Question 3 (10 marks) Find an equation for the plane tangent to the surface z = x²y + xy^2 + In x+R at (1,0,R). Z=
The equation of the plane tangent to the surface z = x²y + xy² + ln x + R at (1, 0, R) is z = x + y + (R - 1).
To find the equation of the plane tangent to the surface z = x²y + xy^2 + ln x + R at the point (1, 0, R), we'll need to find the partial derivatives with respect to x and y, and then use the point-slope form of the tangent plane equation. Here are the steps:
1. Find the partial derivatives of the surface function with respect to x and y:
∂z/∂x = 2xy + y² + (1/x)
∂z/∂y = x² + 2xy
2. Evaluate the partial derivatives at the given point (1, 0, R):
∂z/∂x(1, 0) = 2(1)(0) + (0)² + (1/1) = 1
∂z/∂y(1, 0) = (1)² + 2(1)(0) = 1
3. Use the point-slope form of the tangent plane equation:
z - z₀ = a(x - x₀) + b(y - y₀)
4. Substitute the point (x₀, y₀, z₀) = (1, 0, R) and the partial derivative values a = ∂z/∂x = 1, b = ∂z/∂y = 1:
z - R = 1(x - 1) + 1(y - 0)
5. Simplify the equation:
z - R = x - 1 + y
6. Rearrange the equation to the standard form:
z = x + y + (R - 1)
The equation of the plane tangent to the surface z = x²y + xy² + ln x + R at (1, 0, R) is z = x + y + (R - 1).
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The figure below shows a circle with center
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X, diameter
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IL
, secants
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and
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, and tangent
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. Which of the angles must be right angles? Select all that apply.
Based on the inscribed angle theorem and the tangent theorem, the angles that must be right angles are: ∠XLS, ∠LEG, ∠LTG, and ∠XLQ.
Since, The theorem states that an inscribed angle of a semicircle equals 90°.
And, According to the tangent theorem, a tangent is at right angle at the point of tangency with the radius.
Hence, Based on these theorems, the angles that must be right angles are:
∠XLS, ∠LEG, ∠LTG, and ∠XLQ.
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Below is a list of the criteria that would prove the quadrilateral is a square
a) Opposite sides are parallel
b) 4 congruent sides
c) 4 right angles
Prove each of the criteria listed. Show all work.
The criteria prove that the quadrilateral is not a square
Selecting the criteria that would prove the quadrilateral is a squareFrom the question, we have the following parameters that can be used in our computation:
a) Opposite sides are parallelb) 4 congruent sidesc) 4 right anglesFor parallel opposite sides, we have
A = (-12, 5), B = (-7, 12), C = (5, 7) and D = (0, 0)
Calculate the slopes of opposite sides
So, we have
AD = (0 - 5)/(0 + 12) = -5/12
BC = (12 - 7)/(-7 - 5) = -5/12
AC = (7 - 5)/(5 + 12) = 2/17
BD = (12 - 0)/(-7 - 0) = -12/7
The sides AC and BD are not parallel
For the congruent sides, we have
AD = √[(0 - 5)² + (0 + 12)²] = 13
BC = √[(12 - 7)² + (-7 - 5)²] = 13
AC = √[(7 - 5)² + (5 + 12)²] = 17.11
BD = √[(12 - 0)² + (-7 + 0)²] = 13.89
The four sides are not parallel
For the right angles
The slopes calculated do not show that opposite sides have opposite reciprocals as their slopes
So, the four sides are not right angled
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Consider the following set of equations:
Equation R: −3y = −3x − 9
Equation S: y = x + 3
Which of the following best describes the solution to the given set of equations?
a
No solution
b
One solution
c
Infinite solutions
d
Two solutions
The solution to the given set of equations is Infinite solutions.
We have the equation
R: -3y = -3x -9
S: y = x + 3
Now, solving the equation R and S as
-3y = -3x - 9
3y = 3x + 9
_________
0 = 0 + 0
0 = 0
Also, -3/1 = 3/(-1) = 9/(-3)
-3/1 = -3/1 = -3/1
Thus, the equation have Infinite many solutions.
