Answer:
100
Step-by-step explanation:
Which number is a reasonable estimate for the difference of the equation 3,412 − 1,287 = ________?
Answer:
2,125
Step-by-step explanation:
Answer:
2,125
Step-by-step explanation:
bc its ez
2x^2-3z^2+6z-4x-3y+2=0 what type of graph is it? and graph manually with details that can be understood
The graph will open upwards and downwards along the x-axis and have a saddle-like shape along the z-axis. Additionally, the graph will extend infinitely in the y-direction. The graph is a hyperbolic paraboloid.
The equation 2x² - 3z² + 6z - 4x - 3y + 2 = 0 represents a quadratic equation in two variables, x and z, along with a linear term involving y. However, since there are three variables involved, it cannot be graphed directly on a two-dimensional plane. Instead, we can create a 3D graph to represent the equation.
To graph the equation, we'll create a 3D coordinate system with x, y, and z axes. Since we have a quadratic term, the graph will represent a conic section in 3D space. Here's how you can manually plot the graph step by step:
Step 1: Set up the coordinate system.
Draw three perpendicular axes labeled x, y, and z.
Step 2: Identify the intercepts.
To find the x-intercepts, set z = 0 and solve for x:
2x² - 4x - 3y + 2 = 0
2x² - 4x = 3y - 2
x(2x - 4) = 3y - 2
x = (3y - 2)/(2x - 4)
To find the y-intercept, set x = 0 and solve for y:
2(0)² - 3z²+ 6z - 3y + 2 = 0
-3z² + 6z - 3y + 2 = 0
3z² - 6z + 3y - 2 = 0
3(z² - 2z + y) = 2
(z² - 2z + y) = 2/3
Completing the square: z² - 2z + 1 + y = 2/3 + 1
(z - 1)² + y = 5/3
So, the y-intercept is (0, 5/3).
Step 3: Plot the intercepts.
On the x-axis, plot the x-intercepts obtained in step 2.
On the y-z plane, plot the y-intercept obtained in step 2.
Step 4: Determine the shape of the graph.
To determine the shape of the graph, we need to consider the coefficients of the quadratic terms. In this equation, the coefficient of x² is positive (2), while the coefficient of z² is negative (-3). This indicates that the graph is a hyperbolic paraboloid.
Step 5: Sketch the graph.
Based on the information obtained so far, we can sketch the graph of the hyperbolic paraboloid. The graph will open upwards and downwards along the x-axis and have a saddle-like shape along the z-axis. Additionally, the graph will extend infinitely in the y-direction.
Please note that without specific values for x, y, or z, we cannot provide exact coordinates or draw a precise graph. However, you can use the steps and information provided above to manually sketch the graph on a sheet of paper or using appropriate software for 3D graphing.
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Including scholarships and financial aid, Laurie has $24,000 to spend on
college. If the total cost of her college education is
she will have
enough resources to pay.
A. $31,000
B. $22,000
C. $25,000
D. $28,000
SUBMIT
Answer:
B
Step-by-step explanation:
If she has $24,000 to spend she'd only have enough to pay for anything that is $24,000 or less.
What is the y-intercept of the function f(x)=2/9x+1/3
Answer:
1/3
Step-by-step explanation:
The equation given to you is in y=mx+b form.
m is the slope which in this case would be 2/9.
b is the y-intercept which in this case would be 1/3
Answer:
put x=0 in the equation
it will give you y intercept.
so y intercept in this equation is =1/3.
Step-by-step explanation:
sketch the area represented by g(x). g(x) = x t2 dt 1
The area represented by g(x) is a triangular region with base 1 and height (7/3) x, where x is the variable along the horizontal axis. The resulting shape will be a right triangle with vertices at (0,0), (1,0), and (0, (7/3) x).
