Round 11.625 to the nearest ones place
Answer:
hindi ko maintindihan ang tanong mo
At her birthday party, Sam is serving a slice of cake to each attendee. Of each attendee receives 2 slices, there will be 20 slices left. If 5 attendees do not receive any slices and the rest receive 5 slices each, there will be no cake left. How many attendees were at the party
On solving the provided question, we can say that by having the equation 15 attendees were at the party
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
let x = number of attendees
\(2x\) + 20 = number of slices 5(x-5) = \(2x\) - 20
\(5x\) - 25 = \(2x\) + 20
\(3x\) = 45
\(x\) = 15
\(2x\) + 20 = 50 slices
15 attendees
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could somebody helppp meee pleaseeeeee
Answer:
(6-4)=2
2*49 . 7
91 . 7
13
14
:
(6-4) = 2
2 x 49 = 98 / 7 = 14
( "/" means divide )
Question : Find the length of the missing side. round your answer to the nearest tenth.
Answer:
8.5
Step-by-step explanation:
A group of 8 people bought tickets to a show. the tickets cost $21.48 each. what was the total cost of the tickets? enter your answer in the box. $
A group of 8 people bought tickets to a show. the tickets cost $21.48 each. then we get total cost is $ 171.84.
According to the question, given that
A group of 8 persons purchased show tickets for a price of $21.48 each.
The total cost of the tickets was calculated as follows:
= 8 * 21.48
= 171.84
Therefore, we get total cost = $ 171.84
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions written on the left and the right.
Mathematicians refer to equations with a degree of 1 as linear equations. The largest exponent of terms in these equations is 1, which equals. These can also be broken down into linear equations with one variable, two variables, three variables, etc. A linear equation with the variables X and Y has the usual form an X + b Y - c = 0, where a and b are the corresponding coefficients of X and Y and c is the constant.
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M\QRX=
80
360
180
129
Pls help
Answer:
129
Step-by-step explanation:
The sum of all the angles in a triangle is 180 degrees.
49 + 80 + <QRP = 180
<QRP = 51
The sum of the angles across a straight line is also 180:
<QRP + <QRX = 180
51 + <QRX = 180
<QRX = 129
HELPPPPPPPP PLEASE HELP ME EEEEEE
Answer: The correct answer is b
Step-by-step explanation:
25% off $30 is 22.50 and then when you add 7%ax it turns out to be 24.08
Solve the equation.
-6y=18
so what is y
Answer: -3
Step-by-step explanation:
6 times 3 is 18, so y is -3
The graph of f(x) = 2x + 3 shifts 10 units to the right when it is replaced with the graph of f(x) = 2x − k. What is the value of k? (1 point) 3 7 10 13
Answer:
10
Step-by-step explanation:
k represents how many places the graph will be shifted. -k means that is being shifted to the right and positive means being shifted to the left.
So when moving 10 units to the right, k will equal 10
Answer:
its 10
Step-by-step explanation:
Hey can anyone pls help me in dis real quick!!!!!
Answer:
1) you use any parallel lines or rectangles we can double the triangle to get the area and then divide by 2 as we know the length is 92.5yards and we know the width is 53.5 yards.
We would x these by each other and then divide by 2.
We have the width 53 1/2 yards wide and convert this to decimal if we want.
= 53.5 yards.
We then can count the yards for the length = 90 hash marks = 90 yards+ 2.5
= 92.5yards.
We square then add to find the hypotenuse diagonal line but it is an estimate as the lines inscribed subtends into the corner and it becomes a little larger as bottom line is used. Diagonal is found after by doing a reverse equation on the area.
53.5 x 92.5 then divide by 2 = 4948.75/2 = 2474.375
then 2474.375/ 26.75 = 92.5
This proves the line is isosceles and also find the height of the triangle.
But only as an estimate as the actual line distends
Last answer is B and W are equal measures this is because we do not see a right angle and if we bisected the triangle from the goal line to the left side we would prove the midpoint goal line is actually equal and makes lines of play isosceles where two sides are the same at point B and W.
