Answer:
(x - 3)² + y² = 8²-----------------------
Standard form for the equation of a circle is:
(x − h)² + (y − k)² = r², where the center is (h, k) and the radius is r unitsUsing the given endpoints of the diameter find the center, which is the midpoint:
h = 3, as x-coordinate of both endpoints,k = 0, as the sum of y-coordinates of endpoints.The radius is half the distance between endpoints:
r = (8 - (-8))/2 = 16/2 = 8Substitute values into equation:
(x - 3)² + (y - 0)² = 8² (x - 3)² + y² = 8²I need help graphing 2x-5y=10
Answer:
Try the desmos graphing calculator:
Step-by-step explanation:
You flip a coin five times. The coin lands heads-up the first two times and then lands tails-up the remaining three tImes.
The probability of flipping heads twice followed by tails three times is 1/32 or approximately 0.031.
Each coin flip is an independent event, meaning the outcome of one flip does not affect the outcome of any other flip. Therefore, the probability of getting heads on any one flip is always 1/2, regardless of previous outcomes.
Using this information, we can calculate the probability of flipping heads twice followed by tails three times as:
P(heads) = 1/2
P(tails) = 1/2
P(heads on first flip) = 1/2
P(heads on second flip) = 1/2
P(tails on third flip) = 1/2
P(tails on fourth flip) = 1/2
P(tails on fifth flip) = 1/2
P(heads twice followed by tails three times)
= P(heads on first flip) x P(heads on second flip) x P(tails on third flip) x P(tails on fourth flip) x P(tails on fifth flip)
= (1/2) x (1/2) x (1/2) x (1/2) x (1/2)
= 1/32
Therefore, the probability of flipping heads twice followed by tails three times is 1/32 or approximately 0.031.
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find the future value of 35,000 at 6% semi annually for 12 years
The future value of 35,000 at 6% semi annually for 12 years is 1,33,700.
Present value = 35000
Rate (r) = 6% = 0.06
Time (n) = 12 years semi annually = 23
Future Value = ?
∴ Future Value = PV(1 + r)ⁿ
Future Value = 35000(1 + 0.06)∧23
= 35000(1.06)∧23
= 35000(3.820)
Future Value = 1,33,700
Therefore, the future value of 35,000 at 6% semi annually for 12 years is 1,33,700.
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I NEED HELP PLEASEEE
A description that best compare the graph of the functions is: B. the line for function A is steeper.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation:
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.First of all, we would find the slope of function B;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (-1 + 2)/(3 - 0)
Slope (m) B = 1/3.
At data point (0, -1) and a slope of 1/3, function B can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y + 1 = 1/3(x - 0)
y = 1/3(x) - 1
In conclusion, the line for function A is steeper because it has a greater slope than function B i.e 3 > 1/3.
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What is the equation of the line that passes through the points given in the table x -3, 3, 6 y 3, 5, 6,
A y= -3x - 6
B y = -1/3x + 8
C y= 1/3x + 4
D y= 3x - 12
Answer:
C. y = 1/3x + 4
Step-by-step explanation:
To find the equation of the line that passes through the given points, we can use the slope-intercept form of the equation of a line, which is:
y = mx + b
where m is the slope of the line and b is the y-intercept.
To find the slope of the line, we can use the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are any two points on the line. We can choose the points (x1,y1) = (-3,3) and (x2,y2) = (6,6) from the table.
m = (6 - 3) / (6 - (-3)) = 3/9 = 1/3
Now that we have the slope, we can use the point-slope form of the equation of a line to find the y-intercept:
y - y1 = m(x - x1)
where (x1,y1) is any point on the line. We can choose the point (x1,y1) = (3,5) from the table.
y - 5 = (1/3)(x - 3)
Now we can solve for y to get the equation in slope-intercept form:
y = (1/3)x + (5 - 1/3*3)
y = (1/3)x + 4
Therefore, the equation of the line that passes through the given points is C) y= 1/3x + 4.
100 Points! Algebra question. Looking for an answer to A and B. Photo attached. Please show as much work as possible. Thank you!
A) A above middle C with a frequency of 440 cycles per second is 49 notes up the piano keyboard.
B) frequency of the pitch that is 73 notes up the keyboard is 1760 cycles per second.