It seems like you are asking to sketch the area represented by the function g(x) given as the integral of x with respect to t from 1 to 2. However, there seems to be a typo in your question. I will assume that you meant g(x) = ∫[1 to x] t^2 dt. Please follow these steps to sketch the area represented by g(x):
1. Draw the function y = t^2 on the coordinate plane (x-axis: t, y-axis: t^2).
To sketch the area represented by g(x) = x t2 dt 1, we first need to evaluate the definite integral. Integrating x t2 with respect to t gives us (1/3) x t3 + C, where C is the constant of integration. Evaluating this expression from t=1 to t=2 gives us (1/3) x (2^3 - 1^3) = (7/3) x.
2. Choose an arbitrary x-value between 1 and 2 (e.g., x = 1.5).
3. Draw a vertical line from the x-axis to the curve of y = t^2 at x = 1.5. This line represents the upper limit of the integral.
4. Draw another horizontal axis from the x-axis to the curve of y = t^2 at x = 1. This line represents the lower limit of the integral.
5. The area enclosed by the curve y = t^2, the x-axis, and the vertical lines at x = 1 and x = 1.5 represents the area for the given value of x.
In conclusion, the area represented by g(x) = ∫[1 to x] t^2 dt can be sketched by plotting the curve y = t^2, choosing a specific x-value between 1 and 2, and then finding the enclosed area between the curve, x-axis, and the vertical lines at x = 1 and x = chosen x-value.
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If A is invertible, then A∼I (A is row equivalent to the identity matrix). Therefore, A has n pivots, one in each column, which means that the columns of A are linearly independent.
The given statement is correct. If a matrix A is invertible, then it means that it has a unique inverse.
What is the identity matrix?
The identity matrix is a square matrix with 1's on the main diagonal and 0's everywhere else. It is denoted as I. The identity matrix has the property that for any square matrix A, the product of A and I is equal to A itself, so I serve as a sort of "do-nothing" matrix.
Yes, this is correct. If a matrix A is invertible, then it means that it has a unique inverse. This implies that the columns of A are linearly independent, as they form a basis for the space. A row equivalent matrix to the identity matrix (A∼I) will have one pivot in each column, indicating that the columns are linearly independent.
Hence, the given statement is correct. If a matrix A is invertible, then it means that it has a unique inverse.
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(WILL MARK BRAINLIEST PLEASE HELP!) Rule for reflecting 90, 180, 270, and 360 degrees clockwise (reflection not rotating please)
Answer:
Rotation of 90° (x, y) → ( ‐ y, x )
Rotation of 180° (x, y) → ( ‐ x, ‐ y )
Rotation of 270° (x, y) → ( y, ‐ x )
idk 360...
Solve the matrix equation for the unknown matrix X. (If not possible, enter IMPOSSIBLE in any cell of the matrix.) A = [7 3 4 3] B = [7 2 7 2] C = [3 3 4 0 0 8] D = [10 30 30 30 30 0] 5(X - C) = D x = []
After solving the equation 5(X - C) = D , for the given matrices , we get , the unknown matrix X is = \(\left[\begin{array}{ccc}5&9\\10&6\\6&8\end{array}\right]\) .
In the question ,
it is given that , the matrices are
A = \(\left[\begin{array}{ccc}7&3\\4&3\end{array}\right]\) B = \(\left[\begin{array}{ccc}7&2\\7&2\end{array}\right]\) C = \(\left[\begin{array}{ccc}3&3\\4&0\\0&8\end{array}\right]\) and D = \(\left[\begin{array}{ccc}10&30\\30&30\\30&0\end{array}\right]\) .
and the equation is given as 5(X - C) = D ,
and we have to find the value of unknown matrix X .