So the answer is 1 yard as B runs the length of the goal back to a position of diagonal run.
The diagonal length is 92.5 yards
Step-by-step explanation:
I need help with my Alg 2 work.
Help quickly if possible.
Thanks.
Positive value of a vertically stretches the graph of f when a > 1 or shrinks the graph of f when a < 1. h translates the graph of f to the left when h < 0 or right when h > 0.
What are some examples of how exponential functions are employed in mathematics and in real life?Several real-world scenarios use exponential functions, including population increase, compound interest, radioactive decay, and the spread of diseases. For instance, an exponential function may be used to simulate the expansion of a bacterial population, with the rate of increase being proportional to the population size. Similarly, compound interest, which applies the rate of interest to the principal sum across a number of periods, can be represented by an exponential function.
Positive value of a vertically stretches the graph of f when a > 1 or shrinks the graph of f when a < 1. h translates the graph of f to the left when h < 0 or right when h > 0 and k translates the graph of f up when k > 0 and down when k < 0.
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A polynomial function, f(x) = x⁴ - 5x³ - 28x²+ 188x - 240 , is used to model a new roller coaster section. The loading zone will be placed at one of the zeros. The function has a zero at 5 . What are the possible locations for the loading zone?
b. How can you use polynomial division?
The possible locations for the loading zone in the roller coaster section modeled by the polynomial function f(x) = x⁴ - 5x³ - 28x² + 188x - 240 can be found by identifying the zeros of the function.
Since the function has a zero at x = 5, this indicates that one possible location for the loading zone is at x = 5.
In the context of polynomial functions, a zero of a function is a value of x for which the function equals zero. To find the zeros of the given polynomial function, various methods can be used, such as factoring, synthetic division, or using numerical techniques like the Newton-Raphson method.
In this case, we are given that the polynomial function has a zero at x = 5. This means that when x equals 5, the function f(x) equals zero. Therefore, one possible location for the loading zone is at x = 5.
To determine other possible locations for the loading zone, further analysis of the polynomial function is required. This could involve factoring the polynomial, using polynomial division to find possible rational zeros, or employing numerical methods to approximate the remaining zeros. The specific steps and calculations involved in finding additional zeros would depend on the characteristics of the polynomial function.
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Which is a solution to the system of linear inequalities? Select all that apply.
y>-x+3
y> 3x+1
(1,8)
(0,5)
(-2,9)
(0,0)
(-1, 1)
Multiple choice
Among the 5 options given in the question, the coordinates that satisfy the given inequalities are (1,8), (0,5), (-2,9). And the other two , donot satisfy the inequalities, hence (1,8), (0,5), (-2,9) are the required solutions.
What are the solutions to a system of linear inequalities?The solutions to a system of linear inequalities are the coordinates that satisfy all the inequalities in the system. They are the points that are above the lines of the inequalities.
How can we determine if a point is a solution to a system of linear inequalities?To determine if a point is a solution to a system of linear inequalities, we need to substitute the coordinates of the point into each inequality and check if it makes the inequality true. A point is a solution to the system if it makes all the inequalities true.
To check the solutions for the given linear inequallities,
1. y>-x+3
for (1,8) , 8 > -1+3 i.e 8>2 , Hence Satisfied
for (0,5) , 5> -0+3 i.e 5>3, Hence satisfied
for (-2,9) , 9>-(-2) + 3 i.e 9>5, Hence satisfied
for (0,0), 0>-0 +3 i.e 0>3 , Which is false
for (-1,1) , 1 > 1 +3 ,i.e 1>4, which is false
2.y> 3x+1
for (1,8) , 8 > 3*1+1 i.e 8>4 , Hence Satisfied
for (0,5) , 5> 3*0+1 i.e 5>1, Hence satisfied
for (-2,9) , 9>3*(-2) +1 i.e 9>-5, Hence satisfied
for (0,0), 0>3*0+1 i.e 0>1 , Which is false
for (-1,1) , 1 > 3*(-1)+1 ,i.e 1>-2, which is false
Hence the required solutions are (1,8), (0,5), (-2,9) which satisfy the both inequalities.
