Find a center of mass of a thin plate of density delta = 6 bounded by the lines y = x and x = 0 and the parabola y = 20 - x^2 in the first quadrant. X = y = (Type simplified fractions. )
The center of mass of the thin plate of density delta = 6 bounded by the lines y = x and x = 0 and the parabola is located at (x, y) = (4/15, 1/15).
To find the center of mass of a thin plate,
Calculate the moments and products of inertia with respect to the x and y axes,
And then use them to find the coordinates of the center of mass.
First, determine the limits of integration.
Since the plate is bounded by the lines y=x and x=0 and the parabola y=20-x² in the first quadrant,
Integrate over the following limits.
0 ≤ x ≤ 4, and
x ≤ y ≤ 20 - x²
The mass of the plate can be found by integrating the density delta = 6 over the plate.
m = ∫∫over R δ dA
= ∫∫over R 6 dA
where R is the region bounded by the given curves.
m =[tex]\int_{0}^{4}[/tex] ∫x²⁰⁻ˣ² 6 dy dx
Simplifying the limits, we get,
m = ∫0⁴ 6x(20-x²) dx
Evaluating this integral gives,
m = 960
Next, find the moments and products of inertia.
The moments of inertia are given by,
Ix = ∫∫over R y² δ dA, and
Iy = ∫∫over R x² δ dA
The product of inertia is given by,
Ixy = ∫∫ over R xy δ dA
Substituting the given density delta = 6 and integrating over the region R, we get,
Ix = [tex]\int_{0}^{4}[/tex] ∫x²⁰⁻ˣ² y² 6 dy dx
= 64/3
Iy = [tex]\int_{0}^{4}[/tex] ∫x²⁰⁻ˣ² x² 6 dy dx
= 512/15
Ixy = [tex]\int_{0}^{4}[/tex] ∫x²⁰⁻ˣ² xy 6 dy dx
= 64/3
Using these moments and products of inertia,
The coordinates of the center of mass (X, Y) can be found using the following formulas.
X = Iy / m, and
Y= Iy / m
Substituting the values we have calculated, we get,
X = (512/15) / 960
= 4/15
Y = (64/3) / 960
= 1/15
Therefore, the center of mass of the thin plate is located at (x, y) = (4/15, 1/15).
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What is the first step in constructing a circumscribed circle around triangle XYZ? Construct a line parallel to segment YZ. Construct the perpendicular bisector of segment XY. Construct a copy of angle X. Construct the angle bisector of angle Y.
Answer: Construct the perpendicular bisector of segment XY
Step-by-step explanation:
Construct the perpendicular bisector of segment XYI am pretty sure this is the answer. I assume you r taking flvs just like me. this is the answer because to construct a circumscribed circle u will need to draw a perpendicular bisector to the sides of the polygon. Which o think is the first step.
Draw a coordinate plane. Plot the points: A(3, 4), B(2, 2), C(5, 8), D(7, 12), and E(9, 14). All but one of the points are on the same line. Which one is not?
The point that is not on the same line as the others is E(9, 14).
How to find the point ?The point that is not on the same line as the others would not have the same slope as the others.
Slope between A ( 3, 4) and B (2, 2):
= (4 - 2) / (3 - 2) = 2 / 1
= 2
Slope between B (2 , 2) and C (5, 8):
= ( 8 - 2 ) / (5 - 2)
= 6 / 3
= 2
Slope between C ( 5, 8) and D(7, 12):
= (12 - 8) / (7 - 5)
= 4 / 2
= 2
Slope between D ( 7, 12) and E ( 9, 14):
= ( 14 - 12) / (9 - 7)
= 2 / 2
= 1
We can therefore see that E ( 9, 14) is the odd one out and is not on the same line.
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Ocean sunfishes are well-known for rapidly gaining a lot of weight on a diet based on jellyfish.