How to determine frequency?A. To find how many notes up the piano keyboard the pitch with a frequency of 440 cycles per second is, solve the formula
n = 1 + 12 × log₂(f/27.5) for n,
where f = frequency of the pitch to find and n = number of notes up the keyboard.
Substituting f = 440:
n = 1 + 12 × log_2(440/27.5)
n = 1 + 12 × log_2(16)
n = 1 + 12 × 4
n = 49
Therefore, the A above middle C with a frequency of 440 cycles per second is 49 notes up the piano keyboard.
B. Using the same formula, n = 1 + 12 × log₂(f/27.5), to find the frequency of the pitch that is 73 notes up the keyboard. Solving for f:
73 = 1 + 12 × log₂(f/27.5)
72 = 12 × log₂(f/27.5)
6 = log₂(f/27.5)
2⁶ = f/27.5
f = 27.5 x 2⁶
Therefore, the frequency of the pitch that is 73 notes up the keyboard is:
f = 27.5 x 2⁶ = 1760 cycles per second.
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What is the probability ether event will occur?
Answer:
P(A or B) = 1 - P(neither A nor B)
= 1 - 18/66 = 48/66 = 8/11
= .727 = 72.7%
find the domain of:
this
Answer:
The domain of a function is the set of all real numbers for which the function is defined. In this case, the function is defined when the denominator is not equal to zero. The denominator is equal to zero when x=1. Therefore, the domain of the function is all real numbers except for x=1.
In interval notation, the domain is written as
(-∞,1) ∪ (1,∞)
Step-by-step explanation:
7. Find the coordinate of P that represents
the weighted average of points F and H
when point F weighs three times as
much as point H.
F
H
<+*||||||$||||
-3-2-1 0 1 2 3 4 5 6789
The point at coordinate 3 represents the weighted average.
Point E measures (-1) and has weight 2x weight of F
point F has a measure of 2 and no particular stated weight
point G measures 6 and has a weight of 3x weight of F
Since we can assign a weight to point F and the other weights will be based on that, let's just keep it simple and give point F a weight of 1.
That gives E a weight of 2, and G a weight of 3.
So, E value times E weight is (-1) x 2 = -2
F value times F weight is 2 x 1 = 2
G value times G weight is 6 x 3 = 18
Sum of (value x weight) = 18
Sum of the weights = 2 + 1 + 3 = 6
we get the weighted average by taking the sum of (value x weight) products (18) and then dividing by the sum of the weights (6).
18/6 = 3, the weighted average
Hence, the point at coordinate 3 represents the weighted average.
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points E,F and G are plotted on a number line at -1, 2 and 6 respectively. Find the coordinate o f the point that represents the weighted average of E, F and G, if point E weighs twice as much as point F and point G weighs three times as much as point F.
Express the area of the entire rectangle.
Your answer should be a polynomial in standard form.
The value of area of rectangle is,
⇒ Area = x² + 10x + 21
We have to given that;
Lenght = (x + 7)
Width = (x + 3)
Hence, We can formulate;
The value of area of rectangle is,
⇒ Area = Lenght x width
⇒ Area = (x + 7) (x + 3)
⇒ Area = x² + 7x + 3x + 21
⇒ Area = x² + 10x + 21
Thus, The value of area of rectangle is,
⇒ Area = x² + 10x + 21
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What do I do?
Brief Calculus Question: Find Each limit (if it exist)
For the given function the value of limits are
[tex]\lim _{x\to 0^-}\left(f\left(x\right)\right)[/tex] is 5
[tex]\lim _{x\to 0^+}\left(f\left(x\right)\right)[/tex] is 0
[tex]\lim _{x\to 0}\left x^2+5[/tex]is 5
The given function is f(x)= x²+5, when x≤0
f(x)=2x when x>0
[tex]\lim _{x\to 0^-}\left(f\left(x\right)\right)[/tex]
Which is [tex]\lim _{x\to 0^-}\left x^2+5[/tex]
The given limit is a left hand limit as there is minus in the limits
When we apply x as 0 we get the value 5
Now [tex]\lim _{x\to 0^+}\left(f\left(x\right)\right)[/tex]
So [tex]\lim _{x\to 0^+}\left 2x[/tex]
The given limit is a right hand limit as there is positive in the limits
When we apply x as 0 we get 0
Now [tex]\lim _{x\to 0}\left(f\left(x\right)\right)[/tex]
Which is [tex]\lim _{x\to 0}\left x^2+5[/tex]
We get 5
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You work at Dave's Donut Shop. The company has decided to redesign the box it uses to hold one dozen donuts. There are 12 donuts in one dozen. Each donut has a diameter of 3 and a height of 1.5 inches. The donuts in the original box stood on their side. You have been asked to design a new box that will allow the dozen donuts to lie flat as shown.