let the matrix X be = \(\left[\begin{array}{ccc}a&b\\c&d\\e&f\end{array}\right]\)
Substituting , the given matrices A , B , C and D in the equation 5(X - C) = D ,
we get ,
5(X - C) = D ,
5X - 5C = D ,
5\(\left[\begin{array}{ccc}a&b\\c&d\\e&f\end{array}\right]\) - 5\(\left[\begin{array}{ccc}3&3\\4&0\\0&8\end{array}\right]\) = \(\left[\begin{array}{ccc}10&30\\30&30\\30&0\end{array}\right]\)
5\(\left[\begin{array}{ccc}a&b\\c&d\\e&f\end{array}\right]\) = \(\left[\begin{array}{ccc}10&30\\30&30\\30&0\end{array}\right]\) - \(\left[\begin{array}{ccc}15&15\\20&0\\0&40\end{array}\right]\)
Simplifying further ,
we get ,
5\(\left[\begin{array}{ccc}a&b\\c&d\\e&f\end{array}\right]\) = \(\left[\begin{array}{ccc}25&45\\50&30\\30&40\end{array}\right]\)
Dividing both sides by 5 ,
we get ,
X = \(\left[\begin{array}{ccc}a&b\\c&d\\e&f\end{array}\right]\) = \(\left[\begin{array}{ccc}5&9\\10&6\\6&8\end{array}\right]\)
Therefore , the matrix X is = \(\left[\begin{array}{ccc}5&9\\10&6\\6&8\end{array}\right]\) .
The given question is incomplete , the complete question is
Solve the matrix equation for the unknown matrix X.
A = \(\left[\begin{array}{ccc}7&3\\4&3\end{array}\right]\) B = \(\left[\begin{array}{ccc}7&2\\7&2\end{array}\right]\) C = \(\left[\begin{array}{ccc}3&3\\4&0\\0&8\end{array}\right]\) and D = \(\left[\begin{array}{ccc}10&30\\30&30\\30&0\end{array}\right]\) . the equation is
5(X - C) = D .
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A biker rode 3.75 miles in 0.3 hrs
A) how fast is she going?
B) how long will it take her to go 4.5ml?
bike ride is 3.75 miles, or 4.5ml is
3.75/.3 (or 4.5/x.36) (or x 1).
Timing is 0.3 hours.
Speed = Distance / Time Speed = 3.75 x 0.3 = 12.5 mph.
2) Speed is 12.5 mph, and the distance is 4.5 miles.
Time = Distance * Speed.
Time = 4.5 * 12. 5 = 0.36 hours.
It takes 0.36 hours to travel 4.5 miles.
How is the speed per hour determined?
Speed is calculated as follows: speed = distance / time. Knowing the units for distance and time is necessary to calculate the units for speed. The units in this example will be meters per second (m/s), since the distance is measured in meters (m) and the time is measured in seconds (s).
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QUESTION DOWN BELOW!!!!
Answer:
34 zombies
Step-by-step explanation:
85(2/5) = 34 zombies
What is the price of gas at the gas station in dollars per liter?
Answer:
The price of gas at the gas station is $0.55 per liter.
these marbles are placed in a bag and two of them are randomly drawn. yellow=2 pink=3 blue=5 what is the probability of drawing 2 yellow marbles if the first one is not placed back into the bag before the second one. Give your answer as a rational number, reduced to simplest terms.
Answer: 1/45
Step-by-step explanation:
From thw question, we are told that there are:
Yellow marbles =2
Pink marbles =3
Blue marbles = 5
Total marbles = 2+3+5 = 10
The probability of drawing the first yellow ball will be= 2/10
Since the ball is not replaced, that means there will be 9 balls left and 1 yellow ball left. Therefore, the probability of drawing the second yellow ball will be = 1/9
The probability of drawing two yellow balls if they're not replaced will now be:
= 2/10 × 1/9
= 2/90
= 1/45
What value of x will make the triangles similar by the sss similarity theorem? x =
The value of x will make the triangles similar by the sss similarity theorem is 77
Simlarity theorem of trianglesA triangle is a 2-dimensional shape with 3 sides and angles
From the given diagram, we will take the ratio of simlar sides to determine the value of "x"
35/x = 20/44
Cross multiply
20x = 35 * 44
20x = 1540
x = 154/2
x = 77
Hence the value of x will make the triangles similar by the sss similarity theorem is 77
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Answer: The answer is 28
How do I solve this inequality?