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L is the circle with the equation x²+y²=9
full question in photo :)
The values of the variables, a, b, and c obtained from the equation of the circle and the coordinates of the point P are;
a) a = 2
b = -2
c = 4
What is the general equation of a circle?The general equation of a circle is; (x - h)² + (y - k)² = r²
Where;
(h, k) = The coordinates of the center of the circle
r = The coordinates of the radius of the circle
The specified equation of a circle is; x² + y² = 9
The coordinates of the center of the circle, is therefore, O = (0, 0)
a) The coordinates of the points P and O indicates that the gradient of OP, obtained using the slope formula is; ((3·√3)/4 - 0)/(3/2 - 0) = ((3·√3)/4)/(3/2)
((3·√3)/4)/(3/2) = (√3)/2
The specified form of the gradient is; (√3)/a, therefore;
(√3)/a = (√3)/2
a = 2
The value of a is 2
b) The gradient of the tangent to a line that has a gradient of m is -1/m
The gradient of OP is; (√3)/2, therefore, the gradient of the tangent at P is -2/(√3)
The form of the gradient of the tangent at P is b/(√3), therefore;
-2/(√3) = b/(√3)
b = -2
The value of b is; -2
c) The coordinate of the point on the tangent, (0, (7·√3)/c) indicates
Slope of the tangent = -2/(√3)
((7·√3)/c - ((3·√3)/4))/(0 - (3/2)) = -2/(√3)
((7·√3)/c - ((3·√3)/4)) = (3/2) × 2/(√3) = √3
(7·√3)/c = √3 + ((3·√3)/4) = 7·√3/4
Therefore; c = 4
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A teacher buys the folders listed below
• 5 boxes of red folders with 36 folders in each box
• 6 boxes of blue folders with 32 folders in each boxes
Which number is closest to the total number of red and blue folders that the teacher buys?
180 Red folders, 192 Blue folders, and 372 total folders.
Step-by-step explanation:
I'm not sure if I'm doing this correctly but it seems fitting to me, so basically, I multiplied 5x36 to get 180, then multiplied 6x32 to get 192. Next, I added 180+192 to get 372 total folders.
Find the probability that you roll the same number twice in a row when you toss two fair 6-sided dice.
Answer: 6/36
Step-by-step explanation:
When tossing two number cubes, you can get such sample space
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
There are 36 possible outcomes. Only (1,1), (2,2), (3,3), (4,4), (5,5), and (6,6) use the same number twice.
Hence, the probability that you roll two numbers that are the same in a row is 6/36, or in simplified form, 1/6.
Hope that helps! :)
For the arithmetic sequence beginning with the terms (1, 4, 7, 10, 13, 16. },
what is the sum of the
first 19 terms?
The sum of the first 19 terms of the arithmetic sequence is 532.
We can find the sum of an arithmetic sequence by using the formula:
S = (n/2)(a1 + an)
where S is the sum of the first n terms of the sequence, a1 is the first term, and an is the nth term.
In this case, the first term is 1, and the common difference is 3 (since each term is 3 more than the previous term). So the nth term is:
an = a1 + (n - 1)d
an = 1 + (n - 1)3
an = 3n - 2
We want to find the sum of the first 19 terms, so:
n = 19
an = 3(19) - 2
an = 55
Now we can plug in the values into the formula:
S = (n/2)(a1 + an)
S = (19/2)(1 + 55)
S = 19(28)
S = 532
Therefore, the sum of the first 19 terms of the arithmetic sequence is 532.
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Solve the problem. A vendor sells hot dogs and bags of potato chips. A customer buys 3 hot dogs and 5 bags of potato chips for $16.25. Another customer buys 5 hot dogs and 4 bags of potato chips for $19.50. Find the cost of each item.