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3 Given an initial guess Do the next approximation to the solution of 2-83-80 I=2-02 using Newton's method is SC1=30-7-260-1) Answer Ο Α True О В False
The multiple choice question is "Ο Α True", which means "Option A is true".
Recall that Newton's method involves the iterative formula:
x_(n+1) = x_n - f(x_n)/f'(x_n)
where f(x) is the function we want to solve for, and f'(x) is its derivative.
In this case, we have f(x) = 2x^3 - 83x^2 - 80x - 2.02 and f'(x) = 6x^2 - 166x - 80. So, using the initial guess of x_0 = 3, we have:
x_1 = x_0 - f(x_0)/f'(x_0)
= 3 - (2(3)^3 - 83(3)^2 - 80(3) - 2.02)/(6(3)^2 - 166(3) - 80)
= 2.838
Therefore, the next approximation to the solution using Newton's method with an initial guess of x_0 = 3 is x_1 = 2.838.
The answer to the multiple choice question is "Ο Α True", which means "Option A is true".
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A website plans to purchase advertisements in a local newspaper. Their budget is $600, and they plan to run no more than 10 advertisements. An ad in the weekend edition is $75, and an ad in the weekday paper is $50.
Let x be equal to the number of weekend ads, and y be equal to the number of weekday ads. Excluding the boundary lines shown on the graph, place a point inside the region of the graph that satisfies the system.
Excluding the boundary lines shown on the graph, (4 , 6) is the required ordered pair inside the region of the graph satisfies the given system of linear equation.
The budget of a website to advertise in local newspaper is $600 , and they plan to run no more than 10 advertisements. An ad in the weekend edition is $75, and an ad in the weekday paper is $50.
Let x be equal to the number of weekend ads, and y be equal to the number of weekday ads.
We can compute the point inside the region of the graph that satisfies the system of linear equations that can be formed as,
75x + 50y = 600 ___(1)
x + y = 10 ___(2)
Solving the system of linear equations in (1) and (2) as,
From equation (2), x= 10- y
Substituting x in equation (1) with x= 10- y, we get,
75( 10- y )+ 50y = 600
⇒ 750 - 75y + 50y = 600
⇒ 25y = 150
⇒ y = 6
Thus, x = 10 - 6 = 4
Hence (x, y) = (4 , 6) inside the region of the graph satisfies the given system of equation.
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3/10 en notación decimal
Answer: 0.3
Step-by-step explanation:
3/10 = 30/100 = 0.3
Answer:
0.3
Step-by-step explanation:
Let class A is a prerequisite for classes B and C; class D is a prerequisite for classes B and E; class C is a prerequisite for classes E and F. Assign 2-digit numbers to these classes such that these numbers considered as 2-dimensional vectors will be in a partial order relation determined by the component- wise s between these vectors.
To assign 2-digit numbers to these classes such that these numbers considered as 2-dimensional vectors will be in a partial order relation determined by the component-wise s between these vectors, we can follow the given steps.
1. Identify the classes and their prerequisites:
- Class A is a prerequisite for classes B and C
- Class D is a prerequisite for classes B and E
- Class C is a prerequisite for classes E and F
2. Draw a directed graph representing the prerequisites:
```
A -> B -> E -> F
\-> C -> E
D -----^
```
3. Assign numbers to the classes in such a way that the numbers assigned to prerequisite classes are smaller than those assigned to dependent classes. We can use the following numbering scheme:
- Class A: 10
- Class B: 20
- Class C: 30
- Class D: 40
- Class E: 50
- Class F: 60
4. Represent these numbers as 2-dimensional vectors with the first digit representing the horizontal component and the second digit representing the vertical component:
- Class A: (1,0)
- Class B: (2,0)
- Class C: (3,0)
- Class D: (4,0)
- Class E: (5,0)
- Class F: (6,0)
5. Check if these vectors are in a partial order relation determined by the component-wise ≤ between these vectors:
- (1,0) ≤ (2,0) since 1 ≤ 2
- (1,0) ≤ (3,0) since 1 ≤ 3
- (4,0) ≤ (2,0) since 4 ≤ 2
- (4,0) ≤ (5,0) since 4 ≤ 5
- (3,0) ≤ (5,0) since 3 ≤ 5
- (5,0) ≤ (6,0) since 5 ≤ 6
Therefore, the assignment of numbers to these classes and their representation as 2-dimensional vectors satisfy the partial order relation determined by the component-wise ≤ between these vectors.
