The total amount payable at the end of 4 years is 406
In this given sum we are provided with the values of principal , rate of interest , and the number of years , we are asked to calculate the amount payable after 4 years that is the matured amount which is calculated with the addition of the principal amount and the simple interest. For that we had to first find out the amount of interest and then we need to add that with the principal amount to get the matured amount or the amount that is payable at the end of 4 years.
here we have to apply the formulla of simmple interest :
(principal × rate of interest × no. of years )/ 100
In the given sum principal (p) = 350 , rate of interest (r) = 4% pa , no. of years (n) = 4
Simple interest = pnr/100
= (350 × 4 × 4)/100 = 56
Matured Amount = Principal + Interest
= 350 + 56 = 406
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TRAIN STATIONS A train travels a straight route from Rolesville to Townsend. The railway would like to build a station along the route so that the ratio of the distance from Rolesville to the station and the distance from the station to Townsend is 3:4 . If the coordinates of Rolesville and Townsend on the map are R(1, 2) and T(8, 23) , respectively, what should be the coordinates of the new station?
coordinates of the new station= (5,98/4)
When two lines intersect at a point then the angle between them can be expressed in terms of their slopes and is given by the following formula:
tan θ = |
|where
are the slopes of the line AB and CD respectively.
If
is positive then the angle between the lines is acute. If
is negative then the angle between the lines is obtuse.
Slope of Vertical Lines
Vertical lines have no slope, as they do not have any steepness. Or it can be said, we cannot define the steepness of vertical lines.
A vertical line will have no values for x-coordinates. So, as per the formula of slope of the line,
Slope, m = (y2 – y1)/(x2 – x1)
But for vertical lines, x2 = x1 = 0
Therefore,
m = (y2 – y1)/0 = undefined
In the same way, the slope of horizontal line is equal to 0, since the y-coordinates are zero.
m = 0/(x2 – x1) = 0 [for horizontal line]
Positive and Negative Slope
If the value of slope of a line is positive, it shows that line goes up as we move along or the rise over run is positive.
If the value of slope is negative, then the line goes done in the graph as we move along the x-axis.
Let R,Q,T be the points that divide the line into 3:4 equal parts
Let the Q = (x,y)
R(1, 2) and T(8, 23) ,
x = m1x1+m2x2/m1+m2
y = m1y1+m2y2/m1+m2
X= 3.1+4.8/7
x= 3+32/7
x=35/7
x=5
y=2.3+23.4/3+4
y= 6+92/4
y=98/4
y= 24.5
(x,y) = (5,98/4)
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(100 POINTS ASAP)
Triangle EFG is shown in the graph.
The triangle will be reflected across the x-axis and then dilated by a scale factor of 2 with respect to the origin, resulting in triangle E'F'G'.
What will be the coordinates of G'?
Answer:
The coordinates of G' will be (8, 4)Step-by-step explanation:
Point G has coordinates (4, -2).
After reflection across the x-axis it s coordinates will change as per rule:
(x, y) → (x, - y)Applied to point G:
(4, - 2) → (4, 2)After dilation by a scale factor of 2 the coordinates will change as per rule:
(x, y) → (2x, 2y)Applied to point G:
(4, 2) → (2*4 = 8, 2*2 = 4)G' = (8, 4)4 D
A bear can run 400 feet in 8 seconds.
A horse can run 290 feet in 5 seconds?
Which animal runs at the faster rate?
Horse runs at the faster rate i.e. at the rate of 58 feet per seconds.
According to the given question.
A bear can run 400 feet in 8 seconds.
A horse can run 290 feet in 5 seconds.
As we know that, the measurement of the speed at which something happens is called rate.
Therefore, form distance rate formula (rate = distance/time)
The rate of the bear = 400/8 = 50 feet/sec
And the rate of the horse = 290/5 = 58 feet/sec
Therefore, horse can run faster than bear.
Hence, horse runs at the faster rate i.e. at the rate of 58 feet per seconds.
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How did the new deal hope to stimulate industrial recovery
A salesperson's weekly paycheck is 25% more than a second salesperson's paycheck. The two paychecks total $1075. Find the amount of each paycheck. (Round your answers to the nearest cent.)
Given the geometric series 6+3+3/2….Find
(i) the sum of n terms.
(ii) S infinity. Hence, determine smallest value of n such that S infinity - Sn < 0.001.
12-12[1-(1)]<0.001
The least value is 11.
