Answer:
A= 2000*(1+0.05)^t
Explanation: The equation represents the compound interest formula where A is the amount of money in the account, P is the principal amount (initial investment) which is $2,000, r is the interest rate (expressed as a decimal) which is 5% or 0.05, and t is the number of years. The formula shows that the account balance will increase by 5% each year, meaning the interest will be added to the principal and the new interest will be calculated on the new balance.
Step-by-step explanation:
Determine the solutions of the equation. What solution makes sense for the situation?
The dimensions of the rectangle are 8 inches as width and 13 inches as length.
How to calculate the equation?An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.
The equation is given as:
x² + 5x - 104.
x² + 13x - 8x - 104
x(x + 13) - 8 (x + 13).
x - 8 = 0
x = 0 + 8
Width = 8
Length = x + 5
= 8 + 5.
= 13
The width is 8 inches and length is 13 inches.
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Determine the solutions of the equation. What solution
makes sense for the situation?
A rectangle has a length that is 5 inches greater than its
width, and its area is 104 square inches. The equation (x
+5)x = 104 represents the situation, where x represents
the width of the rectangle.
(x + 5)x = 104
x2 + 5x - 104 = 0
What are the dimensions of the rectangle?
Help meeee thx I don’t know how to do this
Answer:
There are 36 pink blocks in the bin
Step-by-step explanation:
[tex]45\% \text{ of } 80 = 0.45(80)= 36[/tex]
Use the figure to complete the statement. If not similar choose not similar
Answer:
The answer is side side side (SSS)
Answer:
SSS Similarity
Step-by-step explanation:
121/9 = 8/6 = 16/12
Similar by SSS Similarity
which of the following is equivalent to 0.00648?
Identify the transformed function that represents f(x) = ln x stretched vertically by a factor of 5, reflected across the x-axis, and shifted by 6 units left.
A. G(x) = -5ln (x - 6)
B. G(x) = 5ln (x + 6)
C. G(x) = -5ln (x + 6)
D. G(x) = 5ln (x - 6)
The function after transformation is G(x) = -5 ln (x+6) is the correct answer.
The correct answer is an option (C)
Here, the function is f(x) = ln x
A function f(x) is stretched vertically by a factor of 5.
As we know for a vertical stretch, we need to multiply the whole function by the factor of stretching.
If the stretching factor is m, then after stretching the function becomes
⇒ m × f(x)
Here, stretching factor m = 5
So the transformed function would be,
G(x) = 5 f(x)
⇒ G(x) = 5 ln x
Now, function is reflected across the x-axis, so the function becomes
⇒ G(x) = -5 ln (x+6)
Then the function is shifted by 6 units left, so after translation the function becomes
⇒ G(x) = -5 ln (x+6)
Thus, we can conclude that the function f(x) = ln x after transformation would be G(x) = -5 ln (x+6) is the correct answer.
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Dustin’s math classroom has 2 bulletin boards side by side. The teacher said the length of one
board is 1. 25 yards, and the other is 1. 75 yards. What is the total length in feet of the two
bulletin boards side by side?
The total length in feet of the two bulletin boards side by side is 9 feet.
The total length of the bulletin boards when calculated side by side will be done using addition operation. The expression that will form for calculation is -
The total length = length of one bulletin board + length of second bulletin board
Keep the values in formula -
The total length = 1.25 + 1.75
Performing addition on Right Hand Side of the equation
The total length of the two bulletin boards = 3 yards
The total length in feet = 3 × (3 feet)
Performing multiplication
Total length = 9 feet
The total length in feet is 9 feet.
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Solve this equation in the
given domain: 0
*give answer in radians*
3 sin (2x-4)=2
There should be 4 answers.
look at attached photo
Answer: 2.294524311274043, 4.294524311274043, 6.294524311274043 and 8.294524311274043 radians.