The relationship between the elapsed time,
�
tt, in days, since an ocean sunfish is born, and its mass,
�
(
�
)
M(t)M, left parenthesis, t, right parenthesis, in milligrams is modeled by the following function:
�
(
�
)
=
4
⋅
(
81
49
)
�
M(t)=4⋅(
49
81
)
t
M, left parenthesis, t, right parenthesis, equals, 4, dot, left parenthesis, start fraction, 81, divided by, 49, end fraction, right parenthesis, start superscript, t, end superscript
Complete the following sentence about the rate of change in the mass of the sunfish. Round your answer to two decimal places.
The sunfish gains
2
7
7
2
start fraction, 2, divided by, 7, end fraction of its mass every
days.
Step-by-step explanation:
We can use the formula for exponential growth to find the rate at which the sunfish gains mass:
M(t) = M(0) * e^(kt)
where:
M(0) = the initial mass of the sunfish (which we don't know)
k = the growth rate constant (which we also don't know yet)
t = the elapsed time since the sunfish was born (in days)
e = the mathematical constant approximately equal to 2.71828...
We are given the formula for M(t), which is:
M(t) = 4 * (81/49)^t
This means that M(0) = 4 * (81/49)^0 = 4.
To find the growth rate constant k, we can use the fact that the sunfish gains 2/7 of its mass every day. This means that the daily growth rate is 2/7 of the current mass. In other words, the daily growth rate is:
(2/7) * M(t)
We can relate this to the exponential growth formula by taking the derivative of M(t) with respect to t:
dM/dt = k * M(t)
Taking the derivative of M(t), we get:
dM/dt = ln(81/49) * 4 * (81/49)^t
Setting this equal to the daily growth rate, we get:
(2/7) * M(t) = ln(81/49) * 4 * (81/49)^t
Simplifying this expression, we get:
k = ln(81/49) * 4/7
Using a calculator, we can evaluate this expression to get:
k ≈ 0.0919
Therefore, the rate at which the sunfish gains mass is given by:
dM/dt = 0.0919 * M(t)
To find out how much mass the sunfish gains in one day, we can substitute M(t) = 4 * (81/49)^t into this formula and evaluate it at t = 1 (since we want to know the daily rate of change):
dM/dt = 0.0919 * 4 * (81/49)^1
dM/dt ≈ 0.54
This means that the sunfish gains 0.54 milligrams every day. To express this as a fraction of its mass, we can divide by the current mass:
(0.54/4) ≈ 0.1375
So the sunfish gains approximately 2/7 (or 0.2857) of its mass every 2.08 (or 7/2.54) days. Rounded to two decimal places, this is 0.14 or approximately 2/7 of its mass every 2.08 days.
Geometric constructions requires what tools
Compass and straightedge are the two tools you'll need to create geometric constructions.
Explain about the tools for Geometric constructions:Without using numbers, geometric building enables the creation of precise drawings and models. The term "geometric building" refers to the act of precisely drawing something without the aid of numbers.
Your compass and the straightedge are the two tools. You have three tools if you count a pencil as one, the straightedge. As a ruler has numbers, this is the case. There are no numbers involved in proper geometric building. The compass I referenced isn't the kind you is using to draw circles; rather, it's the one with a needle that never points north. This particular compass has a pencil point on one end and a sharp tip on the other. By placing the pointed end down and turning the compass, you may use this tool to draw an arc.know more about the Geometric constructions
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a relay microchip in a telecommunications satellite has a life expectancy that follows a normal distribution with a mean of 92 months and a standard deviation of 3.6 months. when this computer-relay microchip malfunctions, the entire satellite is useless. a large london insurance company is going to insure the satellite for 50 million dollars. assume that the only part of the satellite in question is the microchip. all other components will work indefinitely. a button hyperlink to the salt program that reads: use salt. (a) for how many months should the satellite be insured to be 96% confident that it will last beyond the insurance date? (round your answer to the nearest tenth of a month.) (no response) incorrect: your answer is incorrect. months (b) if the satellite is insured for 84 months, what is the probability that it will malfunction before the insurance coverage ends? (round your answer to four decimal places.) (no response) incorrect: your answer is incorrect. (c) if the satellite is insured for 84 months, what is the expected loss to the insurance company (in dollars)? (round your answer to the nearest dollar.) $(no response) incorrect: your answer is incorrect. (d) if the insurance company charges $3 million for 84 months of insurance, how much profit does the company expect to make (in dollars)? (round your answer to the nearest dollar.) $(no response) incorrect: your answer is incorrect.
