A) The coefficient of determination can be computed using the SSE and SST values in regression and correlation analysis.
SSE (Sum of Squared Errors) is the sum of the squared differences between the actual and predicted values of the dependent variable. SST (Total Sum of Squares) is the sum of the squared differences between the actual values of the dependent variable and their mean.
The coefficient of determination, denoted as R², measures the proportion of the variance in the dependent variable that can be explained by the independent variable(s) in a regression model.
It is calculated as follows:
R² = 1 - (SSE/SST)
Since both SSE and SST are given, you can compute the coefficient of determination.
However, the information provided is not sufficient to calculate the slope, Y-intercept, or X-intercept of the regression line.
Based on the given information, the correct answer is:
A) Coefficient of determination can be computed.
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This coefficient of determination (R²) gives you a measure of how well the regression line fits the data in your correlation analysis.
A) The coefficient of determination can be computed with the known values of SSE (sum of squared errors) and SST (total sum of squares) in regression and correlation analysis. The coefficient of determination is a measure of how well the regression line fits the data and is expressed as a percentage. It represents the proportion of variability in the dependent variable (Y) that can be explained by the independent variable (X).
Based on the information provided, with the known SSE (Sum of Squares Error) and SST (Sum of Squares Total), you can compute the coefficient of determination. So, the correct answer is:
A) Coefficient of determination can be computed
To calculate the coefficient of determination (R²), follow these steps:
1. Calculate the Sum of Squares Regression (SSR) by subtracting SSE from SST:
SSR = SST - SSE
2. Compute the coefficient of determination (R²) by dividing SSR by SST:
R² = SSR / SST
This coefficient of determination (R²) gives you a measure of how well the regression line fits the data in your correlation analysis.
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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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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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Estefanía has 2,593 euros and Rocío has 3,238 euros. How much money does Rocío have more than Estefanía?
The amount of money with Rocio has 645 euros more than Estefania.
Total amount of money with Estefania has = 2,593 euros
Total amount of money with Rocio has = 3,238 euros
When we compare the amount of money of both Estefania and Rocio
Rocio has more amount of money than Estefania .
3,238 Euros is greater than 2,593 Euros
To find out how much money Rocio has more than Estefania,
= Subtract Estefania's amount of money from Rocio's amount of money.
= 3,238 euros (Rocio's money) - 2,593 euros (Estefania's money)
= 645 euros
Therefore, Rocio has 645 euros more amount of money than Estefania.
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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
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:
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
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
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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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.
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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What is the sum and the product of x^2-9x+8
The sum of the roots of x² - 9x + 8 is 9. The product of the roots of x² - 9x + 8 is 8.
What is quadratic equation?A quadratic equation is a second-degree polynomial equation in one variable, typically written in the form ax² + bx + c = 0, where x is the variable and a, b, and c are constants.
According to question:The expression x² - 9x + 8 can be factored as follows:
x² - 9x + 8 = (x - 1)(x - 8)
To check that this factorization is correct, you can expand the expression using the distributive property:
(x - 1)(x - 8) = x² - 8x - x + 8 = x² - 9x + 8
So the factorization is indeed correct.
The sum of the roots of the quadratic equation ax² + bx + c = 0 is given by -b/a, where a, b, and c are the coefficients of the equation. In this case, a = 1, b = -9, and c = 8, so the sum of the roots is:
-sum of roots = -b/a = -(-9)/1 = 9
Therefore, the sum of the roots of x² - 9x + 8 is 9.
The product of the roots of the quadratic equation ax² + bx + c = 0 is given by c/a. In this case, c = 8 and a = 1, so the product of the roots is:
product of roots = c/a = 8/1 = 8
Therefore, the product of the roots of x² - 9x + 8 is 8.
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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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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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Which of these nets can be folded to form a square prism?
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
The wheels on a bike have a diameter of 26 inches. How many full revolutions will the wheels need to make to travel 100 feet?
