The margin of error is an important factor in determining the sample size needed to estimate a parameter, it is not the only factor - False.
Other factors that need to be considered include the level of confidence desired, the variability of the population being sampled, and the size of the population.
The margin of error is the amount of error that is acceptable in the estimate of the parameter. The smaller the margin of error desired, the larger the sample size needed.
A higher level of confidence requires a larger sample size, as there is less room for error in the estimate. The variability of the population being sampled also plays a role in determining the sample size needed.
Finally, the size of the population being sampled also affects the sample size needed.
A smaller population requires a smaller sample size, while a larger population requires a larger sample size to ensure a representative sample.
In summary, while the margin of error is an important factor in determining the sample size needed to estimate a parameter, it is not the only factor.
Other factors that need to be considered include the level of confidence desired, the variability of the population being sampled, and the size of the population.
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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 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:
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.
Evaluate: 2 × [(6 + 1)² + 1]
Answer:
100
Step-by-step explanation:
2 x [(7)^2+1]
2x(49+1)
2x(50)
100
If the mogav train travels at a consistent speed of 480 km/h for one fourth of an hour how far does the train travel
The train travels a distance of 120 kilometers.
To calculate the distance traveled by the train, we can use the formula:
Distance = Speed × Time
Given that the train travels at a consistent speed of 480 km/h and the time is one-fourth of an hour, we can substitute these values into the formula:
Distance = 480 km/h × (1/4) hour
To simplify the calculation, we can convert one-fourth of an hour to minutes. Since there are 60 minutes in an hour, one-fourth of an hour is equal to (1/4) × 60 minutes = 15 minutes.
Now, we can calculate the distance:
Distance = 480 km/h × (1/4) hour
= 480 km/h × (1/4) × 60 minutes / 60 (converting hours to minutes)
= 480 km/h × 15 minutes / 60
= 480 km/h × 0.25
= 120 km
Therefore, distance travelled by train is 120 kilometers.
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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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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
A research survey of 2006 public and private school students in the united states (grades 10-12) between April 12 and June 12,2016 asked students if they agreed with the statements, "if I make a mistake, I try to figure out where I went wrong. " The survey found that 86% students agreed with the statement. The margin of error for the survey is +/- 3. 7%
The survey found that 86% of 2006 US students in grades 10-12 agreed with the statement "if I make a mistake, I try to figure out where I went wrong." The survey's margin of error is +/- 3.7%, so we can be 95% confident the true proportion falls between 82.3% and 89.7%.
This means that we can be 95% confident that the true proportion of students who agree with the statement lies between 82.3% and 89.7%. This interval is calculated as follows
Subtract the margin of error from the sample proportion to get the lower bound: 86% - 3.7% = 82.3%
Add the margin of error to the sample proportion to get the upper bound: 86% + 3.7% = 89.7%
So, we can say with 95% confidence that the true proportion of students who agree with the statement is somewhere between 82.3% and 89.7%.
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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?
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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Simon wants to fill 8 punch bowls for a birthday party. Each punch bowl holds 9 1/5 quarts of punch. How much punch will Simon need?
Write your answer as a fraction or as a whole or mixed number.
PLEASE HELP ME
Answer:
73.52 OR 74.00
Step-by-step explanation:
1.) 8 x 1/5 (I prefer converting to decimals first)
2.) 8.00 x 9.19 = 73.52 ----> (Rounding the ones place up) 74.00
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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The chemical element einsteinium-
253
253253 naturally loses its mass over time. When a sample of einsteinium-
253
253253 was initially measured, it had a mass of
15
1515 grams. The relationship between the elapsed time
�
tt, in weeks, and the mass,
�
week
(
�
)
M
week
(t)M, start subscript, start text, w, e, e, k, end text, end subscript, left parenthesis, t, right parenthesis, left in the sample is modeled by the following function:
Mweek(t)=15⋅(0. 79)t
Complete the following sentence about the daily rate of change in the mass of the sample. Round your answer to two decimal places. Every day, the mass of the sample decays by a factor of
The given information pertains to a sample of einsteinium-253, which naturally loses its mass over time. The initial mass of the sample was 15 grams when it was first measured. The relationship between the elapsed time in weeks, denoted by 't', and the mass of the sample in that week, denoted by 'Mweek(t)', is given by the function.
Mweek(t) = 15 * (0.79)^t.
The daily rate of change in the mass of the sample can be found by taking the derivative of the function with respect to time
Mweek'(t) = 15(0.79)^t ln(0.79)
To find the factor by which the mass decays every day, we can divide the mass at time t by the mass at time t+1.
Mweek(t) / Mweek(t+1) = (15(0.79)^t) / (15(0.79)^(t+1)) = 1/0.79
Therefore, every day, the mass of the sample decays by a factor of approximately 1.26 (rounded to two decimal places).
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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
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.
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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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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this is what i need help with
Answer:
Step-by-step explanation:
x = [tex]\sqrt{12^{2}+9^{2} }[/tex]
x = 15
please help would be amazing
Answer:
(9,8)
Step-by-step explanation:
Solve the first equation
then solve the second equation with the substitute number from the first equation.
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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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
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.
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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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.
The price of an item has dropped to $77 today. Yesterday It was $140. Find the percentage decrease.
The percentage price of the item has decreased by 45%.
What is the definition of percentage?
A percentage is a quantity or ratio that is stated as a fraction of 100.
"%" is the symbol for percentage.
For example, if 25 of 100 students in a class received a "A," we may represent this as a percentage by dividing the number of "A" students by the total number of students and multiplying by 100:
(25/100) x 100% = 25%
This signifies that 25% of the students in the class received a "A".
Now,
To obtain the % drop, subtract the difference between the original and new prices, divide by the original price, then multiply by 100 to get the percentage decrease.
The difference between the original and updated prices is equal to
140 - 77 = 63
So the percentage decrease is:
(63/140) x 100% = 45%
Therefore, the price of the item has decreased by 45%.
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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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A chord is 22 cm long. It is 60 cm from the center of the circle.
What is the radius of the circle?
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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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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3) During the last week of April, Ryan Foss produced 900 dolls. Ryan
receives $.96 per doll, less any defective units. What was Ryan's
gross pay for the last week of April?
Ryan's gross pay for the last week of April was $864, assuming that 96% of the dolls produced were non-defective.
What was Ryan's gross pay for the last week of April?If Ryan produced 900 dolls during the last week of April and receives $.96 per doll, his gross pay before any defective units are taken into account is:
900 dolls x $0.96/doll = $864
If we need to check if a certain percentage of the dolls produced were defective, we can multiply the gross pay by the percentage of non-defective units to find Ryan's actual gross pay.
For example, if 95% of the dolls produced were non-defective, Ryan's gross pay would be:
$864 x 0.95 = $820.80
Therefore, Ryan's gross pay for the last week of April was $820.80, assuming that 95% of the dolls produced were non-defective.
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