New Box: A rectangle with 3 rows of 4 across
The new box costs $0.20 per square foot of cardboard.
The square footage of the box is determined by the total surface area. There are 144 square inches in 1 square foot.
In this task, you will answer six questions to help you design a new donut box.
1.) What is the circumference, in inches, of a donut?
2.) There are 144 square inches in 1 foot. How many square inches are in 2.5 square feet?
3.) To make sure there is enough space for the donuts, Dave wants to add 1/2 inch to the minimum length, width, and height of the box.
Including the additional space, what should be the length, width, and height of the new box, in inches?
4.) Based on your response to question 3, what is the area of the bottom of the new box? How do the length and width of the new box meet Dave's requirements? Include all the necessary work to support your answer.
5.) Using the dimensions from question 3, what is the surface area, in surface area, in square inches, of your new box?
6.) It costs $21.00 for 35 of the original boxes. Dave wants the cost of the new box to be less than or equal to the cost of the original box. Does the new box cost less than the original box? Include all necessary work to support your answer.
The answer to all parts is shown below.
1. The diameter of a donut is 3 inches.
so the circumference is πd = 3π ≈ 9.42 inches.
2. 2.5 square feet is equal to 2.5 x 144 = 360 square inches.
3. The minimum length, width, and height of the box are equal to the diameter and height of the donut, which is 3 inches and 1.5 inches, respectively.
Adding 1/2 inch to each dimension gives a length of 4 inches, a width of 4 inches, and a height of 2 inches.
4. The area of the bottom of the new box is length x width
= 4 x 4 = 16 square inches.
The length and width of the new box meet Dave's requirements because they are each greater than or equal to the minimum length and width of 3.5 inches (3 inches + 1/2 inch).
5. The surface area of the new box can be calculated as follows:
Top and bottom: 2 x (length x width) = 2 x (4 x 4) = 32 square inches
Front and back: 2 x (height x length) = 2 x (2 x 4) = 16 square inches
Sides: 2 x (height x width) = 2 x (2 x 4) = 16 square inches
Total surface area = 32 + 16 + 16 = 64 square inches.
6. The surface area of one original box is equal to the sum of the areas of the top, bottom, and four sides.
Each side has dimensions of 3 inches by 1.5 inches,
so the area of each side is 3 x 1.5 = 4.5 square inches.
The area of the top and bottom is 3 x 3 = 9 square inches.
Therefore, the surface area of one original box is:
Top and bottom: 2 x 9 = 18 square inches
Sides: 4 x 4.5 = 18 square inches
Total surface area = 18 + 18 = 36 square inches.
The surface area of the new box is 64 square inches, so the total cardboard needed for one box is:
64 square inches / 144 square inches per square foot = 0.44 square feet
The cost of cardboard for one box is:
0.44 square feet x $0.20 per square foot = $0.088
To find the cost of 35 new boxes, we multiply the cost per box by the number of boxes:
35 boxes x $0.088 per box = $3.08
Therefore, the new box costs less than the original box, which costs $21.00 for 35 boxes.
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The scatter plot shows the weights and age of a puppy and a good line of fit. The equation for the line of fit shown is:
y = 2x + 1.5
Where x represents the puppy’s age in weeks and y represents the puppy’s weight. Predict the weight of a 12-week-old puppy in pounds. Show your work.
The predicted weight of a 12-week-old puppy is 25.5 pounds.
To predict the weight of a 12-week-old puppy using the line of fit equation y = 2x + 1.5, follow these steps:
1. Identify the value of x: In this case, x represents the puppy's age in weeks, so x = 12.
2. Plug the value of x into the equation: y = 2(12) + 1.5.
3. Solve the equation: y = 24 + 1.5.
4. Calculate the result: y = 25.5.
So, the predicted weight of a 12-week-old puppy is 25.5 pounds.
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Using the best of fit equation given , the predicted weight of a 12 - weeks old puppy would be 25.5lb
Line of fit equationThe line of fit is used to establish a mathematical relationship between two variables. A good line of fit would give a good mathematical relationship between related variables.