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Random samples of 6 male students and 14 female students were asked how many hours a week they exercise with the following results: Males: Sample mean is 5.24 and sample standard deviation is 3.01. Females: Sample mean is 4.22 and sample standard deviation is 2.33. (a) Find a 95% confidence interval for true mean hours of exercise per week in each group. Males. ( ), ( ) Females.( ), ( )
A 95% confidence interval for the true mean hours of exercise per week is (2.08, 8.40) for males and (2.95, 5.49) for females
To find a 95% confidence interval for the true mean hours of exercise per week for each group, we will use the following formula:
[tex]Confidence interval = Sample mean± (t \frac{Sample standard deviation}{\sqrt{n} } )[/tex]
where t is the t-score based on the degrees of freedom and the desired confidence level (95%).
(a) Males:
1. Determine the t-score: For a 95% confidence interval and 6 - 1 = 5 degrees of freedom, the t-score is approximately 2.571.
2. Calculate the margin of error: [tex]2.571 (\frac{3.01}{\sqrt{6} }) = 3.16[/tex]
3. Find the confidence interval: 5.24 ± 3.16 = (2.08, 8.40)
Males: (2.08, 8.40)
(b) Females:
1. Determine the t-score: For a 95% confidence interval and 14 - 1 = 13 degrees of freedom, the t-score is approximately 2.160.
2. Calculate the margin of error: [tex]2.160 (\frac{2.33}{\sqrt{14} }) = 1.27[/tex]
3. Find the confidence interval: 4.22 ± 1.27 = (2.95, 5.49)
Females: (2.95, 5.49)
In conclusion, a 95% confidence interval for the true mean hours of exercise per week is (2.08, 8.40) for males and (2.95, 5.49) for females.
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The diameter of a circle is 21 cm. Find its area to the nearest whole number.
Solve the differential equation using either Taylor or Frobenius
Series Solution."
(iii) (1-x2)y''-2xy'+2y=0
y(x) = a_0 (1 - x^2/3 + 2x^4/45 - 8x^6/315 + ...)
that the solution is only valid for |x| < 1, since the differential equation is singular at x = ±1.
We can solve the given differential equation using the Frobenius method, by assuming that the solution can be represented as a power series:
y(x) = ∑(n=0)^(∞) a_n x^n
Differentiating the series twice, we get:
y'(x) = ∑(n=1)^(∞) n a_n x^(n-1)
y''(x) = ∑(n=2)^(∞) n(n-1) a_n x^(n-2)
Substituting these into the differential equation, we get:
(1-x^2) ∑(n=2)^(∞) n(n-1) a_n x^(n-2) - 2x ∑(n=1)^(∞) n a_n x^(n-1) + 2 ∑(n=0)^(∞) a_n x^n = 0
Simplifying and shifting the indices, we get:
∑(n=0)^(∞) [(n+2)(n+1) a_{n+2} - 2n a_n + 2a_n] x^n = 0
This gives us the following recurrence relation for the coefficients:
(n+2)(n+1) a_{n+2} = 2n a_n - 2a_n
Simplifying further, we get:
a_{n+2} = - (2n/(n+2)(n+1)) a_n
Starting with n = 0, we can compute the coefficients a_n in terms of a_0:
a_2 = - 2/3 a_0
a_4 = 2/15 a_2 = - 4/45 a_0
a_6 = - 2/21 a_4 = 8/315 a_0
a_8 = 2/99 a_6 = - 16/3465 a_0
...
The general form of the solution is then:
y(x) = a_0 (1 - x^2/3 + 2x^4/45 - 8x^6/315 + ...)
that the solution is only valid for |x| < 1, since the differential equation is singular at x = ±1.
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The brick border is 40 cm wide. What is the area of the brick border?
The area of the brick border is: 7.678 m²
What is the area of the composite figure?Using Pythagoras theorem, we can find the diameter of the circle as:
d = √(10² - 6²)
d = √64
d = 8 m
Since the width of the brick border is 40 cm, then converting to meters gives 0.4 m.