The satellite should be insured for 98 months (rounded up to the nearest month) to be 96% confident that the microchip will last beyond the insurance date.
To answer this question, we need to find the number of months for which we can be 96% confident that the microchip will not malfunction. This means we want to find the value of x such that P(X > x) = 0.04, where X is the random variable representing the life expectancy of the microchip.
We know that X follows a normal distribution with mean μ = 92 months and standard deviation σ = 3.6 months. Therefore, we can standardize X to the standard normal distribution Z ~ N(0, 1) using the formula
Z = (X - μ) / σ
We can then rewrite the probability P(X > x) as
P(X > x) = P(Z > (x - μ) / σ)
1.75 = (x - 92) / 3.6
Solving for x, we get
x = 98 months
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The given question is incomplete, the complete question is:
A relay microchip in a telecommunications satellite has a life expectancy that follows a normal distribution with a mean of 92 months and a standard deviation of 3.6 months. when this computer-relay microchip malfunctions, the entire satellite is useless. a large london insurance company is going to insure the satellite for 50 million dollars. assume that the only part of the satellite in question is the microchip. all other components will work indefinitely. a button hyperlink to the salt program that reads: use salt.for how many months should the satellite be insured to be 96% confident that it will last beyond the insurance date?
X+2y=-2
-3x+2y=-10
Solving each system of equations by adding and subtracting
The value of x and y is 2 , -2
The equation are as follows:
x+2y=-2....(i)
-3x+2y=-10.....(ii)
Now, Solving each system of equations by adding and subtracting:
And, find the value of x and y
Multiply by 3 in equation (i) we get:
3x + 6y = - 6 ---(iii)
And add the equations (ii) and (iii)
3x + 6y + (-3x) + 2y = -6 - 10
6y + 2y = -16
8y = -16
y = -2
Now, For solving the value of x :
Subtract the equation (i) and (ii), we get:
x + 2y - (-3x) - 2y = -2 + 10
x + 3x = 8
4x = 8
x = 2
Now, The value of x and y is 2 , -2
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To landscape his 70 ft by 60 ft backyard, Austin is planning first to put down a 4 inch layer of topsoil. He can buy bags of topsoil at $2.50 per 3-ft3 bag, with free delivery. Or he
can buy bulk topsoil for $22.00/yd, plus a $20 delivery fee. Which option is less expensive?
Buying bulk topsoil is less expensive than buying bags of topsoil in this case.
Describe Volume?Volume is a measure of the amount of space occupied by a three-dimensional object. It is typically measured in cubic units, such as cubic meters (m³), cubic centimeters (cm³), or cubic feet (ft³).
To find the volume of a simple object such as a cube, rectangular prism, or cylinder, you can use a formula that involves multiplying the length, width, and height of the object. For example, the formula for the volume of a rectangular prism is V = lwh, where V is the volume, l is the length, w is the width, and h is the height.
For more complex objects, such as irregular shapes or those with curved surfaces, you can use techniques such as integration or approximation to find the volume.
First, we need to determine how many cubic feet of topsoil Austin needs to cover his backyard with a 4 inch layer. We can start by calculating the volume of his backyard in cubic feet:
Volume = length x width x depth
Volume = 70 ft x 60 ft x (4 in / 12) ft
Volume = 1400 ft³
So Austin needs 1400 cubic feet of topsoil to cover his backyard with a 4 inch layer.
