The equation in terms of t that models the situation is given by
[tex]8192(1+\frac{0.01}{12} )^{12t} = 25710[/tex].
We know that the interest on a loan or deposit that is accrued on both the initial principal and the total interest from prior periods is known as compound interest and it can be calculated as
[tex]A = P(1+\frac{r}{n})^{nt}[/tex],
where P is the initial principal, r is the rate of interest, n is the number of times interest was charged for each time period, t is the amount of time that has passed and A is the final amount.
Here, P = 8192, r = 10% = 10/100 = 0.01, n = 12 and A = 25,710
So, we can write
[tex]8192(1+\frac{0.01}{12} )^{12t} = 25710[/tex]
Therefore the required equation is
[tex]8192(1+\frac{0.01}{12} )^{12t} = 25710[/tex]
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Simplify the polynomial
x+2y+1−(2x+y+5)
Help its assignment
Answer:
- x + y - 4
Step-by-step explanation:
Given polynomial:
[tex] \rm \: x+2y+1-(2x+y+5)[/tex]
Solution:
Removing parentheses,we obtain
[tex]x + 2y + 1 - 2x - y - 5[/tex]Collecting and combining like terms,we obtain
[tex]x - 2x + 2y - y + 1 - 5[/tex][tex] \boxed{ - x + y - 4}[/tex]Done!
Which expression could help you find the distance
between (10, 4) and (-6, 4)?
O [10] +1-41
O 1101 +141
O 1-61 +141
O |10| +-61
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
Correct Expression :
[tex]\qquad \tt \rightarrow \: |10| + | - 6| [/tex]
[tex]\qquad \tt \rightarrow \: distance = 16\:\: units\degree[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex] \textsf{Using distance formula -} [/tex]
[tex]\qquad \tt \rightarrow \: \sqrt{(x_2 - x_1) {}^{2} + (y_2 - y_1) {}^{2} } [/tex]
[tex]\qquad \tt \rightarrow \: \sqrt{( - 6 - 10) {}^{2} + (4 - 4) {}^{2} } [/tex]
[tex]\qquad \tt \rightarrow \: \sqrt{( - 16) {}^{2} + 0} [/tex]
[tex]\qquad \tt \rightarrow \: \sqrt{256} [/tex]
[tex]\qquad \tt \rightarrow \: 16 \: \: units[/tex]
For short it can be expressed as :
[tex]\qquad \tt \rightarrow \: |10| + | - 6| = 10 + 6 = 16[/tex]
[ y - coordinate of both the points are same ]
Correct option - D
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
find the area of the shaded portion in each of the following
Answer:
30.5 cm^2
Step-by-step explanation:
General outlineFind the area of the full circleFind the area of the rectangleFind the difference (full circle area - rectangle area)Step 1. Find the area of the full circleRecall the formula for the area of a circle: [tex]A_{circle}=\pi r^2[/tex] where [tex]\pi \approx 3.14[/tex], and "r" is the radius of the circle (distance from center to any point on the edge).
From the diagram, the radius is 5cm.
[tex]A_{circle}=\pi r^2[/tex]
[tex]A_{circle}=(3.14)(5[cm])^2[/tex]
[tex]A_{circle}=78.5[cm^2][/tex]
Step 2. Find the area of the rectangleRecall the formula for the area of a rectangle: [tex]A_{rectangle}=bh[/tex] where "b" is the base of the rectangle (length of bottom or length of top), "h" is the height of the rectangle (distance from bottom to top).
From the diagram, the base is 8cm, and the height is 6cm.
[tex]A_{rectangle}=bh[/tex]
[tex]A_{rectangle}=(8[cm])(6[cm])[/tex]
[tex]A_{rectangle}=48[cm^2][/tex]
Step 3. Find the difference (full circle area - rectangle area)Having found the areas for each of the first parts, we can find the difference to find the shaded area:
[tex]A_{shaded}=A_{circle}-A_{rectangle}[/tex]
[tex]A_{shaded}=(78.5[cm^2])-(48[cm^2])[/tex]
[tex]A_{shaded}=30.5[cm^2][/tex]
Please help with this certain math problem
Answer: For this real-valued function;
[tex]fog = 2\sqrt{x-1} + 1\\ Domain = [1, )[/tex]
Step-by-step explanation:
COMPOSITE FUNCTIONIf f and g are functions, then the composite function or composition, of g and f is defined by
[tex]( f o g ) (x) = f(g(x))[/tex]
Given the functions [tex]f(x)=2x+1[/tex] , [tex]g(x)=\sqrt{x-1}[/tex],
Now composition for this;
[tex]fog = f(g(x))f(g(x)) = f(\sqrt{x-1} )[/tex]
[tex]f(\sqrt{x-1})[/tex]means we are to interchange variable x in [tex]f(x)[/tex] with the function [tex]\sqrt{x-1}[/tex]
[tex]f(\sqrt{x-1}) = 2(\sqrt{x-1})+1f(\sqrt{x+1}) = 2(\sqrt{x-1})+1fog = 2(\sqrt{x-1})+1[/tex]
The function inside the square root, x-1, must be more significant than or equal to zero (x-10), for the function to exist on any real-valued function.