Step-by-step explanation: We can start by isolating the sin function on one side of the equation:
sin (2x-4) = 2/3
Next, we can use the inverse sine function (sin^-1) to find the value of 2x-4:
2x-4 = sin^-1(2/3)
We know that the domain of the inverse sine function is [-1,1], so the value of 2/3 falls in that range. To find the value of x, we can add 4 to both sides and divide both sides by 2:
x = (sin^-1(2/3) + 4) / 2
The value of sin^-1(2/3) is approximately 0.5890486225480862 radians and that's the first solution in the range [0, pi], and we can add multiples of pi to get the other solutions.
x = (0.5890486225480862 + 4) / 2 = 2.294524311274043 radians (in the range [0, pi])
x = (0.5890486225480862 + 4 + pi) / 2 = 4.294524311274043 radians (in the range [pi, 2pi])
x = (0.5890486225480862 + 4 + 2pi) / 2 = 6.294524311274043 radians (in the range [2pi, 3pi])
x = (0.5890486225480862 + 4 + 3pi) / 2 = 8.294524311274043 radians (in the range [3pi, 4*pi])
So there are four solutions to this equation: 2.294524311274043, 4.294524311274043, 6.294524311274043 and 8.294524311274043 radians.
[tex]3\sin(2x-4)=2\implies \sin(2x-4)=\cfrac{2}{3}\implies 2x-4=\sin^{-1}\left( \cfrac{2}{3} \right) \\\\\\ 2x=\sin^{-1}\left( \cfrac{2}{3} \right)+4\implies x=\cfrac{\sin^{-1}\left( \frac{2}{3} \right)+4}{2} \\\\\\ x=\cfrac{\sin^{-1}\left( \frac{2}{3} \right)}{2}+2\implies x\approx\cfrac{0.73}{2}+2\implies \stackrel{II~Quadrant}{x\approx 2.365}\hspace{5em}\stackrel{III~Quadrant}{\stackrel{\frac{\pi -0.73}{2}+2}{x\approx 3.206}}[/tex]
Alex has an 80% chance of passing a test. Brad has a 60% chance of passing the test. Work out the probability that Alex and Brad both fail the test
If Alex has an 80% chance of passing a test and Brad has a 60% chance of passing the test ,then the probability that Alex and Broad both fail the test is 0.8 or 8% .
The percent chance that Alex passes the test is = 80% = 0.8 ;
So , probability that Alex fails the test is = 1 - 0.8 = 0.2 ;
the percent chance that Brad passes the test is = 60% = 0.6 ;
So , the probability that Brad fails the test is - 1 - 0.6 = 0.4 ;
we have to find the probability that Alex and Broad both fail the test ,
the required probability of both failing can be found by using formula :
= (probability Alex fails the test) × (probability Brad fails the test)
= 0.2 × 0.4
= 0.8 .
Therefore , the probability that both fail the test is 0.8 or 8% .
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A researcher observes and records the height of a weight moving up and down on the end of a spring. At the beginning of the observation the weight was at its highest point. From its resting position, it takes 8 seconds for the weight to reach its highest position, fall to its lowest position, and return to its resting position. The difference between the lowest and the highest points is 20 in. Assume the resting position is at y = 0
Assume the resting position is at y=0, so the function is y = 10sin(π/4 x + π/4).
First one the first point will not be on the midline and will be at the maximum height.
In physics, amplitude refers to the greatest displacement or distance that a point on a vibrating body or wave can move relative to its equilibrium location.
amplitude = 10 = A and y = Asin(Bx - C) + D
Time = 8 seconds
B = 2π/time
B = 2π/8
B = π/4
The sine graph is pushed back by π/2 units since the weight is at its maximum position at x = 0; as a result, C = π/2, D = 0 (the midline is y = 0).
y = 10sin(π/4 x + π/4) is the function.
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The complete question is:
A researcher observes and records the height of a weight moving up and down on the end of a spring. At the beginning of the observation the weight was at its highest point. From its resting position, it takes 12 seconds for the weight to reach its highest position, fall to its lowest position, and return to its resting position. The difference between the lowest and the highest points is 10 in. Assume the resting position is at y = 0. Use the sine tool to graph the function. The first point must be on the midline and the second point must be a maximum or minimum value on the graph closest to the first point.
An amusement park is building a new water slide which is supported by beams of 40 feet and 25 feet. To support the weight of the ride effectively, a support beam (EF) needs to be added to hold the guide wires (AC and BD) in place. What will the height of the support beam need to be for this new ride?
As per the formula of area of triangle, the height of the support beam need to be for this new ride is 3.2 feet.