Option 1: Bags of Topsoil
Each bag of topsoil covers 3 cubic feet, so Austin needs 1400 / 3 = 466.67 bags of topsoil. Since he can only buy whole bags, he will need to buy 467 bags. Each bag costs $2.50, so the total cost of the topsoil would be:
Total cost = number of bags x cost per bag
Total cost = 467 x $2.50
Total cost = $1167.50
Since delivery is free, the total cost of the topsoil is $1167.50.
Option 2: Bulk Topsoil
Bulk topsoil costs $22.00 per cubic yard, and Austin needs 1400 / 27 = 51.85 cubic yards. Since he can only buy whole yards, he will need to buy 52 yards. The cost of the topsoil itself would be:
Cost of topsoil = volume of topsoil x cost per cubic yard
Cost of topsoil = 52 yd³ x $22.00/yd³
Cost of topsoil = $1144.00
There is also a $20 delivery fee, so the total cost of the topsoil would be:
Total cost = cost of topsoil + delivery fee
Total cost = $1144.00 + $20.00
Total cost = $1164.00
Therefore, buying bulk topsoil is less expensive than buying bags of topsoil in this case.
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Question 3(Multiple Choice Worth 5 points)
(Systems of Linear Equations MC)
Which point is a solution to the system of linear equations?
y = −x + 4
x − 3y = 12?
(0, 3)
(1, 2)
(6, −2)
(4, −4)
Answer:
4 -4
Step-by-step explanation:
this is what i need help with
Answer:
Step-by-step explanation:
x = [tex]\sqrt{12^{2}+9^{2} }[/tex]
x = 15
Solid A and solid B are similar.
The ratio of the volume of solid A to the volume of solid B is 27:1000
The surface area of solid A is 810 cm²
Calculate the surface area of solid B.
The surface area of solid B is 9000 cm².
What is ratio?
A ratio is a comparison of two quantities or values, often expressed as a fraction. Ratios can be used to express the relationship between two or more quantities.
Since solids A and B are similar, their corresponding linear dimensions are proportional. Let the scale factor be k, such that the dimensions of solid A are k times larger than the corresponding dimensions of solid B.
The ratio of their volumes is given as 27:1000. Therefore:
(volume of A) / (volume of B) = 27/1000
Let the volume of solid B be V. Then the volume of solid A is (27/1000)V.
Since the surface area of a solid is proportional to the square of its linear dimensions, we have:
[tex]$\frac{surface\ area\ of\ A}{surface\ area\ of\ B} = \frac{k_{A}^{2}}{k_{B}^{2}}$[/tex]
where kA and kB are the linear dimensions of solids A and B respectively.
Since the solids are similar, we can write:
[tex]$k_{A} / k_{B} = \frac{(volume\ of\ A)^{\frac{1}{3}}}{(volume\ of\ B)^{\frac{1}{3}}}$[/tex]
kA / kB = (volume of A)^(1/3) / (volume of B)^(1/3)
Substituting the given volume ratio and solving for kA / kB, we get:
[tex]$k_A/k_B = \left(\frac{27}{1000}\right)^{1/3} = 0.3$[/tex][tex]$k_A/k_B = \left(\frac{27}{1000}\right)^{1/3} = 0.3$[/tex]
Therefore, kA = 0.3 kB.
Now we can substitute the given surface area of solid A and solve for the surface area of solid B:
(surface area of A) / (surface area of B) = (kA)² / (kB)²
810 / (surface area of B) = 0.3²
(surface area of B) = 810 / 0.09
(surface area of B) = 9000 cm²
Therefore, the surface area of solid B is 9000 cm².
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Evaluate: 2 × [(6 + 1)² + 1]
Answer:
100
Step-by-step explanation:
2 x [(7)^2+1]
2x(49+1)
2x(50)
100
Dealer's Costs for New Vehicles
A. $29,300
C. $31.800
Base sticker price 90% of price
Options
Destination Fee
80% of included options
$800.00
Calculate the dealer's cost for a truck with
$30,000 sticker price and $5,000 in options.