[tex]if, x-1 \geq 0\\x\geq 0+1\\x \geq 1[/tex]
As a result, the range of the variable x must only include values that are larger than or equal to 1.
Hence, Domain = [1, )
DOMAIN = The domain of [tex]fog[/tex] is the set of all numbers [tex]x[/tex] in the domain of [tex]g[/tex] such that [tex]g(x)[/tex] is in the domain of [tex]f[/tex].Learn more about Composition and Domain here; https://brainly.com/question/6390405
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The graph shows the function f(x).
On a coordinate plane, a cube root function goes through (8, 2), has an inflection point at (0, negative 1), and goes through (8, negative 3).
Which equation represents f(x)?
f(x) = Negative RootIndex 3 StartRoot x EndRoot
f(x) = Negative RootIndex 3 StartRoot x minus 1 EndRoot
f(x) = Negative RootIndex 3 StartRoot negative x EndRoot minus 1
f(x) = Negative RootIndex 3 StartRoot negative x EndRoot
The equation that represents the given data is [tex]\RM \\f(x) = -\sqrt[3]{-x} ,[/tex] Option D is the correct answer.
What is a Function ?It is a statement where two variables , one dependent and one independent are related.
It is given that
a cube root function goes through (8, 2), has an inflection point at (0, negative 1), and goes through (8, negative 3).
The equation given in the options are
[tex]\rm f(x) = -\sqrt[3]{x} \\f(x) = -\sqrt[3]{x-1} \\f(x ) =-\sqrt[3]{-x} -1 \\f(x) = -\sqrt[3]{-x}[/tex]
The function goes through (8,2)
Substituting the values
f(x) = -2
f(x) = [tex]\sqrt[3]{7}[/tex]
f(x) = -3
f(x) = 2
The equation that represents the given data is
[tex]\RM \\f(x) = -\sqrt[3]{-x} ,[/tex] Option D is the correct answer.
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Answer:
D
Step-by-step explanation:
Factor the binomial expansion. 81x4 – 648x3 + 1,944x2 – 2,592x + 1,296
Answer:
[tex]648[/tex]([tex]x^{3} + 3x^{2} - 4x + 2[/tex])
Step-by-step explanation:
When factoring an expression like this, you need to divide all of the parts by a common number or variable. In this case, the only thing all of these numbers share is that they are divisible by 648. So, you would divide each number by 648 to simplify it, getting 1, 3, 4, and 2. Put these numbers in front of their respective variables, and put 648 outside of the parentheses to get the final answer.
Answer:
(3x – 6)4
Step-by-step explanation:
(
Given that a = 7 cm and b = 8 cm,
work out the area of the triangle.
Give your answer rounded to 1 DP.
a
cm²
b
The diagram is not drawn accurately.
Answer:
28cm²
Step-by-step explanation:
The area of a triangle is given as:
= 1/2 × b × h
= 1/2 × 7 × 8
= 28cm²
Jordan wrote the expression 850p to represent the following scenario.
The cost of renting a bowling alley for a party is $850. The price per person depends on how many people attend the party. Write an expression for the price per person if p people attend.
Explain why Jordan's expression is incorrect. Provide the correct expression that represents the scenario.
Using proportions, the expression for the price per person is:
[tex]P = \frac{850}{p}[/tex]
Jordan's expression is wrong because the price per person is inverse proportional to the number of people in the party, not direct proportional.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The cost of renting a bowling alley for a party is $850, hence the cost per person is given by:
[tex]P = \frac{850}{p}[/tex]
Jordan's expression is wrong because the price per person is inverse proportional(that is, the amount is divided by p) to the number of people in the party, not direct proportional.