[tex]$$\begin{aligned}&\mathrm{S}=\frac{1}{1-(1 / 2)}=2 \\&\mathrm{~S}_{\mathrm{n}}=\frac{1-(1 / 2)^{\mathrm{n}}}{1-(1 / 2)}=2-\frac{1}{2^{\mathrm{n}-1}}\end{aligned}$$[/tex]
[tex]$$\mathrm{S}-\mathrm{S}_{\mathrm{n}}=\frac{1}{2^{\mathrm{n}-1}} < \frac{1}{1000} \text { or } 2^{\mathrm{n}-1} \geq 1000$$[/tex]
Now [tex]$2^{10}=32 \times 32=1024$[/tex]
[tex]$$\therefore n-1 \geq 10 \text { or } n \geq 11$$[/tex]
Hence the least value is 11.
If you have a positive term in your quadratic equation, it will also have a minimum value. This minimum value can be found by graphing the function or solving one of the two equations. If you have the equation y = a[tex]x^2[/tex] + bx + c, you may use the equation min = c - [tex]b^2[/tex]/4a to determine the minimum value.
A quadratic equation is a second-order polynomial equation in a single variable x a[tex]x^2[/tex]+bx+c=0. with a ≠ 0 . The fundamental theorem of algebra assures that it has at least one solution because it is a second-order polynomial equation.
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The marching band needs to create rows for its performance. There are 30 instruments and 18 flag bearers. Only one type of performer can be in each row. What is the maximum number of performers in each row so that all the rows are equal in length?
The maximum number of performers in each row so that all the rows are equal in length is 6.
The greatest common divisor (HCF) of two numbers is the largest number that divides both numbers perfectly. Highest Common Divisor (HCF) is also known as Greatest Common Divisor (GCD).Simply put, the HCF (Highest Common Factor) of two natural numbers x and y is the largest number that divides both x and y.It is given that there are 30 instruments and 18 flag bearers.
Prime factorization of 30 is given by
[tex]30=2\times3\times5[/tex]
Prime factorization of 18 is given by
[tex]18=2\times3\times\ 3[/tex]
The prime factorization of 30 and 18 have 2 and 3 as common prime number so HCF will be [tex]2\times3=6[/tex]
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3x-7y=11;x=-3,0,3
Solve for y
Answer:
y = 3x/7 - 11/7
Step-by-step explanation:
3x/7 - 7y/7 = 11/7
-11/7 +y -11/7 +y
3x/7 - 11/7 = y
(Multiplying Rational Numbers MC)
Lorie ordered a shed to hold her gardening supplies. The shed had a length of 10.25 ft, a width of 14 ft, and a height of 7 ft.
Determine the volume, V. using the formula V = wh
31.45 cubic ft
103.32 cubic ft
O 983 2 cubic ft J
1.033.2 cubic ft
The shelter has a volume of (E) 1108.25ft³.
What exactly is a Cuboid?A cuboid is a three-dimensional figure with six faces, all of which are rectangular.The volume of a three-dimensional figure is the space it occupies.Formula: V = lwh
Put the values in the formula as follows:
V = 16.25 × 11 × 6.2V = 1108.25 ft³Therefore, (E) 1108.25ft³ is the volume of the shelter.
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The correct question is given below:
Lorie ordered a shed to hold her gardening supplies. The shed had a length of 16.25 ft, a width of 11 ft, and a height of six and one-fifth ft. Determine the volume, V, using the formula V = lwh.
a. 31.45 cubic ft
b. 103.32 cubic ft
c. 983 2 cubic ft J
d. 1.033.2 cubic ft
e. 1108.25
Denise is going on vacation and taking her dog Pickles along. Pickles eats 4 cups of Hungry Hound dog food each day. Denise wants to know how many days she can feed Pickles from a 24-cup bag of Hungry Hound.
Which equation can Denise use to find the number of days d she can feed Pickles from the bag.
Answer:
D
Step-by-step explanation:
Se can feed pickle freom the bag
AAAAAAAAAAnswer: 24/4 = 6
What is the factored form of 82+12?
O 442+80)
O4(2x+3)
O ax(x+4)
O 8x(+4)
Answer:
Option 2
Step-by-step explanation:
Rory has 6 pounds of ground beef to make meatballs. He uses 5/8 pound per meatball to make 9 meatballs. How many 1/8 pound meatballs can Rory make with the remaining beef?
Rory can make 43 metaballs from the remaining beef.