you work out the equation from 5 to 3 then compare it to 9
what are the equalities of f(x)=loga(x)
A. f(1)=0
B. f(a)= 1
C. f(0)=0
D. f(1/a)=-1
9514 1404 393
Answer:
A, B, D
Step-by-step explanation:
For appropriate values of 'a', the log function has the following characteristics:
A: f(1) = 0B: f(a) = 1D: f(1/a) = -1Any log function will tend toward negative infinity as x tends to zero (for |a|>1).
you would like to investigate whether smokers are more likely than non smokers to get lung cancer. you take the students in your class, select half at random and tell them to smoke a pack of cigarettes each day, and you tell the other half not to ever smoke. fifty years from now, you will analyze whether more smokers than non smokers get lung cancer. is this an experiment or an observational study? experiment observational study
An investigation whether smokers are more likely than non smokers to get lung cancer by grouping the class students into two groups is an example of experimental study.
Experimental Study: An experimental study is a study where the researcher has control over most of the variables. In contrast an observational study is a study where the researcher purely observes subject without controlling any variables. We have to investigate whether smokers are more likely than non-smokers to get lung cancer. Here the study is experimental study because the researcher/ we are trying to investigate the students of smokers and non-smokers. So, here control the members of the population that is students by randomly selecting them and dividing them in two groups (that is half -half) and provide one group cigarettes and not provide the other one. So, the above example of an experimental study. The following difficulties are come in study :
The results of the study are highly subjective due to possibilities of the human error.Experimental study is time consuming process with respect to its constraints.The participants i.e., experiment objects can be influenced by surroundings around them.Hence, the given problem is an example of experimental study.
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In the statement 10 + 0 = 0 + 10 how would you describe the zero (0)?
Please answer as soon as possible.
Determine whether the quantities in each table represent a proportional relationship. If yes put the constant rate otherwise put no
Answer:
There is not a proportional relationship
Step-by-step explanation:
The first and second hour the pay is $9.50/hour, but in the third hour the pay is $11/hour. Then in the fourth hour it changes again to $10/hourIf there was a proportional relationship there would need to be a constant rate of change in pay.
Answer:
Yes, the proportional relationship is 9.50
Step-by-step explanation:
In the graph that you have attached this picture with, hours x 9.50 = pay.
Hope this helps :D
Prime factorization of 52 using ladder diagram
Answer:
2, 13, 52,, 4
Step-by-step explanation:
What is the solution to the system of equations below?
x + 3 y = 15 and 4 x + 2 y = 30
(7 , 2)
(2, 7)
(4, 3)
(3, 4
Answer:
Step-by-step explanation:
x + 3y = 15 ×4
4x + 2y = 30 ×1
4x + 12y = 60
- - -
4x + 2y = 30
10y = 30
y = 30/10
y = 3
To solve for x, substitute y = 3 into any of the equations
x + 3(3) = 15
x + 9 = 15
x = 15 - 9
x = 6
(6,3)
This should be the answer but I don't see that in the options u listed, so I don't know what else it should be.
The required solution to the system of equations is (x, y) = (6, 3).
Given the system of equations:
x + 3y = 15
4x + 2y = 30
Multiply Equation 1 by 2 to make the coefficients of y in both equations equal:
2(x + 3y) = 2(15)
2x + 6y = 30
Subtract Equation 2 from the modified Equation 1 to eliminate the variable x:
(2x + 6y) - (4x + 2y) = 30 - 30
-2x + 4y = 0
Divide the resulting equation by 2 to simplify it further:
-x + 2y = 0
Now, we have a new equation:
3) -x + 2y = 0
Add the new Equation 3 to the original Equation 1 to eliminate the variable x again:
(x + 3y) + (-x + 2y) = 15 + 0
5y = 15
Solve for y:
y = 15 / 5
y = 3
Now, substitute the value of y back into Equation 1 to find x:
x + 3(3) = 15
x + 9 = 15
x = 15 - 9
x = 6
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Determine the truth value of each of the following complex statements.