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Graph the following pair of quadratic functions and describe any similarities/differences observed in the graphs.
f(x) = 8x² +2
h(x) = -8x²-2
a. fopens upward with a y-intercept at (2, 0); h opens downward with a y-intercept at (-2, 0)
b. f opens downward with a y-intercept at (0, -2); h opens upward with a y-intercept at (0, 2)
c. fopens downward with a y-intercept a(0, 2); h opens upward with a y-intercept at (0, -2)
d. fopens upward with a y-intercept at (0, 2); h opens downward with a y-intercept at (0, -2).
The f(x) opens upward with a y-intercept at (0, 2); h(x) opens downward with a y-intercept at (0, -2) , Option D is the right answer.
What is a Function ?A function is a law that defines relation between two variables.
The function given in the question is
f(x) = 8x² +2
h(x) = -8x²-2
The graph is plotted and the similarities or differences are studied ,
It can be seen from the graph that
f(x) opens upward with a y-intercept at (0, 2); h(x) opens downward with a y-intercept at (0, -2).
Therefore Option D is the right answer.
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Henry knows that the circumstance of a circle is 18pi inches. What is the area of the circle?
a. 36pi in²
b. 81pi in²
c. 162pi in²
d. 324pi in²
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{Option B, 81}\pi\textsf{ in}^2[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{Circumference = 18}\pi[/tex]
Find: [tex]\textsf{The area of the circle}[/tex]
Solution: We need to first determine the radius using the circumference formula and once we get the radius then we can plug in the value into the area formula and get our final answer.
Determine the radius
[tex]c = 2 \pi * r[/tex][tex]18\pi = 2 \pi * r[/tex][tex]\frac{18\pi}{2\pi} = \frac{2 \pi}{2\pi} * r[/tex][tex]\frac{18\pi}{2\pi} = r[/tex][tex]9 = r[/tex]Determine the area
[tex]A = \pi * r^2[/tex][tex]A = \pi * (9)^2[/tex][tex]A = \pi * (9 * 9)[/tex][tex]A = 81\pi[/tex]Therefore, the correct answer would be option B, 81π in2.
At the city museum child admission is $6.10 and adult admission is $9.20. On Wednesday, 144 tickets were sold for a total sales of 1083.00. How many adult tickets were sold that day
Given that 2x^2-5 = a(x+2)^2 _ b(x+1)+x for all values of X, find the value of a, of b and of c
It looks like you're asking to solve for the coefficients [tex]a,b,c[/tex] such that
[tex]2x^2 - 5 = a(x+2)^2 - b(x+1) + c[/tex]
Expanding the right side gives
[tex]2x^2 - 5 = ax^2 + 4ax + 4a - bx - b + c[/tex]
[tex]2x^2 - 5 = ax^2 + (4a - b)x + (4a - b + c)[/tex]
The coefficients on both sides must be equal, so
[tex]\begin{cases}a = 2 \\ 4a-b = 0 \\ 4a - b + c = -5\end{cases}[/tex]
Solving the system yields [tex]\boxed{a=2 \implies b = 8 \implies c = -5}[/tex].
Suppose y varies Inversely with x, and y = -1 when x = 3. What Inverse variation equation relates x and y?
The product of variables in inverse proportion is constant, so the equation is [tex]\boxed{xy=-3}[/tex]
Please answer! I will give you the brainliest :)
Answer:
K
Step-by-step explanation:
(1*500 * 5) + (10 * 3*500)
44. What percent of Mary Brown's year-to-date
gross pay has been withheld for federal tax
purposes?
A. 10%
B 13%
C. 17%
D. 20%
45. For the pay period covered on this
paycheck, what percent of Mary Brown's
gross pay was withheld for all taxes and
voluntary dues?
A 10%
B. 13%
C 17%
D. 20%
Based on the amount of federal taxes withheld till date, the percent of Mary Brown's year-to-date that have been withheld is A. 10%.
The percent of the gross pay that has been withheld for all taxes and voluntary dues is C. 17%.
How much federal taxes have been withheld?= Fed tax till date / YTD Gross
= 662.26 / 6,318.17
= 10%
How much taxes and voluntary dues have been withheld?= (Fed tax + ST Tax + Med tax + Vol Due) / Current gross
= (111.42 + 17.09 + 12.25 + 2.5) / 845.10
= 17%
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Figure ABCD is a rhombus. Find the value of x.
58°
x = [ ? ]°
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: x = 32°[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
Diagonals of a Rhombus bisect each other at 90°
[tex]\qquad \tt \rightarrow \: x + 58 + 90 = 180[/tex]
[ Sum of interior angles of a triangle ]
[tex]\qquad \tt \rightarrow \: x + 148 = 180[/tex]
[tex]\qquad \tt \rightarrow \: x = 180 - 148[/tex]
[tex]\qquad \tt \rightarrow \: x = 32 \degree[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
The diagonals of the rhombus intersect at right angle. Then the value of x will be 32°.