What are maths operations?An operation is a function in mathematics that converts zero or more input values (also known as "operands" or "arguments") to a well-defined output value. The operation's arity is determined by the number of operands.Binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse, are the most commonly studied operations. A zero-arity operation, also known as a nullary operation, is a constant. The mixed product is an example of an arity 3 operation, also known as a ternary operation.Rory has 6 pounds of ground beef on hand for making meatballs.
He makes 9 meatballs with 5/8 pounds of meat per meatball.
We must subtract 5/8 from 6.
6 - 5/848-5/843/8There are 43/8 pounds of ground beef remaining.
As a result, the number of 1/8 pound meatballs produced from 21/8 pound ground beef can be calculated as follows:
43/8 ÷ 1/843/8 × 8/1= 43Therefore, Rory can make 43 metaballs from the remaining beef.
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Help asap but only if you are sure!
Answer:
D.
Step-by-step explanation:
[tex]17\% = 0.17\\0.25 = 0.25\\2/9 = 0.22\\\\0.17 \rightarrow 0.22 \rightarrow 0.25[/tex]
Answer:
D
Step-by-step explanation:
17%, 2/9= 22%, 0.25= 25%
Find all possible values for A, B, and C
AB + AB + AB + AB=CA
AAnswer:
Las Letras A B C , en matematicas el valor puede variar ; ya que ya depende del valor que se le otorge o ya si es una operacion , pues el valor que se obtiene , es decir las letras en matematicas no tiene o poseen un valor fijo
Step-by-step explanation:
Evaluate.
Remember Order of Operations!
(PEMDAS)
(-7+3²) × 8
Answer:
16
Step-by-step explanation:
[tex]-7+3^2\\3^2\\=9\\=-7+9\\=-7+9 = 2\\=2\times \:8\\2\times \:8=16\\\boxed{16}[/tex]
Electricity rates. The table to the right shows the electricity
rates charged by Better Than Lightning Utilities in the winter
months.
a. Write a piecewise definition of the monthly charge W(x) for a
customer who uses x kWh in a winter month.
b. Determine the graph of W(x)
Winter (November-June)
Base charge, $8.50
First 300 kWh or less at 0.0650/kWh
Over 300 kWh at 0.0850/kWh
The piecewise function for the monthly charge W(x) for a customer who uses x hours of electricity is given by:
W(x) = 50 + 0.0650x, 0 ≤ x ≤ 300.W(x) = 69.5 + 0.0850x, x > 300.The graph of the function is given at the end of the answer.
What is a piecewise-defined function?A piecewise-defined function is a function that has different definitions, depending on the input of the function.
For this problem, we have that:
The input is the number of kWh electricity used.The output is the monthly charge.The monthly charge is calculated differently according to the number of kWh of electricity used, divided into two cases as follows:
First 300 kWh : 0 ≤ x ≤ 300.More than 300 kWH: x > 300.For up to 300 hours, the base charge of $50 plus the hourly fee of $0.0650 is charged, hence:
W(x) = 50 + 0.0650x, 0 ≤ x ≤ 300.
For more than 300 hours, the customer is charge 50 + 300 x 0.0650 = $69.5, plus the hourly fee of $0.0850, hence:
W(x) = 69.5 + 0.0850x, x > 300.
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Solve this question please for me
f (x) - 2/3x - 7 find the inverse
If you pick a number between one and three and the computer picks a number between one and four, how many different outcomes are
possible if the two numbers are added together? (Hint: You may find it useful to complete a table for this problem)
2
4
7
6
None of these
The possible outcomes for the sum are the numbers in the set:
{2, 3, 4, 5, 6, 7}
So there are 6 possible outcomes.
How many outcomes are possible?
You can select a number between 1 and 3, so the options are {1, 2, 3}
The computer selects a number between 1 and 4, so the options are {1, 2, 3, 4}
The possible aditions, in the form of "your number + computer number" are:
1 + 1 = 2
2 + 1 = 3
3 + 1 = 4
1 + 2 = 3
2 + 2 = 4
3 + 2 = 5
1 + 3 = 4
2 + 3 = 5
3 + 3 = 6
1 + 4 = 5
2 + 4 = 6
3 + 4 = 7
So the possible outcomes for the sum are the numbers in the set:
{2, 3, 4, 5, 6, 7}
So there are 6 possible outcomes.
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help me with this Select all the expressions that are equivalent to 78 • 7.