A. $2.75 for a hot dog; $2.00 for a bag of potato chips
B.$2.50 for a hot dog; $1.75 for a bag of potato chips
C.$2.50 for a hot dog: $2.00 fora bag of potato chips
D. $1.75 for a hot dog; $2.50 for a bag of potato chips
Answer
ok the answer is C
Step-by-step explanation:
1.75*4=7
.75*2=1.5
7+1.5=8.50
A function is a type of ___________.
relation
range
domain
vertical line test
Consider the following initial-value problem. y′′+9y=cos(3t),y(0)=5,y′(0)=4 Take the Laplace transform of the differential equation a L{y}=s/(s2+9)2+(5s+4)/(s2+9).
The Laplace transform of the given initial-value problem is \(Y(s) = (s^3 + 14s^2 + 39s + 90)/(s^2 + 9)^3.\)
To find the Laplace transform of the given initial-value problem, we apply the Laplace transform to the differential equation and the initial conditions separately.
Taking the Laplace transform of the differential equation y'' + 9y = cos(3t), we have: L{y''} + 9L{y} = L{cos(3t)}
Using the properties of the Laplace transform and the derivatives property, we get:
\(s^2Y(s) - sy(0) - y'(0) + 9Y(s) = s/(s^2 + 9)^2 + L{cos(3t)}\)
Substituting the initial conditions y(0) = 5 and y'(0) = 4, and using the Laplace transform of cos(3t), we have:
\(s^2Y(s) - 5s - 4 + 9Y(s) = s/(s^2 + 9)^2 + 3(s^2 + 9)/(s^2 + 9)^2\)
Simplifying the equation further, we obtain:
\((s^2 + 9)Y(s) = s/(s^2 + 9)^2 + (3s^2 + 30)/(s^2 + 9)^2 + 5s + 4\)
Combining the terms on the right side, we have:
\((s^2 + 9)Y(s) = (s + 3s^2 + 30 + 5s(s^2 + 9) + 4(s^2 + 9))/(s^2 + 9)^2\)
Simplifying the numerator, we get:
\((s^2 + 9)Y(s) = (s^3 + 14s^2 + 39s + 90)/(s^2 + 9)^2\)
Finally, dividing both sides by s^2 + 9, we obtain:
\(Y(s) = (s^3 + 14s^2 + 39s + 90)/(s^2 + 9)^3\)
Therefore, the Laplace transform of the given initial-value problem is Y(s) =\((s^3 + 14s^2 + 39s + 90)/(s^2 + 9)^3\).
By applying the Laplace transform to the differential equation y'' + 9y = cos(3t), we obtain the equation (\(s^2\)+ 9)Y(s) = \((s + + 30 + 5s(s^2 + 9) + 4(s^2 + 9))/(s^2 + 9)^2.\) Simplifying further, we find\(Y(s) = (s^3 + 14s^2 + 39s + 90)/(s^2 + 9)^3\). This represents the Laplace transform of the solution y(t) to the initial-value problem. The initial conditions y(0) = 5 and y'(0) = 4 are incorporated into the transformed equation as \(y(0) = 5s/(s^2 + 9) + 4/(s^2 + 9)\).
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Automatic Transmissions, Inc., has the following estimates for its new gear assembly project: price = $940 per unit; variable cost = $340 per unit; fixed costs = $3.4 million; quantity = 53,000 units. Suppose the company believes all of its estimates are accurate only to within ±15 percent. What values should the company use for the four variables given here when it performs its best-case scenario analysis? What about the worst-case scenario?
In the worst-case scenario, the company should use the following values: price = $799 per unit, variable cost = $289 per unit, fixed costs = $2.89 million, and quantity = 60,950 units.
In the best-case scenario analysis for Automatic Transmissions, Inc.'s new gear assembly project, the company assumes the upper limit of the ±15 percent range for its estimates. For the price per unit, they take a 15 percent increase, resulting in a value of $1081. Similarly, the variable cost per unit is increased by 15 percent to $391. The fixed costs are also adjusted upwards by 15 percent, reaching $3.91 million. Finally, the quantity is decreased by 15 percent, leading to a value of 45,050 units.