Answer:
Step-by-step explanation:
distance traveled by one revolution = circumference of the wheel
= 2πr = 2π(13 inches) = 26π inches
number of revolutions = distance traveled / distance traveled by one revolution
100 feet = 1200 inches
= 1200 inches / 26π inches
≈ 45.91 full revolutions
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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please help asap this is for geometry its R.4
The value of k is given as follows:
k = 2.
What are the trigonometric ratios?The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:
Sine of angle = length of opposite side to the angle divided by the length of the hypotenuse.Cosine of angle = length of adjacent side to the angle divided by the length of the hypotenuse.Tangent of angle = length of opposite side to the angle divided by the length of the adjacent side to the angle.For this problem, we have that the parameters are given as follows:
k is the hypotenuse.The side length adjacent to the angle of 45º is of [tex]\sqrt{2}[/tex].Hence the equation to obtain k is given as follows:
[tex]\sin{45^\circ} = \frac{\sqrt{2}}{k}[/tex]
[tex]\frac{\sqrt{2}}{2} = \frac{\sqrt{2}}{k}[/tex]
k = 2.
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a one-hectare forest community is sampled in early august. the sample yields 12 small trees, 4 types of vines, as well as 17 native shrubs that represent 10 species. what can be estimated from the sample for the shrubs in the forest community?
Based on the sample of a one-hectare forest community in early August, an estimate can be made for the total number and diversity of shrub species present in the community.
From the sample of the one-hectare forest community, several estimates can be made for the shrubs in the forest community:
Abundance: The abundance of shrubs in the one-hectare forest community can be estimated by multiplying the number of shrubs in the sample by 10 (the number of species represented by the sample). Therefore, an estimate of the total number of shrubs in the one-hectare forest community would be 17 x 10 = 170 shrubs.
Species richness: The sample contained 10 species of shrubs. This can be used as an estimate of the total number of shrub species in the one-hectare forest community.
Diversity: The diversity of the shrub community in the one-hectare forest can be estimated using the data on species richness and abundance. The most commonly used metric for estimating diversity is the Shannon-Wiener diversity index, which takes into account both the number of species and their relative abundance.
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The histogram below shows the results of a survey on the number of traffic tickets received by a random group of drivers. 3 86 76 51 Number of People A 1 9 2 Traffic Tickets 10 8 6 Number of Traffic Tickets Step 6: How many people received either 4 or 5 traffic tickets? 12
In reference to the given histogram, an absence of bars signifying either 4 or 5 traffic tickets implies that no one from the selection had accumulated this amount.
How to explain the histogramIt should be noted that to make sure our point is accurate, we can sum the heights of the separate bars for 3, 6 and 8 tickets which demonstrate the total people included within the survey who have acquired the relevant number of traffic citations.
The height of the bar for three violations measures out at 1.
Conversely, a measurement of 2 denotes the bar for six infringements.
An assessment of 1 has been given to the bar with regards to eight offences.
Due to the lack of representation mentioned in the histogram concerning both 4 and 5 transgressions, it confirms our inference: nobody from the selection received four or five traffic tickets.
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Corey buys 27 inches of trim for a craft project
If Corey buys 27 inches of trim for a craft project, Corey bought 3/4 of a yard of trim for the craft project.
To determine what fraction of a yard Regina buys, we need to know how many inches are in a yard. There are 36 inches in a yard.
To convert 27 inches to yards, we need to divide by 36:
27 ÷ 36 = 0.75 yards
So Corey bought 0.75 yards of trim for the craft project.
To find the fraction of a yard, we need to express 0.75 as a fraction with a denominator of 1:
0.75 = 75/100 = 3/4
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Complete question is:
Corey buys 27 inches of trim for a craft project. What fraction of a yard does Regina buy?