In math the term area is defined as “b” be the base and “h” be the height of a triangle, then the formula to find the area of a triangle is given by. Then the Area of triangle is calculated as,
=> A = (½) b h square units.
Here we have know that an amusement park is building a new water slide which is supported by beams of 40 feet and 25 feet.
Then based on the formula of area of triangle, the height of the support beam need to be for this new ride is calculated as,
=> 40 = 1/2 x 25 x h
=> h = 80/25
=> h = 3.2
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the feather on an arrow form two congruent parallelograms. the parallelograms are reflection of each other over the line that contains their shared side show that m
Find AB… pls help thx
[tex]\textit{midsegment of a trapezoid}\\\\ m=\cfrac{a+b}{2} ~~ \begin{cases} a,b=\stackrel{parallel~sides}{bases~\hfill }\\[-0.5em] \hrulefill\\ a=11.5\\ m=18.7 \end{cases}\implies 18.7=\cfrac{11.5+b}{2} \\\\\\ 37.4=11.5+b\implies 25.9=b=AB[/tex]
Chef Malik decided to spend the grant money to package and deliver his meals to reach more community members. Each vegetarian meal now costs $2.25 to make and each meat meal now costs $2.75. Chef Malik wants to serve at least 400 meals and spend no more than $800.
A solution for the given system of linear inequalities is the shaded area below the solid line.
How to write and solve the system of inequalities graphically?In order to write a system of linear inequalities to describe this situation, we would assign variables to the cost of vegetarian meal and cost of meat meal, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the cost of vegetarian meal.Let the variable y represent the cost of meat meal.Since each vegetarian meal cost $2.25 to make while each meat meal cost $2.75 and Chef Malik can spend no more than $800, a linear inequality which represents this situation is given by;
2.25x + 2.75y ≤ 800
Additionally, Chef Malik wants to serve at least 400 meals;
x + y ≥ 400
Next, we would use an online graphing calculator to graphically solve the system of linear inequalities.
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Complete Question:
Chef Malik decided to spend the grant money to package and deliver his meals to reach more community members. Each vegetarian meal now costs $2.25 to make and each meat meal now costs $2.75. Chef Malik wants to serve at least 400 meals and spend no more than $800.
Write and solve the system of inequalities graphically.
Andy is using wooden boards that are 0. 45 feet wide to build a deck. How many rows of boards are needed to completely cover a space that is 21 feet wide?
Andy is using wooden boards that are 0. 45 feet wide to build a deck. The number of rows of boards are needed to completely cover a space is 47 rows of boards.
Divide the total width (21 feet) by the width of each board (0. 45 feet):
21 / 0. 45 = 46. 666666
Round the result up to the next whole number:
47 rows of boards
In mathematics, division is the process of dividing a number into equal parts and calculating the maximum number of equal parts that may be formed. For instance, dividing 15 by 3 results in the division of 15 into 3 groups of 5 each.
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What is the midpoint of the line segment with the endpoints J(–9, –4) and K(7, 8)? (–5, –1) (–2, 1) (–1, 2) (3, 5)
Answer:
(-1,2)
Step-by-step explanation:
Recall the midpoint formula:
[tex]\frac{x^1+x^2}{2}[/tex] to solve for the X coordinate and [tex]\frac{y^1+y^2}{2}[/tex] to solve for Y.
Replace the variables with their appropriate numbers.
[tex]X(\frac{-9+7}{2})[/tex] [tex]Y(\frac{-4+8}{2})[/tex]
[tex]X(\frac{-2}{2} )[/tex] [tex]Y(\frac{4}{2} )[/tex]
[tex]X(-1)[/tex] [tex]Y(2)[/tex]
Therefore, the answer is (-1,2)
A tank can be filled by an inlet pipe in 12 hours and emptied by a drain pipe in 16 hours. How long will it take to fill the tank if both pipes are left open?
It will take 48 hours, to fill the tank if both pipes are left open simultaneously.