73 • 73
71879
(73)3
74 + 75
74 • 75
The expressions that are equal to 7⁸ x 7 are:
B. For (7¹⁸)/7⁹
C. For (7³)³
E. For 7⁴ x 7⁵
What are the fundamentals of exponential functions?Exponential functions now have formula f(x) = bx, where b > 0 and b 1. As in any exponential expression, b serves termed the base and x is called its exponent. The proliferation of bacteria is an example of such an exponential function.
According to the given data:A. For 7³ x 7³
simplify using exponent rule with the same base: aⁿ x aˣ
= aⁿ ⁺ ˣ
= 7³ ⁺ ³
Calculate the sum or difference: 7⁶
Calculate power : 117649
simplify using exponent rule with the same base: aⁿ x aˣ
= aⁿ ⁺ ˣ
= 7⁸ ⁺ ¹
Calculate the sum or difference: 7⁹
Calculate power : 40353607
Check equivalency: False
Solution: False
B. For (7¹⁸)/7⁹
Reduce the fraction: 7⁹
Calculate power : 40353607
simplify using exponent rule with the same base: aⁿ x aˣ
= aⁿ ⁺ ˣ
= 7⁸ ⁺ ¹
Calculate the sum or difference: 7⁹
Calculate power : 40353607
Check equivalency: True
Solution: True
C. For (7³)³
simplify using exponent power rule : 7⁹
Calculate power : 40353607
simplify using exponent rule with the same base: aⁿ x aˣ
= aⁿ ⁺ ˣ
= 7⁸ ⁺ ¹
Calculate the sum or difference: 7⁹
Calculate power : 40353607
Check equivalency: True
Solution: True
D. For 7⁴ + 7⁵:
Calculate the power: 2401 + 16807
Calculate the sum or difference: 19208
simplify using exponent rule with the same base: aⁿ x aˣ
= aⁿ ⁺ ˣ
= 7⁸ ⁺ ¹
Calculate the sum or difference: 7⁹
Calculate power : 40353607
Check equivalency: False
Solution: False
E. For 7⁴ x 7⁵:
simplify using exponent rule with the same base: aⁿ x aˣ
= aⁿ ⁺ ˣ
= 7⁴ ⁺ ⁵
Calculate the sum or difference: 7⁶
Calculate power : 40353607
simplify using exponent rule with the same base: aⁿ x aˣ
= aⁿ ⁺ ˣ
= 7⁸ ⁺ ¹
Calculate the sum or difference: 7⁹
Calculate power : 40353607
Check equivalency: True
Solution: True
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I understand that the question you are looking for is:
Select all the expressions that are equivalent to 7⁸ x 7.
A. For 7³ x 7³
B. For (7¹⁸)/7⁹
C. For (7³)³
D. For 7⁴ + 7⁵:
E. For 7⁴ x 7⁵
Answer:
none
Step-by-step explanation:
point steeler
Giselle paid an accountant 25$ per hour to do her taxes plus a 100$ one-time fee. Her total bill was $250. How many hours did the accountant work?
What is the domain of g
Answer:
A
Step-by-step explanation:
The domain of g(x) is the set of all real numbers. Meaning that all the numbers between the min and max of g would be -7 ≤ x ≤ 7.
The temperatures at sunrise and sunset are shown in the table. What was the temperature change on each day? On which day did the temperature change the most?
The temperature changes for each day are 32.12 °C (Day 1) and 33.02 °C (Day 2), respectively. The day 2 registered the highest temperature change.
How to analyze and interpret temperature changes
Herein we find a table with the temperatures at sunrise and sunset in two days and we need to determine the temperature change for each period and conclude in what day the change was the highest. The temperature change can be found by using the following formula:
ΔT = T' - T
Where:
T - Temperature at sunrise, in degrees Celsius.T' - Temperature at sunset, in degrees Celsius.The temperature changes for each day are 32.12 °C (Day 1) and 33.02 °C (Day 2), respectively. The day 2 registered the highest temperature change.
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4. What is the probability of pulling either a fork or a spoon out of the bag?
We the Probability of pulling either fork or spoon as 1.
We are given that:
We have a fork and a spoon in a bag.
Total number of items in a bag = 1 + 1 = 2
Now, we need to tell the probability of either pulling a fork or a spoon.
Now,
Probability of pulling a fork = 1 / 2 = 0.5
Probability of pulling a spoon = 1 / 2 = 0.5
So, the Probability of pulling either of them will be = 1 / 2 + 1 / 2 = 1
Therefore, we the Probability of pulling either fork or spoon as 1.