On the other hand, in the worst-case scenario analysis, the company assumes the lower limit of the ±15 percent range for its estimates. The price per unit is decreased by 15 percent, resulting in $799. The variable cost per unit is decreased to $289. The fixed costs are adjusted downwards to $2.89 million. Lastly, the quantity is increased by 15 percent to 60,950 units.
Therefore, in the worst-case scenario, the company should use the following values: price = $799 per unit, variable cost = $289 per unit, fixed costs = $2.89 million, and quantity = 60,950 units
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We give JMP output of regression analysis. Above output we give the regression model and the number of observations, n, used to perform the regression analysis under consideration. Using the model, sample size n, and output:
Model: y = β0 + β1x1 + β2x2 + β3x3 + ε Sample size: n = 30
(1) Report the total variation, unexplained variation, and explained variation as shown on the output. (Round your answers to 4 decimal places.)
(2) Report R2 and R¯¯¯2R¯2 as shown on the output. (Round your answers to 4 decimal places.)
(3) Report SSE, s2, and s as shown on the output. (Round your answers to 4 decimal places.)
(4) Calculate the F(model) statistic by using the explained variation, the unexplained variation, and other relevant quantities. (Round your answer to 2 decimal places.)
(5) Use the F(model) statistic and the appropriate critical value to test the significance of the linear regression model under consideration by setting α equal to .05.
(6) Find the p−value related to F(model) on the output. Using the p−value, test the significance of the linear regression model by setting α = .10, .05, .01, and .001. What do you conclude?
Based on the given regression model and the number of observations (n = 30), we can analyze the JMP output to obtain various statistical measures. The output provides information on the total variation, unexplained variation, and explained variation, as well as R-squared (R²) and adjusted R-squared (R¯²).
Additionally, the output includes SSE, s², and s, which are measures of error and variability. Furthermore, we can calculate the F(model) statistic using the explained and unexplained variation. By comparing the F(model) statistic to the critical value and p-value, we can test the significance of the linear regression model at different significance levels.
(1) The JMP output should provide the values for total variation, unexplained variation, and explained variation. These measures help us understand the distribution of the dependent variable (y) and the extent to which the independent variables (x₁, x₂, x₃) explain the variation in y.
(2) R-squared (R²) and adjusted R-squared (R¯²) provide information about the proportion of variation in the dependent variable explained by the independent variables. These values range from 0 to 1, with higher values indicating a better fit of the model to the data.
(3) SSE (Sum of Squares Error), s² (mean squared error), and s (standard error) quantify the magnitude of the residuals or errors in the model. SSE represents the sum of squared differences between the actual y-values and the predicted y-values.
(4) The F(model) statistic is calculated using the ratio of explained variation to unexplained variation, and it helps assess the overall significance of the regression model. It compares the mean squared error of the model to the mean squared error of the residuals.
(5) To test the significance of the linear regression model, the F(model) statistic should be compared to the critical value for a given significance level (α = 0.05).
(6) The p-value related to F(model) can also be obtained from the JMP output. By comparing the p-value to the chosen significance level (α), we can determine whether the linear regression model is statistically significant. If the p-value is less than α, we reject the null hypothesis and conclude that the model is significant.
Overall, the JMP output and subsequent calculations and tests provide a comprehensive analysis of the linear regression model's significance and performance in explaining the variation in the dependent variable.
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Based on the given regression model and the number of observations (n = 30), we can analyze the JMP output to obtain various statistical measures. The output provides information on the total variation, unexplained variation, and explained variation, as well as R-squared (R²) and adjusted R-squared (R¯²).
Additionally, the output includes SSE, s², and s, which are measures of error and variability. Furthermore, we can calculate the F(model) statistic using the explained and unexplained variation. By comparing the F(model) statistic to the critical value and p-value, we can test the significance of the linear regression model at different significance levels.
(1) The JMP output should provide the values for total variation, unexplained variation, and explained variation. These measures help us understand the distribution of the dependent variable (y) and the extent to which the independent variables (x₁, x₂, x₃) explain the variation in y.
(2) R-squared (R²) and adjusted R-squared (R¯²) provide information about the proportion of variation in the dependent variable explained by the independent variables. These values range from 0 to 1, with higher values indicating a better fit of the model to the data.