We are given the following data -
The time taken to fill the tank by inlet pipe = 12 hrs
so, the rate of filling = 1/12
The time taken to empty the tank by drain pipe = 16 hrs
so, the rate of emptying = - 1/16
Therefore, the total work done by both pipes can be given by the following formula -
(1/rate of filling) + (1/rate of emptying) = (1/rate of net change)
1/12 + (-1/16) = (1/Rn)
Therefore, (1/Rn) = 1/12 - 1/16 = 1/48
To find how long it will take to fill the tank, we need to find the reciprocal of the rate of net change:
1/Rn = 1/(1/48)
Rn = 48
So it will take 48 hours, to fill the tank if both pipes are left open.
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jose needs 20 1/3 feet of string for a project. he has lengths of string that are 9 1/2 feet, 3 1/4 feet and 4.5 feet long does jose have enough string for his project?
Answer: To check if Jose has enough string for his project, we need to add the lengths of the strings he has and compare it to the amount of string he needs for the project.
The length of the first string is 9 1/2 feet, the second string is 3 1/4 feet and the third string is 4.5 feet.
To add these lengths we need to convert them all to the same unit of measurement.
3 1/4 feet can be converted to 3.25 feet
So the total length of the strings Jose has is 9 1/2 + 3.25 + 4.5 = 17.25 feet
Jose needs 20 1/3 feet of string for his project, and he has 17.25 feet of string.
So he doesn't have enough string for his project.
Step-by-step explanation:
if 750 amounts to 885 in three years at a simple interest, find the rate of interest?
PLEASE ANSWER THE QUESTION ITS URGENT!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
The Rate of Interest is 6%.
Step-by-step explanation:
S.I= Amount - Principle
S.I=885-750=135.
Rate= S.I*100/(P*T)
Rate=(135*100)/(750*3)
Rate=6%
Simple Interest:Simple interest is a quick and easy method of calculating the interest charge on a loan.
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I need help with substitution the two parts are 4x+5y=48 and 7x-3y=-10. i need to find x and y
The solution to the simultaneous equation is x = 38 and y = 8
How to determine the valueFrom the information given, we have the equations;
4x+5y=487x-3y=-10From equation (1), make 'x' the subject of formula;
4x = 48 - 5y
Divide both sides by 4
x = 48 - 5y/4
Substitute the value x in equation (2)
7(48 - 5y/4) - 3y = -10
expand the bracket
336 - 35y/4 - 3y = -10
Find the lowest common multiple
336 - 35y - 12y/4 = -10
336 - 47y/4 = -10
cross multiply
336 - 47y = -40
collect like terms
-47y = 376
y = 8
Substitute the value into equation 3
x = 48 - 5(8)/4
x = 48 - 10
x = 38
Hence, the values are 38 and 8
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Dylan drove from Liverpool to Sunderland at an average speed of 50 mph for 3 hours and 30 minutes. He then drove from Sunderland to Edinburgh at an average speed of 65 mph for 2 hours. Work out how many miles Dylan travelled in total.
Answer:
305 miles
Step-by-step explanation:
You want to know how far Dylan travelled if he drove 50 mph for 3.5 hours and 65 mph for 2 hours.
DistanceDistance is the product of speed and time. The total distance Dylan travelled will be the sum of lengths of the legs of his trip.
distance = speed · time
total distance = speed1 · time1 + speed2 · time2
= (50 mi/h)(3.5 h) +(65 mi/h)(2 h) = 305 mi
Dylan travelled a total of 305 miles.
In the diagram below, (5, 2) is the midpoint of a segment with one endpoint (-1, 8). What is the other endpoint of the segment? Show your work or explain how you find your answer.
The line segment AB has point B(x, y) = (11, - 4) as its other endpoint.
How to determine the coordinates of the missing endpoint of a line segment
Herein we find the case of a line segment, of which the coordinates of its midpoint and one of its endpoints are known. Midpoint and endpoints are related by following expression:
0.5 · A(x, y) + 0.5 · B(x, y) = M(x, y)
Where:
A(x, y), B(x, y) - EndpointsM(x, y) - MidpointIf we know that A(x, y) = (- 1, 8) and M(x, y) = (5, 2), then the coordinates of the other midpoint are:
0.5 · (- 1, 8) + 0.5 · B(x, y) = (5, 2)
(- 1, 8) + B(x, y) = 2 · (5, 2)
(- 1, 8) + B(x, y) = (10, 4)
B(x, y) = (11, - 4)
The point B(x, y) = (11, - 4) is an endpoint of line segment AB.