In the question above; our line of fit equation is y = 2x + 1.5
x = puppy's age ; y = weight
To obtain the value of y for any value of x ; we substitute either of the given value .
For x = 12
y = 2(12 ) + 1.5
y = 24 + 1.5
y = 25.5
Hence, weight of puppy after 12 weeks will be 25.5lbs
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In triangle PSW, the measure of ZP is (x² - 11x + 146), the measure of ZS is 39", and the
measure of ZW is (3x +44). Which statements about triangle PSW are true?
Select two correct answers.
A. Side PS has the longest length of the three sides.
B. Side SW has the shortest length of the three sides.
C. The measure of ZW is less than the measure of ZS.
D. The length of side PS is greater than the length of side PW.
E. The length of side SW is greater than the length of side PW.
The length of side SW is greater than the length of side PW.
Side SW has the shortest length of the three sides.
What is a triangle?A triangle is a two-dimensional geometric shape that is defined by three straight sides and three angles. It is the simplest polygon with three sides and three vertices.
We know that the magnitude x is gotten from;
x² - 11x + 146 + 39 - 3x +44 = 180 (Sum of angles in a triangle)
x²- 11x - 3x + 146 + 39 +44 = 180
x²- 14x + 229= 180
x²- 14x = 180 - 229
x²- 14x = -49
Hence;
x²- 14x + 49 = 0
x = 7
Thus;
<P = 7^2 - 11(7) + 146 = 49 - 77 + 146 = 118
<W = 3(7) + 44 = 65
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In 2017 the population of Rexburg, Idaho was 28,337 people. The population was expected to grow at a rate of about 1.53% per year. Based on these numbers, what would we predict the population of Rexburg will be in the year 2020?
(Round to the nearest whole number.)
Number
people
Answer:
29658
Step-by-step explanation:
N = A (1 + increase) ^n
Where N is future amount, A is initial amount, increase is percentage increase/decrease, n is number of mins/hours/days/months/years.
N = 28337 (1 + 0.0153)^3
= 28337 (1.0153)^3
= 29658 to nearest number
The table shows how many Calories Lance burns jogging on a treadmill for different lengths of time. Lance's goal today is to burn 380 Calories. If he has been jogging for 25.5 minutes, for how many more minutes does he still need to jog? Assume the situation is proportional.
Lance needs to jog for an additional 316.08-25.5 = 290.58 minutes to burn 380 Calories.
The information given in the table to produce a direct equation that relates the number of Calories burned to the time spent jogging. Let's use the pitch- intercept form y = mx b, where y represents the number of Calories burned( in hundreds), x represents the time spent jogging( in twinkles), m represents the rate of Calories burned( in hundreds per nanosecond), and b represents the original Calories burned( in hundreds). To find m, we can use the points( 10, 13) and( 15, 19), which represent two ordered dyads on the line. We can find the pitch of the line using the pitch formula
m = ( y2- y1)/( x2- x1) m = ( 19- 13)/( 15- 10)
m = 1.2 So the equation for the line is y = 1.2 x b.
To find b, we can use the point
( 10, 13) = 1.2( 10) b b = 0.7
So the complete equation for the line is y = 1.2 x0.7 Now we can use this equation to break for x, the number of twinkles Lance needs to jog to burn 380 Calories.
380 = 1.2 x0.7 = 1.2 x x = 316.08
So Lance needs to jog for an additional 316.08-25.5 = 290.58 minutes to burn 380 Calories.
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Rewrite the equation 5(x – 3) = x + 13 with 6 substituted for x. Write a question mark over the equal sign to show that you're testing to see if the equation is true. edmentum math practice. PLEASE HELP ME.
Answer:
Step-by-step explanation:
5(x - 3) ? x + 13
if x = 6
5(6 - 3) ? 6 + 13
15 ? 19
15 ≠ 19
Step-by-step explanation:
When substituting 6 for x, the equation becomes:
5(6 - 3) ?= 6 + 13
Now, we can solve both sides of the equation:
5(3) ?= 6 + 13
15 ?= 19
Since these are not equal, the equation is not true for x = 6.
Use the graph to complete the statement. O is the origin. T<2,1> x r(90°, 0) : (4,-1)
After transformation, we will have the point as (3, 5).
What is a rotation in a transformation ?A rotation is described as a type of transformation which is a turn and that turns the figure in either a clockwise or counterclockwise direction.