(3) SSE (Sum of Squares Error), s² (mean squared error), and s (standard error) quantify the magnitude of the residuals or errors in the model. SSE represents the sum of squared differences between the actual y-values and the predicted y-values.
(4) The F(model) statistic is calculated using the ratio of explained variation to unexplained variation, and it helps assess the overall significance of the regression model. It compares the mean squared error of the model to the mean squared error of the residuals.
(5) To test the significance of the linear regression model, the F(model) statistic should be compared to the critical value for a given significance level (α = 0.05).
(6) The p-value related to F(model) can also be obtained from the JMP output. By comparing the p-value to the chosen significance level (α), we can determine whether the linear regression model is statistically significant. If the p-value is less than α, we reject the null hypothesis and conclude that the model is significant.
Overall, the JMP output and subsequent calculations and tests provide a comprehensive analysis of the linear regression model's significance and performance in explaining the variation in the dependent variable.
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This problem is for you to prove a Big-Theta problem
2n - 2√n ∈ θ(n) (√ is the square root symbol)
To prove, you need to define c1, c2, n0 , such that n > n0 , and
0 ≤ c1n ≤ (2n - 2√n) and (2n - 2√n) ≤ c2n
Can you use inequality to find a set of c1, c2, n0 values that satisfied the above two inequalities?`
we can choose c1 = 0 and n0 large enough such that the inequality holds. We have shown that 2n - 2√n ∈ θ(n) with c1 = 0, c2 = C, and n0 sufficiently large.
To prove that 2n - 2√n ∈ θ(n), we need to find constants c1, c2, and n0 such that for all n > n0, the following two inequalities hold:
0 ≤ c1n ≤ 2n - 2√n and 2n - 2√n ≤ c2n
Let's start with the second inequality:
2n - 2√n ≤ c2n
Divide both sides by n:
2 - 2/n^(1/2) ≤ c2
Since n^(1/2) → ∞ as n → ∞, we can make the second term on the left-hand side as small as we want by choosing a large enough value of n. So, we can find some constant C such that 2 - 2/n^(1/2) ≤ C for all n > n0. Then we can choose c2 = C and n0 large enough such that the inequality holds.
Now let's move on to the first inequality:
0 ≤ c1n ≤ 2n - 2√n
Divide both sides by n:
0 ≤ c1 ≤ 2 - 2/n^(1/2)
Again, since n^(1/2) → ∞ as n → ∞, we can make the second term on the right-hand side as small as we want by choosing a large enough value of n. So, we can find some constant D such that 0 ≤ c1 ≤ 2 - 2/n^(1/2) ≤ D for all n > n0. Then we can choose c1 = 0 and n0 large enough such that the inequality holds.
Therefore, we have shown that 2n - 2√n ∈ θ(n) with c1 = 0, c2 = C, and n0 sufficiently large.
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Translate the sentence into an equation Eight times the sum of a number and 4 equals 6 use the variable c for the unknown number.
PLS HELP MEE
The bundles are stacked and tied into blocks that are 1,2 meters high. How many bundles are used to make one block of cardboard
The number of bundles that is used to make one block of the cardboard is given as follows:
24 bundles.
How to obtain the number of bundles?The number of bundles that is used to make one block of the cardboard is obtained applying the proportions in the context of the problem.
The length of each bundle is given as follows:
50 mm = 50 x 0.001 = 0.05m.
The length of the block is given as follows:
1.2 m.
Hence the number of bundles is given as follows:
1.2/0.05 = 24 bundles.
Missing InformationThe complete problem is:
"The 150 mm bundles are stacked and tied into blocks that are 1,2 meters high. How many bundles are used to make one block of cardboard".
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a full circle has 360° or 2π radians. given this, how many degrees are in 1 radian?
Answer:
1 radian ≈ 57.2958
Borderline
Your late grandfather left you and your cousin his property in his will. Below is a map of the
property with a road that cuts through the property
North Property Border
Road
South Property Border
1. On the diagram, two angles (<1 und 2) formed by the road, and the borders are congruent.
What is the relationship
between the north and south property borders of your prandfather's
land?