Area of semi circle with brick border = ¹/₂(π * (8.8/2)²) = 30.411 m²
Area of semi circle without brick border = ¹/₂(π * (8/2)²) = 25.133 m²
Area of circular part of border = 30.411 m² - 25.133 m²
= 5.278 m²
Area of rectangular part of border = 6 * 0.4 = 2.4 m²
Total area of border = 5.278 m² + 2.4 m²
= 7.678 m²
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The Cp statistic is more useful than the Cpk statistic since it can better account for non-centered distributions.TrueFalse
False.
The Cp and Cpk statistics are both used to assess the capability of a process to meet specifications, but they have different purposes.
The Cp statistic is a measure of how well the process spread (variation) fits within the specification limits. It assumes that the process mean is centered on the target value. It is calculated as the ratio of the specification width to the process spread (six times the process standard deviation).
The Cpk statistic, on the other hand, takes into account both the process spread and the deviation of the process mean from the target value. It is calculated as the minimum of two values: the difference between the process mean and the closest specification limit divided by three times the process standard deviation (assuming the process is centered within the specification limits), or the Cp value adjusted for the deviation of the process mean from the target value.
Both statistics have their uses and limitations depending on the situation. If the process mean is not centered on the target value, the Cpk statistic may be more useful than the Cp statistic since it takes into account both the spread and centering of the process.
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-4² +20 ÷ 5 what is the answer? Explain please!!!!!!
Answer: -12
Step-by-step explanation:
a wire whose length is given as x inches is bent into a square. express the length of a side of the square in terms of x.
Therefore, the length of a side of the square is x/4 inches by the equation.
In this context, we have a wire that we need to bend into a square. A square has four equal sides, so if we let s be the length of one side of the square, then the total length of the wire must be 4s.
The equation 4s = x represents this relationship, where x is the total length of the wire.
To solve for s, we can isolate s on one side of the equation by dividing both sides by 4. This gives us:
4s / 4 = x / 4
Simplifying, we get:
s = x / 4
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The graph shows the location of point P and point R. Point R is on the y-axis and has the same y-coordinate as point P. Point Q is graphed at ( n , ¯ 2 ) . The distance from point P to point Q is equal to the distance from point P to point R. What is the distance from point P to point Q? What is the value of n? Explain how you determined the distance from point P to point Q, and the value of n. Enter your answers and your explanations in the space provided.The graph shows the location of point P and point R. Point R is on the y-axis and has the same y-coordinate as point P. Point Q is graphed at ( n , ¯ 2 ) . The distance from point P to point Q is equal to the distance from point P to point R. What is the distance from point P to point Q? What is the value of n? Explain how you determined the distance from point P to point Q, and the value of n. Enter your answers and your explanations in the space provided.
The value of n is 5.
Given that, the Coordinate of P = (n,3)
R is on y-axis & the y-coordinate of P & R are equal.
So coordinate of R = (3,0)
Coordinate of Q = (n,-2)
Using distance formula,
Distance between P & Q =
[tex]=\sqrt{(n-n)^2+(-3-(-2)^2} \\\\=\sqrt{(3+2)^2} \\\\= \sqrt{25} = 5[/tex]
Distance between P & R =
[tex]\sqrt{(n-0)^2+(3-3)^2}[/tex]
= n
According to the question it is given that distance between P & Q is equal to the distance between P & R. So, n = 5.
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26. If BD = 8x - 27 and EC-2x + 33, find BD
The length of BD is 53 units.
We are given here that BD is (8x - 27) units and EC is (2x + 33) units. BD and EC are the diagonals of a trapezoid. As we know that diagonals of a trapezoid are equal. Therefore, we will equate the given diagonals of a trapezoid.
BD = EC
Substituting the given values of BD and EC
8x - 27 = 2x + 33
combining the like terms
8x - 2x = 33 + 27
6x = 60
x = 60/6
x = 10
Now, as we have to find BD, we will substitute the value of x in the given equation for BD.