What is a rectangle?It is a polygon with four sides. The total interior angle is 360 degrees. In a rhombus, opposite sides are parallel and equal.
Figure ABCD is a rhombus.
Its diagonals intersect at right angle.
Let the another angle be x. Then we have
x + 58° + 90° = 180°
x + 148° = 180°
x = 32°
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yo
24
yx
SECTION B
(a) Identity element;
(b) Inverse of 3 and -5 under *
Range y
[30 marks]
Answer all the questions in this section. All questions carry equal marks.
1. A binary operation is defined on the set of real numbers, R, by x + y = x + y + 10.
Find the:
X
x
Inverse
Answer:
Sike
Step-by-step explanation:
That's the wrong number only 123
A sample of 40 11th graders were asked to select a favorite pattern out of 6
choices. The following display shows what their favorite color patterns were.
The counts have been recorded in the accompanying table according to
pattern and the number of students who selected that pattern. What is the
missing value in the table?
NEN
OA. 12
OB. 10
O C. 11
D. 13
Color Pattern
Blue on gray
Green
Pink polka dots
Purple
Red and orange
stripes
Yellow
Frequency
6
7
8
7
3
The missing value in the table is 12 , Option A is the correct answer.
What is a Graph ?A graph is a mathematical representation of the data available , It makes the study of the data over a wide period easier.
It is given in the question that there are 40 students and the frequency they select for each pattern is mentioned as number , which can be seen in the image attached with the answer.
It has been asked to determine the missing value in the frequency table corresponding to the pink Polka dots
The other number in the frequency table is 4, 6 ,8 ,7, 3
Total students are 40
Therefore the value corresponding to the pink polka dot is given by
40 - ( 4+6+7+8 +3)
= 12
Therefore The missing value in the table is 12 , Option A is the correct answer.
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3149 can be divide?
Answer:
yes.
but it will be in decimals if you divide by two. And if you divide it by another rank, it will surely give a whole number. please this all I can do for you and add me to your followers
Pls help! Answer the question in the pic. I will give five stars, thanks, and brainliest!
*20 POINTS*
(6-^8)^4 please helpppp
[tex](6^-^8)^4[/tex]
[tex]=6^-^2^4[/tex]
[tex]=\frac{1}{6^2^4}[/tex]
Find X and QT. The shape is a Rhombus
Answer:
See below ~
Step-by-step explanation:
Sides of a rhombus are equal.
⇒ QT = TS
⇒ x² - 4x - 10 = 6x + 14
⇒ x² - 10x - 24 = 0
⇒ x² + 2x - 12x - 24 = 0
⇒ x (x + 2) - 12 (x + 2) = 0
⇒ (x + 2)(x - 12) = 0
⇒ x = -2 or x = 12
Substitute both values and see which gives a positive value for QT :
When x = -2 :
QT = (-2)² - 4(-2) - 10QT = 4 + 8 - 10QT = 2When x = 12 :
QT = (12)² - 4(12) - 10QT = 144 - 48 - 10QT = 86The 2 possible answers are :
x = -2, QT = 2x = 12, QT = 86*Will give 30pts*Consider function f. f(x)=2x^2.What is the value of (f•f)(x)?
Answer:
[tex]\textbf {B}[/tex]
Step-by-step explanation:
f(x) = 2x²
f [f(x)]
f [2x²] = 2(2x²)²
f[f(x)] = 2(4x⁴)
f[f(x)] = 8x⁴
Work out (4 x 3)² ÷ 6
An expression is defined as a set of numbers, variables, and mathematical operations. The solution of (4 x 3)² ÷ 6 is 24.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The solution of the expression (4 x 3)² ÷ 6 is,
(4 x 3)² ÷ 6
= (12)² ÷ 6
= 144 ÷ 6
= 24
Hence, the solution of (4 x 3)² ÷ 6 is 24.
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what are the coordinates of this point help plssssssssssssssss
Answer:
(-2, -4)
Step-by-step explanation:
Use the (x,y) thing:
x = -2
y = -4
therefore, (-2, -4)
Which one is it I need to finish this page fast
Answer:
E; 10% off %20 sweater with $6 shipping
Step-by-step explanation:
Similar to what I said last time,
this time is with percentages,
How to calculate percent off?