Explain how you know
2. How are <3 and <1 related to each other
Explain how you know
Answer:
1. The North and South property border lines are parallel
2. ∠3 and ∠1 are supplementary angles
Step-by-step explanation:
The given parameters are;
The North and South Property Boarders are given
The road intersects (transverses) the North and South Property Boarders
∠1 and ∠2 in the given diagram are congruent
1. Given that ∠1 ≅ ∠2, and from the diagram, ∠1 and ∠2 are alternate interior angles, we have that alternate interior formed by the transversal of two parallel lines are congruent
Therefore, the North and South property border lines are parallel
2. ∠3 and ∠1 are same side interior angles
When two parallel lines have a common transversal passing through them, then the same side interior angles are supplementary
Therefore, ∠3 and ∠1 are supplementary (angles whose sum is 180°)
The proof is that ∠3 and ∠2 are supplementary, because they are the angles on a straight line
∠2 ≅ ∠1 which is given
∴ ∠2 = ∠1 by definition of congruency
∠3 and ∠1 are therefore, supplementary, by substitution property of equality
In a simple linear regression model, if the plots on a scatter diagram lie on a straight line, what is the standard error of the estimate?a. +1b. 0c. Infinityd. -1
Answer:
In a simple linear regression model, if the plots on a scatter diagram lie on a straight line, what is the standard error of the estimate b. 0
Step-by-step explanation:
If the plots on a scatter diagram lie on a straight line in a simple linear regression model, it indicates a perfect fit between the predictor variable and the response variable. In this case, the standard error of the estimate would be 0.
The standard error of the estimate represents the average distance between the observed values and the predicted values by the regression model. When the scatter diagram forms a perfect straight line, it means that the regression model can precisely predict the response variable using the predictor variable without any error.
Consequently, the residuals, which are the differences between the observed and predicted values, become zero for all data points, resulting in a standard error of 0. It is important to note that this scenario of a perfect fit on a scatter diagram is rare in real-world data, as there are typically variations and uncertainties in the relationship between variables.
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based on only the given information, it is guaranteed that ABC ~ XYZ true or false
In reference to question 21 above, how much work is required to move a +150μC point charge from P to Q ? (Answer: 0.056 J ) Question 23 A capacitor has a very large capacitance of 10 F. The capacitor is charged by placing a potential difference of 2 V between its plates. How much energy is stored in the capacitor? (Answer: 20J) Question 24 A parallel plate capacitor has plates of area 2.0×10−3 m2 and plate separation 1.0×10−4 m. Determine the capacitance of this system if air fills the volume between the plates. (Answer: 1.8×10−10 F ) Question 25 A potential difference of 120 V is established between two parallel metal plates. The magnitude of the charge on each plate is 0.020 C. What is the capacitance of this capacitor? (Answer: 170μF )
In question 21, the work required to move a +150μC point charge from P to Q is 0.056 J. In question 23, the energy stored in a capacitor with a very large capacitance of 10 F and a potential difference of 2 V is 20 J. In question 24, the capacitance of a parallel plate capacitor with an area of 2.0×10−3 m2 and plate separation of 1.0×10−4 m, filled with air, is 1.8×10−10 F. In question 25, the capacitance of a capacitor with a potential difference of 120 V and a charge of 0.020 C on each plate is 170μF.
Question 21: To calculate the work required, we use the formula W = qΔV, where q is the charge and ΔV is the potential difference between the points P and Q.
Question 23: The energy stored in a capacitor can be calculated using the formula E = (1/2)CV^2, where C is the capacitance and V is the potential difference across the capacitor.
Question 24: The capacitance of a parallel plate capacitor can be determined using the formula C = ε0A/d, where ε0 is the permittivity of free space, A is the area of the plates, and d is the separation between the plates.
Question 25: The capacitance of a capacitor can be found using the formula C = Q/V, where Q is the charge on each plate and V is the potential difference across the capacitor.
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