B. $30,000
D. $31,000
Question 1(Multiple Choice Worth 2 points)
(Comparing Data MC)
The box plots display measures from data collected when 20 people were asked about their wait time at a drive-thru restaurant window.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 8.5 to 15.5 on the number line. A line in the box is at 12. The lines outside the box end at 3 and 27. The graph is titled Super Fast Food.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 9.5 to 24 on the number line. A line in the box is at 15.5. The lines outside the box end at 2 and 30. The graph is titled Burger Quick.
Which drive-thru typically has more wait time, and why?
Burger Quick, because it has a larger median
Burger Quick, because it has a larger mean
Super Fast Food, because it has a larger median
Super Fast Food, because it has a larger mean
The correct answer for the given dataset will be: Burger Quick, because it has a larger median.
What is a box plot?A box plot,also known as a box-and-whisker plot, is used for graphical representation of summary statistics from a data set. It helps by providing a visual representation of a data set's central tendency, dispersion, and skewness, making it straightforward to identify important data aspects.
As per given data, Burger Quick typically has more wait time compared to Super Fast Food.
The box plot for Burger Quick displays a higher interquartile range (from 9.5 to 24) than Super Fast Food (from 8.5 to 15.5), indicating that Burger Quick has a broader dispersion in the middle 50% of the data. Also, the median (shown by the line in the box) for Burger Quick is 15.5, but the median for Super Fast Food is 12. This implies that the average wait time at Burger Quick is longer than at Super Fast Food.
The lines outside the box (whiskers) also demonstrate that the range of values for Burger Quick (from 2 to 30) is greater than for Super Fast Food (from 3 to 27), implying that Burger Quick has a longer wait time.
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pls help
which number would make the statement true?
click full image
Answer:
0.535 is the correct choice.
six integers have a range of 13. The integers are 5,9,7,12,3,x. Find the value of x
Thus, for the given range of data of six integers the value of x is found as: x = 16.
Explain about the range of data:The difference here between maximum and smallest values in a data set is known as the range. Employing the exact same units as the data, it measures variability. More variability is shown by larger values.
Take the highest value and deduct the lowest value from it to determine the range in statistics.
A data set's range
Range is equal to the highest and lowest values.
Since the formula subtracts any smaller value from the larger one, it is impossible for it to be negative.
Given data:
six integers: 5,9,7,12,3,x.
Range = 13
The formula for the range ;
Range = maximum value - minimum value
x - 3 = 13
x = 13 + 3
x = 16
Thus, for the given range of the data of six integers the value of x is found as: x = 16.
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at how many points on the interval is the line tangent to parallel to the secant line connecting the function endpoints?
The line tangent to f(x) = x + sin(x) is parallel to the secant line connecting the endpoints at x = π on the interval [-2π, 2π].
Let's begin by finding the slope of the secant line connecting the endpoints of the function. The endpoints of the function on the interval [-2π, 2π] are (-2π, -2π + sin(-2π)) and (2π, 2π + sin(2π)), which evaluate to (-2π, 0) and (2π, 0), respectively.
The slope of the secant line is
m = (0 - 0)/(2π - (-2π)) = 0
Since we want the tangent line to be parallel to the secant line, the slope of the tangent line should also be 0. We can find the equation of the tangent line using the point-slope form
y - (x + sin(x)) = 0
y = x + sin(x)
To find the points on the interval where the tangent line is parallel to the secant line, we need to find the values of x where the derivative of f(x) is equal to 0 (i.e., where the slope of the tangent line is 0). The derivative of f(x) is
f'(x) = 1 + cos(x)
Setting this equal to 0 and solving for x, we get
cos(x) = -1
x = π
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The given question is incomplete, the complete question is:
At how many points on the interval [-2pi, 2pi] is the line tangent to f(x)=x+sin x parallel to the secant line connecting the function endpoints?
mean and median of 11, 41, 36, 4, 7
Answer:
Median = 11
Mean = 19.8
Step-by-step explanation:
Arrange data points from small to large - Median will be the number in the middle
4 7 11 36 41
To get the mean add the numbers together and divide by the number of numbers there are.