The rotation does not alter the shape.
When we Rotate (4,-1) 90° anticlockwise centered at the origin yields the point (1, 4).
We next transform the point (1, 4) two units to the right and 1 unit up results in the point (3, 5).
We can also rotate 90° clockwise that would result in some different point on this coordinate system. We will also have some 2D figures like a triangle or a rectangle instead of a straight line
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Consider circle T with radius 24 in. and θ = StartFraction 5 pi Over 6 EndFraction radians.
Circle T is shown. Line segments S T and V T are radii with lengths of 24 inches. Angle S T V is theta.
What is the length of minor arc SV?
20π in.
28π in.
40π in.
63π in
Answer:
20π in.
Step-by-step explanation:
The central angle of minor arc SV is θ = 5π/6 radians, which is 150 degrees. The length of a minor arc is given by the formula s = rθ, where r is the radius of the circle. Substituting r = 24 in. and θ = 5π/6, we get:
s = 24 × 5π/6 = 20π in.
Therefore, the length of minor arc SV is 20π in.
Solve -8x = 56 for x.
Ox=6
Ox= -7
Ox=7
Ox= -8
Answer:
-7
Step-by-step explanation:
you divide -8 on both sides
the two -8 on your left will cancel each other
and 56 divided by-8=-7
PLEASE PLEASE HELP WILL MARK BRAINLIST!!!!!!!!!!!!
The inequality for this problem is defined as follows:
y ≤ 2x - 6.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation shown as follows:
y = mx + b
The coefficients m and b have the meaning presented as follows:
m is the slope of the function, representing the increase/decrease in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, representing the numeric value of the function when the input variable x has a value of 0. On a graph, it is the value of y when the graph of the function crosses or touches the y-axis.The function in this problem crosses the y-axis at y = -6, hence the intercept b is given as follows:
b = -6.
When x increases by 3, y increases by 6, hence the slope m is given as follows:
m = 6/3
m = 2.
Hence the function is:
y = 2x - 6.
The inequality is composed by the values to the left of the solid line, hence it is given as follows:
y ≤ 2x - 6.
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A sporting goods store records the sales of gloves over a 10-day period. They also record each day’s low temperature. The scatter plot shows the data and a good line of fit. The equation for the line of fit shown is y = -1.2x + 122. What is the y-intercept of the equation, and what does it mean?
The y- intercept represents the anticipated number of gloves vended on a day when the low temperature is 0 degrees.
The terms you mentioned are formerly included in the problem description. The y- intercept of the equation is the value of y when x = 0. In the given line of fit equation,
y = -1.2 x 122, the y- intercept is 122. The y- intercept represents the anticipated number of gloves vended on a day when the low temperature is 0 degrees. In this case, when the low temperature is 0,
the store is prognosticated to vend 122 gloves. Keep in mind that this is an estimate grounded on the line of fit and may not be an exact value.
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What's the probability of rolling a prime number on a fair six-sided die?
Answer:
66.666%
Step-by-step explanation:
the numbers on the dice would be 1,2,3,4,5,6
1,2,3,5 are all prime numbers.
4/6 =2/3 =66.666%
If f(x) = -2, which of the following is the inverse of f(x)?
O A. f¹(x) = 6-2
OB. f¹(x) = 6 6x+2
C. ƒ˜¹(x) = 2z-3
6
O D. f¯¹(x) = 2x+3
The inverse of function f(x) when f(x) = -2 is f¯¹(x) = 2x + 3.So, the correct option is D.
To find the inverse of a function, we switch the x and y variables and solve for y. So, if f(x) = -2, we have:
x = -2
y = f(x) = -2
Switching x and y, we get:
x = f¯¹(y)
y = -2
Solving for f¯¹(y), we get:
f¯¹(y) = 2y + 3
Therefore, the inverse of f(x) when f(x) = -2 is f¯¹(x) = 2x + 3.
To find the inverse of a function, we need to swap the input (x) and output (f(x)), and then solve for the new input. Given f(x) = -2, let's find the inverse:
1. Swap the input and output: x = -2
2. Solve for the new input: Since the function f(x) is a constant function and doesn't involve x, the inverse of f(x) when f(x) = -2 is f¯¹(x) = 2x + 3.
Therefore, Option D is the correct inverse of f(x).
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!! Will give brainlist !!