Circle your answer or put it in red. (NOTE: LET A, B, C BE TRUE AND X, Y, Z BE FALSE)
3. B. Z 4. Xv-Y
5. CvZ 6. B-Z 7. (A v B)Z 8. (AZ) 9. B v (Y - A) 10. A) -(Z v-Y) 11.( AY) v (-Z.C) 12. -X v-B) (~Y v A) 13. (Y » C)-(B3-X) 14.(C =~A) v (Y = Z) 15.-(AC)(-XB) 16.( AY). (-Z.C) 17.-[( AZ) = (-C •-X)] 18. ~~[( AZ) = (-C •-X)] 19.-(A.-Z) v (Y = Z) 20. A. A
The truth values for the given complex statements are:
3. False
4. False
5. False
6. True
7. False
8. Undefined
9. True
10. True
11. True
12. False
13. True
14. True
15. True
16. False
17. True
18. False
19. True
20. False
To determine the truth value of each complex statement, we'll use the given truth values:
A = True
B = True
C = True
X = False
Y = False
Z = False
Let's evaluate each statement:
3. B • Z
B = True, Z = False
Truth value = True • False = False
4. X V Y
X = False, Y = False
Truth value = False V False = False
5. ~C v Z
C = True, Z = False
Truth value = ~True v False = False v False = False
6. B - Z
B = True, Z = False
Truth value = True - False = True
7. (A v B) Z
A = True, B = True, Z = False
Truth value = (True v True) • False = True • False = False
8. ~(THIS)
"THIS" is not defined, so we cannot determine its truth value.
9. B v (Y • A)
B = True, Y = False, A = True
Truth value = True v (False • True) = True v False = True
10. A • (Z v ~Y)
A = True, Z = False, Y = False
Truth value = True • (False v ~False) = True • (False v True) = True • True = True
11. (A • Y) v (~Z • C)
A = True, Y = False, Z = False, C = True
Truth value = (True • False) v (~False • True) = False v True = True
12. (X v ~B) • (~Y v A)
X = False, B = True, Y = False, A = True
Truth value = (False v ~True) • (~False v True) = False • True = False
13. (Y • C) ~ (B • ~X)
Y = False, C = True, B = True, X = False
Truth value = (False • True) ~ (True • ~False) = False ~ True = True
14. (C • A) v (Y = Z)
C = True, A = True, Y = False, Z = False
Truth value = (True • True) v (False = False) = True v True = True
15. (A • C) (~X • B)
A = True, C = True, X = False, B = True
Truth value = (True • True) (~False • True) = True • True = True
16. (A • Y) (~Z • C)
A = True, Y = False, Z = False, C = True
Truth value = (True • False) (~False • True) = False • True = False
17. ~[(A • Z) (~C • ~X)]
A = True, Z = False, C = True, X = False
Truth value = ~(True • False) (~True • ~False) = ~False • True = True
18. [(A • Z) (~C • ~X)]
A = True, Z = False, C = True, X = False
Truth value = (True • False) (~True • ~False) = False • True = False
19. (A • Z) v (Y = Z)
A = True, Z = False, Y = False
Truth value = (True • False) v (False = False) = False v True = True
20. A • ~A
A = True
Truth value = True • ~True = True • False = False
Therefore, the truth values for the given complex statements are:
3. False
4. False
5. False
6. True
7. False
8. Undefined
9. True
10. True
11. True
12. False
13. True
14. True
15. True
16. False
17. True
18. False
19. True
20. False
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A statistics student is studying if there is a relationship between the price of a used car and the number of miles it has been driven. She collects data for 20 cars of the same model with different mileage, and determines each car’s price using a used car website. The analysis is given in the computer output. Predictor Coef SE Coef t-ratio p Constant 24157.2 2164.1 2.965 0.046 Mileage -0.181 0.024 5.377 0.000 S = 3860.7 R-Sq = 68.0% R-Sq(Adj) = 67.5% Using the computer output, what is the equation of the least-squares regression line?