In the EAI sampling problem, the population mean is $51,800 and the population standard deviation is $4,000. When the sample size is n = 30, there is a .5034 probability of obtaining a sample mean within +/- $500 of the population mean. A. What is the probability that the sample mean is within $500 of the population mean if a sample of size 60 is used (to 4 decimals)?
B. What is the probability that the sample mean is within $500 of the population mean if a sample of size 120 is used (to 4 decimals)?
A) The probability that the sample mean is within $500 of the population mean for a sample of size 60 is 0.6611
B) The probability that the sample mean is within $500 of the population mean for a sample of size 120 is 0.7362
The EAI (Error of the Estimate) sampling problem is a specific case of the Central Limit Theorem, which states that the distribution of sample means from a population with a finite variance will be approximately normally distributed as the sample size increases.
The formula for calculating the standard error of the mean is
SE = σ/√n
where SE is the standard error, σ is the population standard deviation, and n is the sample size.
For n = 30, SE = 4,000/√30 = 729.16
A. For a sample size of n = 60, SE = 4,000/√60 = 516.40
To find the probability that the sample mean is within $500 of the population mean, we need to calculate the z-score for a range of +/- $500
z = (x - μ) / SE
where x is the sample mean, μ is the population mean, and SE is the standard error.
For a range of +/- $500, the z-scores are
z = ($51,300 - $51,800) / 516.40 = -0.969
z = ($52,300 - $51,800) / 516.40 = 0.969
Using a standard normal distribution table, the area between z = -0.969 and z = 0.969 is 0.6611.
B. For a sample size of n = 120, SE = 4,000/√120 = 368.93
Following the same steps as above, the z-scores for a range of +/- $500 are
z = ($51,300 - $51,800) / 368.93 = -1.364
z = ($52,300 - $51,800) / 368.93 = 1.364
Using the standard normal distribution table, the area between z = -1.364 and z = 1.364 is 0.7362.
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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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A chord is 22 cm long. It is 60 cm from the center of the circle.
What is the radius of the circle?
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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in which one of the four scenarios would you consider a non-parametric test? group of answer choices when we are dealing with time series when we have numeric data and want to plot a regression line when we want to perform multiple regression when we only have ordered data
Non-parametric tests are statistical tests that do not require specific assumptions about the population distribution, such as normality or equal variances. They are useful in situations where the data does not meet the assumptions of parametric tests, or when the variables are ordinal or categorical.
There are some additional examples of non-parametric tests.
When the data is skewed or has outliers: If the data is not normally distributed, non-parametric tests such as the Wilcoxon rank-sum test or the Kruskal-Wallis test can be used instead of the t-test or ANOVA.When the sample size is small: If the sample size is small, it may be difficult to determine if the data is normally distributed or if variances are equal. In this case, non-parametric tests such as the Mann-Whitney U test or the Wilcoxon signed-rank test may be more appropriate.When the data is categorical or ordinal: If the data is categorical or ordinal, non-parametric tests such as the Chi-square test or Spearman's rank correlation coefficient can be used instead of parametric tests.When the data violates assumptions of independence: If the data is not independent, non-parametric tests such as the Friedman test or the McNemar's test may be used.Hence, non-parametric tests offer a flexible alternative to traditional parametric tests and can be useful in a variety of situations.
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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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Sue and 4 friends share half a pizza. Each piece of pizza is the same size. Sue believes each piece of pizza has an angle measure of 30º. Is Sue correct? Explain.
Sue statement that each piece of pizza has an angle measure of 30º is incorrect
Stating if Sue's statement is correctAssuming the pizza is circular, we know that the total angle measure of a circle is 360 degrees.
If we cut the pizza into halves, we have two equal pieces, each with an angle measure of 180 degrees.
If Sue and her 4 friends share half a pizza, they are sharing one of these equal pieces.
If we divide the 180 degree angle of the piece of pizza by 5 (Sue and her 4 friends plus Sue herself), we get an angle measure of 36 degrees, which is what Sue believes.
Therefore, Sue is incorrect.
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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.
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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