(Need help asap!!)
Determine the measure of each arc.
The length of the arc are
Arc MN = 72 degrees
Arc NQR = 180 degrees
Arc NQ = 108 degrees
Arc MRP = 193 degrees
Arc QR = 72 degrees
Arc QMR = 288 degrees
Arc PQ = 13 degrees
Arc PRN = 265 degrees
Arc MQN = 288 degrees
How to find the length of each arcThe relationship between central angle and intercepted arc is that they are equal. This is used in solving the length of arcs
hence we have that
angle ROQ = angle NOM = 72 degrees (vertical angles)
Arc MN = angle NOM = 72 degrees
Arc NQR = 180 degrees (semicircle)
Arc NQ
angle POQ = 180 - 72 - 95
angle POQ = 13
Arc NQ = 95 + 13 = 108 degrees
Arc MRP = 180 + 13 = 193 degrees
Arc QR = 72 degrees
Arc QMR = 360 - 72 = 288 degrees
Arc PQ = 13 degrees
Arc PRN = 360 - 95 = 265 degrees
Arc MQN = 360 - 72 = 288 degrees
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if tan theta = 12/5 and cos theta= -5/13 then what is sin theta?
Answer:
- 12/13-----------------------------
To find sin theta, we can use the identity:
sin² θ + cos² θ = 1We know cos θ, so we can solve for sin θ:
sin² θ + (-5/13)² = 1 sin² θ + 25/169 = 1 sin² θ = 144/169 sin θ = ± 12/13Since tan θ is positive and cos θ is negative, sin θ must be negative as:
tan θ = sin θ / cos θTherefore, the answer is:
sin θ = - 12/13Suppose you found a CD that pays 4.9% interest compounded monthly for 3 years.
If you deposit $11,000 now, how much will you have in the account in 3 years? (Round to the nearest cent.)
$
What was the interest earned? (Round to the nearest cent.)
$
Now suppose that you would like to have $20,000 in the account in 3 years. How much would you need to deposit now? (Round to the nearest cent.)
Answer: 11,000 now = 12,697.52$, The interest earned was 1,697.52$
20,000 now = 23086.41$ the interest earned was 3,086$.
Step-by-step explanation: 11,000(1.049)^3 solve the equation and voila.
Q.#2 20,000(1.049)^3
Ju used 6
bags of mulch in her front yard and
2 bags of mulch in her backyard. How many
bags of mulch has Ju used (in simplest form)?
Answer:
she used 8 bags of mulch altogether.
Step-by-step explanation:
if this isn't correct, you may want to reword or specify the question.
What is the surface area of the triangular prism?
S.A.=blank ft/2
4ft,3ft,2ft,5ft
PLEASE HELP!
I NEED IT FOR MONDAY BEFORE MIDNIGHT
I’LL GIVE BRAINLEST
LEFEL F NET AND SURFACE AREA
The surface area of the triangular prism is 84 ft/2
How to solveThe surface area of a triangular prism is found with: Area = bh + (s1 + s2 + s3)L.
Given a 4ft base, 3ft height, 5ft slant height, and 2ft length, we substitute to get:
Area = (4ft3ft) + 3(5ft*2ft) =
[tex]12ft^2 + 30ft^2 = 42ft^2.[/tex]
In the specified format, the surface area of the triangular prism is 84 ft/2.
This is because the format given is blank ft/2
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Could you provide the formula to calculate the surface area of a triangular prism, given dimensions of 4ft, 3ft, 2ft, and 5ft? The surface area should be presented as (blank ft/2).
Point C is located at the origin.
a The slope of line £ is 3/4.
b The equation for £ is y = 3/4x + 3.
c The radius of OC is 5.
d The distance from £ to OC along the y-axis is 3.
How to calculate the valueThe slope of a line is the change in y over the change in x. In this case, the change in y is 3 and the change in x is 4. So, the slope of line £ is 3/4.
The equation for a line can be written in the form y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is 3/4 and the y-intercept is 3. So, the equation for £ is y = 3/4x + 3.
The radius of a circle is the distance from the center to any point on the circle. In this case, the center of the circle is at the origin, which is at (0, 0). The point on the circle is at (-4, 3). So, the radius of the circle is the distance from (0, 0) to (-4, 3).
This distance can be found using the Pythagorean theorem:
r² = 4² + 3²
r² = 25
r = 5.
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