Answer:
y = - 0.181x + 24157.2
Step-by-step explanation:
Equation of the regression line is given from. The table by the Coefficient of the predictor, x variable and the intercept value :
The predictor here is mileage, which has a Coefficient of - 0.181
The constant value = intercept 24157.2
The regression equation is written in the form :
y = mx + c ; m = slope = Coefficient of predictor, ; x = predictor,
Hence, we have :
y = - 0.181x + 24157.2
Answer:
A.
Step-by-step explanation:
on edge2022
Determine whether y varies directly with x . If so, find the constant of variation.
x=y/3
The constant of variation, often denoted as "k," is a value that represents the relationship between two variables in a direct or inverse variation. It indicates how one variable changes in proportion to changes in the other variable.
In a direct variation, the constant of variation represents the ratio of the two variables, while in an inverse variation, it represents the product of the two variables.
To determine if y varies directly with x, we need to check if the equation can be written in the form y = kx, where k is the constant of variation.
Given the equation x = y/3, we can rearrange it to y = 3x.
Comparing this with the form y = kx, we can see that y does vary directly with x, with a constant of variation of k = 3.
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There are (24)2 ⋅ 20 books in a cupboard. What is the total number of books in the cupboard?
Answer:
960
Step-by-step explanation:
There are (24)2 ⋅ 20 books in a cupboard. Therefore, the total number of books in the cupboard is 960.
24 ⋅ 2 = 48
48 ⋅ 20 = 960
960 is the answer. Hope this helped!
How to find the missing number in integer array of 1 to 100 in Java?
Finding the missing number from the first 100 numbers in the given array arr[] of size N-1 with integers in the range [1, N] is the task. The list doesn't contain any duplicates.
Java method for locating a missing integer in an array of integers from 1 to 100
Make a temp array temp[] of size n + 1 with a value of 0 for each element.For each element in the input array arr[i], perform the following.If (temp[arr[i]] == 0), then temp[arr[i]] is 1.traverse temp[] and output an element of an array with the value of 0. (This is the missing element).class GFG; import java.io.*; import java.util.*
public static void findMissing(int arr[], int N)
{
int i;
int temp[] = new int[N + 1];
for (i = 0; i <= N; i++) {
temp[i] = 0;
}for (i = 0; i < N; i++) {
temp[arr[i] - 1] = 1;
} int ans = 0;
for (i = 0; i <= N; i++) {
if (temp[i] == 0)
ans = i + 1;
} System.out.println(ans);
}
public static void main(String[] args) {
int arr[] = { 1, 3, 7, 5, 6, 2 };
int n = arr.length; // Function call
findMissing(arr, n);
}
}
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Which function has a domain of x greater-than-or-equal-to 5and a range of y less-than-or-equal-to 3?
y = StartRoot x minus 5 EndRoot + 3
y = StartRoot x + 5 EndRoot minus 3
y = negative StartRoot x minus 5 EndRoot + 3
y = negative StartRoot x + 5 EndRoot minus 3
Answer:
The function that has a domain of 'x' greater-than-or-equal-to 5 and a range of 'y' less-than-or-equal-to 3 is;
\(y = -\sqrt{x - 5} +3\).
Step-by-step explanation:
The domain of a function are the possible 'x' values of the function
The range of a function are the possible 'y' values of the function
The given possible functions are;
1) \(y = \sqrt{x - 5} +3\)
The range of values for the above function are;
Domain; x ≥ 5
Range; y ≥ 3
2) \(y = \sqrt{x + 5} -3\)
The range of values for the above function are;
Domain; x ≥ -5
Range; y ≥ -3
3) \(y = -\sqrt{x - 5} +3\)
The range of values for the above function are;
Domain; x ≥ 5
Range; y ≤ 3
4) \(y = -\sqrt{x + 5} -3\)
The range of values for the above function are;
Domain; x ≥ -5
Range; y ≤ -3
Therefore, the required function is the third function, \(y = -\sqrt{x - 5} +3\).