Divide the number by 100 (move the decimal place two places to the left).
Multiply this new number by the percentage you want to take off.
Subtract the number from step 2 from the original number. This is your percent off number.
________________________________________________________
A. 35% off a $35 sweater with 4 dollar shipping is basically
0.35 x 35 = 12.25 and 35-12.25 = $22.75 + the $4 shipping fee (if no tax)
which the total would be $26.75
B. 20% off $35 is
0.2x35=7 and 35-7 = 28 so your total is $28
C. 30% off $30 with $6 for shipping is
0.3x30=9 and 30-9 is $21 plus the shipping fee
$27
D. $20 sweater with $5 shipping is $25 no discount involved :D
E. 10% off %20 sweater with $6 shipping is
0.1x20 is 2 which 20 - 2 = 18 and plus shipping fee 18+6 is $24
________________________________________________________
Hope this helped again.
A student draws two parabolas on graph paper. Both parabolas cross the x-axis at (-4, 0) and (6, 0). The y-intercept
of the first parabola is (0, -12). The y-intercept of the second parabola is (0, -24). What is the positive difference
between the a values for the two functions that describe the parabolas? Write your answer as a decimal rounded to
the nearest tenth.
Answer:
1/2
Step-by-step explanation:
First parabola f(x1) = a ( x+4)(x-6) use point 0,-12 to find a = 1/2
= 1/2 (x+4)(x-6)
Second parabola a ( x+4) (x-6) using point 0, -24 shows a = 1
f(x2) = (1)(x+4)(x-6)
Difference between the 'a' values = 1 - 1/2 = 1/2
When you raise (almost) anything to the power zero, you get 1.
Answer:
z^0= 1
(2v+2)^0 = 1
3^0 = 1
0^0= 0
Step-by-step explanation:
When you raise (almost) anything to the power zero, you get 1 and when you raise 0 to any number except 0 is 0
To draw a graph for y = 3/4x + 7, a person can draw a point at x of 0 and y of a second point by going up 3 and over.
then draw a line through the points.
Thus, for drawing the graph for y = 3/4x + 7.
For drawing the graph for y = 3/4x + 7, a person can draw a point at x of 0 and y of __7_, a second point by going over 3 and up __8.25__, and then draw a line through the points.
How to know if a point lies in the graph of a function?All the points (and only those points) which lie on the graph of the function satisfy its equation.
Thus, if a point lies on the graph of a function, then it must also satisfy the function.
For this case, the equation given to us is:
y=3/4x+7
Any equation of the form y=mx+c where m and c are constants and x and y are variables is the equation of a straight line.
For a straight line to be characterized, only two points are sufficient.
For x = 0, the y-coordinate would be such that it would satisfy the equation
y=3/4x+7
Putting x = 0, we get:
y=3/4(0)+7
y=7
Thus, the y-coordinate of the point on this line whose x-coordinate is 0 is 7. Thus, (0,7) is one of the point coordinates on the considered line.
Putting x = 3, we get:
y=3/4(3)+7
y=9.25
Thus, the y-coordinate of the point on this line whose x-coordinate is 0 is 9.25. Thus, (0,9.25) is another of the point's coordinates on the considered line.
Thus, for drawing the graph for y = 3/4x + 7, a person can draw a point at x of 0 and y of __7_, a second point by going over 3 and up __8.25__, and then draw a line through the points.
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Let E be the event where the sum of two rolled dice is greater than or equal to 7. List the outcomes in Ec.
Answer:
(1, 1) (1, 2) (1, 3) (1,4)
(1,5) (2,1) (2,2) (2,3)
(2,4) (3,1) (3,2) (3,3)
(4,1) (4,2) (5,1)
Step-by-step explanation:
An event is a specified set of results of a random experiment in probability theory. The number of possible outcomes that Event E has is 21.
What is an event?An event is a specified set of results of a random experiment in probability theory. Because the sample space is the collection of all potential outcomes of a random experiment, another definition of an event is any subset of a sample space.
Let E be the event where the sum of two rolled dice is greater than or equal to 7. Therefore, the outcomes in E are represented in red in the given table below.
(1, 6)
(2, 6)
(3, 6)
(4, 6)
(5, 6)
(6, 6)
(2, 5)
(3, 5)
(4, 5)
(5, 5)
(6, 5)
(3, 4)
(4, 4)
(5, 4)
(6, 4)
(4, 3)
(5, 3)
(6, 3)
(5, 2)
(6, 2)
(6, 1)
Hence, the number of possible outcomes that Event E has is 21.
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