The total is 99
5 numbers
99/5
= 19.8
Hope this helps
Can someone help me out with this question please
The x-coordinate when Q has a y-coordinate of -4 is given as follows:
x = 3 or x = -3.
What is the equation of a circle?The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle, while the diameter of the circle is the distance between two points on the circumference of the circle that pass through the center. Hence, the diameter’s length is twice the radius length.
The circle in this problem has the parameters given as follows:
Center at the origin.Radius of 5.Hence the equation is given as follows:
x² + y² = 25.
When the y-coordinate is of -4, the x-coordinate is given as follows:
x² + (-4)² = 25
x² + 16 = 25
x² = 9
x = -3 or x = 3.
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Anumeha mows lawns. She charges an initial fee and a constant fee for each hour of work.F represents Anumeha's fee (in dollars) for working t hours. F = 6 + 12t How much does Anumeha charge for each hour of work?
Answer:
if she worked 2h it would be 2×12 for the hourly charge which would be 24and then the 24+6where 6 is the base charge.
Step-by-step explanation:
The intial few would be 6.as we can see in the equation
f(t)=6+12t
t would be the amount of hours and 12 is the rate per hour.
Four fiths of the footballs team's 30 points were scored on pass plays. How many points did the team score on pass plays?
Answer: 24 points
Step-by-step explanation:
4/5 is equal to 0.80. Multiply 30 by 0.80 and you get 24 points.
For the month of January, the amount of
snowfall was 3 inches above average.
Required polynomial is (x+3) where x is amount of average snowfall.
Here given in January, the amount of snowfall was 3 inches above average.
1. The average snowfall for January was a certain amount (let's call this 'A' inches).
2. The actual snowfall for January was 3 inches more than the average.
3. To calculate the actual snowfall for January, we can use the equation: Actual Snowfall = Average Snowfall (A) + 3 inches.
So, if we knew the average snowfall (A), we could easily find the actual snowfall by adding 3 inches to it.
Let amount of average snowfall be x inches.
So, snowfall in January month = (x+3) inches .
Therefore, required polynomial is (x+3) where x is amount of average snowfall.
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Correct answer is " Find a polynomial of the statement For the month of January, the amount of snowfall was 3 inches above average"
15 POINTS!!!!
5. If LN=4x-17 and MO = 2x + 13, what are the lengths of the diagonals of rectangle LMNO?
M
LN =
MO =
N
work:
Characteristics of
Kites
The length of the diagonal from L to N is approximately 60.8, and the length of the diagonal from M to O is approximately 47.0.
How to determine the lengths of the diagonals of rectangle LMNOTo find the lengths of the diagonals of rectangle LMNO, we first need to find the length of MN and LO.
Since LMNO is a rectangle, we know that opposite sides are congruent, so LN = MO and LO = MN.
Given that LN = 4x - 17 and MO = 2x + 13, we can set them equal to each other and solve for x:
4x - 17 = 2x + 13
2x = 30
x = 15
Now that we know x, we can find LN and MO:
LN = 4x - 17 = 4(15) - 17 = 43
MO = 2x + 13 = 2(15) + 13 = 43
Therefore, MN = LO = 43.
To find the length of the diagonals, we can use the Pythagorean theorem. Let's call the diagonal from L to N d1, and the diagonal from M to O d2:
d1^2 = LM^2 + LN^2
d1^2 = MN^2 + LN^2
d1^2 = 43^2 + 43^2
d1^2 = 3698
d1 ≈ 60.8
d2^2 = MO^2 + LM^2
d2^2 = MN^2 + LM^2
d2^2 = 43^2 + 18^2
d2^2 = 2209
d2 ≈ 47.0
Therefore, the length of the diagonal from L to N is approximately 60.8, and the length of the diagonal from M to O is approximately 47.0.
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Cathy & Gina sold baked goods at the festival, they were able to sell 18 items. The pies were $8 and loaves
of bread were $4. They made $112. How many loaves of bread did they sell?