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please help! ill give branliest
Answer: That is a cold front
Step-by-step explanation:
It is a cold front because the warm air is rising because it is less dense than the cold air which is why the cold air isn’t rising because the cold air is denser than that of the warm air so it just continues moving forward
Find the domain and range of the function F(t) = sec(3.14t/4)
The domain of sec(3.14t/4) is all real numbers except 2+4n, where n is any integer and range of sec(3.14t/4) is [tex](\infty,-1] \cup [1,\infty)[/tex].
The Domain of a function f(x) is the set of all values for which the function is defined.
The Range of a function is the set of all values that f takes.
As, [tex]sec x=\frac{1}{cos x}[/tex] , so sec x is defined where [tex]cos x \neq 0[/tex].
It implies, sec(3.14t/4) is defined where [tex]cos(3.14t/4)\neq 0[/tex].
The cosine is 0 at [tex](2n+1)\frac{\pi }{2}[/tex] , where n is any integer.
Now, [tex]\frac{3.14t}{4} =\frac{(2n+1)\pi }{2}[/tex]
[tex]\frac{\pi t}{4} =\frac{(2n+1)\pi }{2}[/tex]
[tex]t=2(2n+1)\\t=2+4n[/tex]
Since, the range of cos x is [-1,1], so sec x will never be less than 1, but can grow infinitely large as cos x approaches 0.
Thus, The domain of sec(3.14t/4) is all real numbers except 2+4n, where n is any integer and range of sec(3.14t/4) is [tex](\infty,-1] \cup [1,\infty)[/tex].
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John painted his most famous work, in his country, in 1930 on composition board with perimeter 108.56 in. If the rectangular painting is 5.97 in. taller
than it is wide, find the dimensions of the painting.
What is the width?
(Simplify your answer. Type an integer or decimal rounded to two decimal places as needed.)
The width of the rectangular painting painted by John is 24.15 inch.
What is referred as the rectangle?A rectangle is a quadrilateral with parallel sides that are equal to one another and all four vertices that are equal to 90 degrees. As a result, it is also known as an equiangular quadrilateral. Because the opposite sides of a rectangle are equal as well as parallel, it is also known as a parallelogram.For, the given question;
The perimeter of the rectangular painting painted by the John is 108.56 in.
The formula for the perimeter of the rectangle is;
Perimeter = 2(length + width)
Thus,
2(length + width) = 108.56
The rectangular painting is 5.97 in. taller than it is wide.
It means;
Length = 5.97 + width
Put the value in perimeter.
2(5.97 + width + width) = 108.56
11.94 + 4 width = 108.56
width = 24.155
width = 24.155 (decimal rounded to two decimal places)
Therefore, the width of the painting is 24.15 inch.
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What is the approximate length of the diameter, d?
7in
14in
22in
44in
Answer:
14 in
Step-by-step explanation:
the formula for the circumference of a circle is
2×pi×r
or (because the diameter is 2×r)
pi×d
with r being the radius and d being the diameter.
44 = pi×d
d = 44/pi = 14.00563499... in ≈ 14 in
A parking lot has two types of parking spaces. Some parking spaces are rectangles and other spaces are parallelograms that are not rectangles. Plans for the parking spaces are drawn on grid paper. a. Which parking space covers the greater area, space A or space B? Show your work.
Parking space B covers a greater area.
Here, we are given a parking lot has two types of parking spaces- rectangles and parallelograms, as shown in the figure.
Let us calculate the area of each figure one by one-
Area of rectangle = length × breadth
Here, length = 6 units
breadth = 3 units
Thus, area of rectangle = 6 × 3
= 18 square units
Now, area of a parallelogram = base × height
here, base = 4 units
height = 5 units
Area = 4 × 5
= 20 square units
⇒ the area of the parallelogram is greater than the rectangle
Thus, parking space B covers a greater area.
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Your question was incomplete. Check for the missing figure below.
Shawn reads 5 pages in 20 minutes. He spends the same amount of time per page. How long will it take him to read 11 pages?
Answer:
44
Step-by-step explanation:
20 ÷ 5 = 4 minutes per page
4 x 11 pages = 44
Let f(x) = -3x+5 and g(x)=x²-2. Find the difference (g - f)(x).
(g-f)(x) =
Answer: f(x^2) = x^2 - 5