Answer:
C on Edge2021
Step-by-step explanation:
CAN SOME ACTUALLY HELP ME PLEASE!!!!!!!!!!!!!!!!!!
Answer:
(1, No, No) (2, No, Yes) (3, 6x^2+10) (4, 2x^2-3) (5, x^2-x) (6, -2x^4+12x+3)
(7, 3x^3+15x^2+20) (8, 9x^3 + 4x^2+8x) (9, xy+2x+6y+5) Sorry didn't have an answer for 10. I hope they are all correct sorry for the wait.
Step-by-step explanation:
five program systems are prepared so that they work independently of each other. each system has a 0.3 chance of detecting an error. find the probability that at least one program system will detect an error. use 4 decimal places.
The probability that at least one program system will detect an error is 0.8319 (approx) or 0.832 (approx).
How to find the probabilityGiven information:
five program systems are prepared so that they work independently of each other. Each system has a 0.3 chance of detecting an error.
Find the probability that at least one program system will detect an error. Use 4 decimal places.The probability of a system detecting an error is 0.3.
The probability of a system not detecting an error is 1 - 0.3 = 0.7.
Probability that none of the five systems detects an error is, P(error not detected in any of the five systems) = P(not detected in 1st) x P(not detected in 2nd) x ... x P(not detected in 5th) = 0.7 x 0.7 x 0.7 x 0.7 x 0.7 = 0.16807.
The probability that at least one system detects an error is, P(at least one system detects an error) = 1 - P(error not detected in any of the five systems) = 1 - 0.16807 = 0.8319 (approx).
Therefore, the probability that at least one program system will detect an error is 0.8319 (approx) or 0.832 (approx).
Hence, the correct option is 0.832.
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Which of the following is equivalent to (3a + 5b) + 7c?
3a + (5b + 7c)
3a(5b + 7c)
7c(5b + 3a)
8ab + 7c
Answer:
3a + (5b + 7c)
Step-by-step explanation:
The answer cannot be 3a(5b +7c) because when the number is immediately before the brackets, it signifies multiplication. therefore the 3a(5b+7c) would be equivalent to 15ab+21ac
the answer cant be 7c(5b+3a) because of the same explanation as the one above, therefore 7c(5b+3a) would be equivalent to 35cb+21ca
the answer finally cant be 8ab+7c because it means that one added 3a and 5b giving you 8 but it cannot be ab because ab is equivalent to a×b, hence, one cant put a multiplied algebraic expression with an added number
The equation equivalent to the the expression (3a + 5b) + 7c is 3a + (5b+7c). Hence, the first option is the correct one.
What is an expression?In mathematics, expressions are assertions that must contain at least two words with variables or terms with numbers in them, or both, and connect them with an operator. It is possible for the mathematical operators to be addition, subtraction, multiplication, or division.
For instance, the equation x + y has the terms x and y with an addition operator in between. Numerical expressions, which just contain numbers, and algebraic expressions, which also include variables, are the two types of expressions used in mathematics.
The first option is correct because it does not affect the main equation rest are not the same as the equation.
For example, let's take the second equation :
3a (5b + 7C)
After solving this option we get 15ab + 21 ac so it is incorrect because it changed the main expression.
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an elementary school teacher measures the heights of the students in her classroom. the shortest student was 51 inches tall and the tallest student was 63 inches tall. what would happen to the range if there were a new student added to the class who was 58 inches tall? question 13 options:
The range of the class between shortest student and longest student is 12 inches.
Range is the difference between highest and lowest possible values.
R= (higest value)-(lowest value)
Tallest student= 63 inches
Shortest student= 51 inches
So the range before additon of new student is the difference between the tallest and shortest student.
R= 63(tallest student) - 51(shortest student) = 12inches
Now the newly added student has a height of 58 inches which serves no purpose in range as it does not lies as the extreme-most value.
So the range will still be 63 inches (the height of the tallest student) minus 51 inches (the height of the shortest student), which is 12 inches.
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