Answer:
Step-by-step explanation:
They sold 34 loafs of bread
C an someone show me step by step how to do this and correctly please
A city just opened a new playground for children in the community. An image of the land that the playground is on is shown.
A polygon with a horizontal top side labeled 45 yards. The left vertical side is 20 yards. There is a dashed vertical line segment drawn from the right vertex of the top to the bottom right vertex. There is a dashed horizontal line from the bottom left vertex to the dashed vertical, leaving the length from that intersection to the bottom right vertex as 10 yards. There is another dashed horizontal line that comes from the vertex on the right that intersects the vertical dashed line, and it is labeled 12 yards.
What is the area of the playground?
900 square yards
855 square yards
1,710 square yards
1,305 square yards
Fierro brothers, a discount broker, charges their customers a $19 flat fee per trade. The sondo investment house charges a 2% commission. For what amount of stock would both brokers charge the same commission?
Answer:
yes it will be the same
Step-by-step explanation:
Let’s call the amount of stock traded “x”. Then we can set up an equation like this:
$19 = 0.02x
To solve for x, we can divide both sides by 0.02:
$950 = x
Therefore, if you trade $950 worth of stock, both Fierro Brothers and Sondo Investment House would charge you the same commission.
a b c or d please help quick
Answer:
D.
Step-by-step explanation:
By looking at them I feel like D. is the best option
which graph represents f(x) =3x-2
The graph that represents f(x) =3x-2 is the graph (b)
Which graph represents f(x) =3x-2From the question, we have the following parameters that can be used in our computation:
The equation: f(x) = 3x - 2
From the above equation, we have
f(x) = 3x - 2
The above equation is a linear function with the following features
Slope = 3
y-intercept = -2
This means that the graph intersects with the y axis at y = -2
Using the above as a guide, we have the following:
The graph intersects with the y axis at y = -2 and has a slope of 2 is graph (b)
Hence, the graph that represents f(x) =3x-2 is graph (b)
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through ten games of basketball this season, jevonte has made 7 out of 8 of his free-throws. which word or phrase describes the probability that jevonte will hit his next free throw?
The probability that Jevonte will hit his next free throw is "likely" or "high".
Since Jevonte has made 7 out of 8 of his free throws so far, he has a success rate of 87.5%, which is quite high. Therefore, it is reasonable to expect that he will continue to make his free throws at a similar rate, making it likely that he will hit his next free throw.
what is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain. A probability of 0.5 (or 50%) means the event is just as likely to occur as it is not to occur. Probability is used extensively in fields such as mathematics, statistics, physics, engineering, economics, and many other areas to model and analyze uncertain events or situations.
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The length of a rectangle is
double its width and the area of
the rectangle is 288 cm². What is
the perimeter of the rectangle?
The perimeter of the rectangle is 72 cm.
what you mean by perimeter?Perimeter is the total distance around the boundary of a two-dimensional shape. It is the sum of the lengths of all sides or edges of the shape.
The perimeter is usually measured in units such as centimeters (cm), meters (m), feet (ft), or inches (in), depending on the unit of measurement used for the sides or edges.
Let's start by assigning variables to the length and width of the rectangle.
Let x be the width of the rectangle in cm.
Then, the length of the rectangle is double the width, which is 2x cm.
We know that the area of the rectangle is 288 cm², so we can set up an equation:
Area = Length x Width
288 = 2x * x
Simplifying the equation, we get:
288 = 2x²
Dividing both sides by 2, we get:
144 = x²
Taking the square root of both sides, we get:
x = ± 12
Since x cannot be negative (as it represents a length), we take x = 12 cm as the width of the rectangle.
The length of the rectangle is 2x, which is 24 cm.
Now we can find the perimeter of the rectangle, which is given by the formula:
Perimeter = 2(Length + Width)
Substituting the values we found, we get:
Perimeter = 2(24 + 12) = 72 cm
Therefore, the perimeter of the rectangle is 72 cm.
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