by-step explanation:
h(x) = sin x
f(x) = | 3x - 4 |
g(x) = 2x² - 6
h( [tex]\frac{\pi }{2}[/tex] ) = sin ( [tex]\frac{\pi }{2}[/tex] ) = 1
f ( 1 ) = | 3 × 1 - 4 | = 1
g ( 1 ) = 2( 1² ) - 6 = - 4
g ( f ( h ( [tex]\frac{\pi }{2}[/tex] ) ) ) = - 4
Using the area model below, write the standard form of the product.
- 3x
2.
x2
-14x
5
Answer:
-3x³ + 44x² - 43x + 10
Step-by-step explanation:
[tex]\left[\begin{array}{ccc}&-3x&2\\x^2&-3x^3&2x^2\\-14x&42x^2&-28x\\5&-15x&10\end{array}\right][/tex]
= -3x³ + 2x² + 42x² - 28x - 15x + 10 = -3x³ + 44x² - 43x + 10
the Satya Vansh become an important dynasty in the world of
Answer: it’s 352425262625251452 is 4th of July and I am present
Step-by-step explanation:
1. Which of the following is a nonlinear function?
A. The items at a clothing store are sold at a discount of 20% off the original price.
B. The number of dogs in a town increases by 20 per neighborhood per year.
C. A soccer manufacturing company spends $5 on each soccer ball.
OD. The number of students enrolling at a high school increases each year by a factor of 1.25.
Find the reciprocal of 4i
1/4i
i/-4
i/4
16i