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Pleas answer these questions..
Refer to the image attached.
Find the indicated real n the root(s) of a. n=9, a=-512
[tex]\sqrt[9]{-512}\qquad \begin{cases} -512=-2\cdot -2\cdot -2\cdot -2\cdot -2\cdot -2\cdot -2\cdot -2\cdot -2\\ \qquad 2^9 \end{cases} \\\\\\ \sqrt[9]{(-2^9)}\implies -2[/tex]
Can someone help me please? I'm struggling :(
Answer:
Ariel's plant is 1.6 inches taller than Dyani's.
It doesn't seem that you can multiply the measurement of Dyani's plant anymore than Ariel's. So I believe that would be 0 inches.
Step-by-step explanation: You can multiply Dyani's measurement with number like 1.0, 1.2, etc. You still wouldn't be able to multiply it anymore.
I hope this helps!
In the Olympic National Park, there are currently 3310 squirrels,
and the population is increasing at an annual rate of 4%.
a. Write an exponential function to model the squirrel
population in terms of the number of years from now.
b. Explain what each value in the model represents.
Dredict the number of couvrole that will be in the region
WXYZ is a parallelogram. The position vectors of W, X and Y are (2,1), (6,3) and (4,7) respectively. Determine in the form (x,y) the vectors, WX, XY, WZ, OZ
In the parallelogram, the coordinates form of the vectors WX, XY, WZ, OZ are (18,3), (24, 21), (2x, y) and (0,0).
The term coordinate in math is known as the set of values that represents the exact position on the coordinate plane
Here we know that WXYZ is a parallelogram and the position vectors of W, X and Y are (2,1), (6,3) and (4,7) respectively.
Then the value of the coordinate vectors are calculated as,
=> WX = (2,1) x (6,3) = (18, 3)
And the value of XY is calculated as,
=> XY = (6,3) x (4,7) = (24, 21)
And we know that the value of Z is (x, y), then the vector is calculated as,
=> WZ = (2,1) x (x, y) = (2x, y)
Finally the value of OZ is calculated as,
=> OZ =(0,0) x (x , y) = (0, 0)
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what is D=8 cm and R =4.7 in ,
The circumference of the circles are 25.12 cm and 29.516 in
How to determine the circumference of the circleFrom the question, we have the following parameters that can be used in our computation:
(a) D = 8 cm and (b) R = 4.7 inches
Given the diameter, the circumference is
C = πD
So, we have
C = 3.14 * 8 cm = 25.12 cm
Given the radius, the circumference is
C = 2πR
So, we have
C = 2 * 3.14 * 4.7 in = 29.516 in
Hence, the circumference is 29.516 in
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Complete question
What is the circumference of the circle given its diameter (D) of its radius (R)
(a) D = 8 cm and (b) R = 4.7 inches
The Lockheed Martin F-22
Military Raptor can travel
3,000 miles in 2 hours.
What is it's top speed?
Answer:
1,500
Step-by-step explanation:
It's preetty fast but it cannot be the record holder of " Lockheed SR-71 Blackbird " Which it's top speed i 2,100 miles per hour !!
2. A child's bank contains $6.30 in dimes and quarters. There are twice as
many dimes as quarters. How many of each kind of coin are in the bank?
The child has 14 quarters and 28 dimes if child's bank contains $6.30 in dimes and quarters.
What is Algebraic expression ?
Algebraic expression can be defined as the combination of variables and constants.
With coin problems you need to keep track of the count of the coins and the value.
d = number of dimes
10d = value of the dimes in cents
q = number of quarters
25q = value of the quarters in cents
10d + 25q = 630 cents
d = 2q
substitute
10(2q) + 25q = 630
20q + 25q = 630
45q = 630
q = 14
d = 2q
d = 2*14 = 28
Check the values to be sure this answer is right.
25(14) = 350 cents
10(28) = 280 cents
total = 630 cents
Therefore, The child has 14 quarters and 28 dimes.
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how do i find the square root of a circle
Answer: by putting some clothes on
Step-by-step explanation:
comon man put some clothes on man do it for the kids