BD = 8x - 27
BD = 8(10) - 27
BD = 80 - 27
BD = 53
Therefore, BD is 53 units.
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The complete question is " If BD = 8x - 27 and EC-2x + 33, find BD with respect to the image shown."
Problem 1. Let (X,d) be a metric space. For any x ∈ X, show that x ∈ iso(X) (that is, x is an isolated point of X) if and only if {x} is open
in (X, d). (In (Y,d), a metric space, y is an isolated point of S if there exists an open ball around y which contains no other points of S.)
To show that x ∈ iso(X) if and only if {x} is open in (X, d)
We need to prove both directions: (1) if x ∈ iso(X), then {x} is open in (X, d) and (2) if {x} is open in (X, d), then x ∈ iso(X).
(1) If x ∈ iso(X), then x is an isolated point of X. By definition, this means there exists an open ball B(x, r) centered at x with radius r > 0 such that B(x, r) ∩ X = {x}. Now, consider the set {x}. To show that {x} is open in (X, d), we need to show that for each point x in {x}, there exists an open ball centered at x that is entirely contained in {x}. Since B(x, r) ∩ X = {x}, it follows that B(x, r) ⊆ {x}. Thus, {x} is open in (X, d).
(2) If {x} is open in (X, d), then for each point x in {x}, there exists an open ball B(x, r) centered at x with radius r > 0 such that B(x, r) ⊆ {x}. In other words, B(x, r) ∩ X = {x}. This means that no other points of X are in B(x, r), which is the definition of an isolated point. Therefore, x ∈ iso(X).
In conclusion, x ∈ iso(X) if and only if {x} is open in (X, d).
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i need help quickly please
The simplified expression is (8x² - 7x - 4) / [(4x + 1)(x - 1)(4x - 1)].
We have,
To simplify the expression
2(x - 1) / (4x² - 3x - 1) + (x + 2) / (4x² + 7x - 2)
we need to find the least common denominator (LCD) of the two denominators:
(4x² - 3x - 1) and (4x² + 7x - 2).
To find the LCD, we need to factor in both denominators.
We can factor the first denominator as:
4x² - 3x - 1 = (4x + 1)(x - 1)
We can factor the second denominator by using the quadratic formula or by factoring by grouping:
4x² + 7x - 2 = (4x - 1)(x + 2)
Therefore, the LCD is the product of the factors of both denominators, with each factor appearing once at most:
LCD = (4x + 1)(x - 1)(4x - 1)(x + 2)
To get each fraction to have the same denominator, we need to multiply the numerator and denominator of the first fraction by (4x - 1) and the numerator and denominator of the second fraction by (x - 1):
2(x - 1)(4x - 1) / [(4x + 1)(x - 1)(4x - 1)] + (x + 2)(x - 1) / [(4x + 1)(x - 1)(4x - 1)]
Now that both fractions have the same denominator, we can add the numerators and simplify:
[2(x - 1)(4x - 1) + (x + 2)(x - 1)] / [(4x + 1)(x - 1)(4x - 1)]
Multiplying out the numerator and simplifying, we get:
[8x^2 - 7x - 4] / [(4x + 1)(x - 1)(4x - 1)]
Therefore,
The simplified expression is (8x² - 7x - 4) / [(4x + 1)(x - 1)(4x - 1)]
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Which of the following is false (a) A chi-square distribution with k degrees of freedom is more right-skewed than a chi-square distribution with k + 1 degrees of freedom. (b) A chi-square distribution never takes negative vales (e) The degrees of freedom for a chisquare test are deter- (d) P(X'>10) İs greater when clf k + 1 than whet te) The area under a chi-square density curve is alk mined by the sample size df alwrv equal to
The false statement is (a) A chi-square distribution with k degrees of freedom is more right-skewed than a chi-square distribution with k + 1 degrees of freedom.
In fact, as the degrees of freedom increase, the chi-square distribution becomes more symmetric and approaches a normal distribution.
The other statements are true: (b) A chi-square distribution never takes negative values, (c) The degrees of freedom for a chi-square test are determined by the number of categories being compared minus one, (d) P(X'>10) is greater when the degrees of freedom are k + 1 than when they are k, and (e) The area under a chi-square density curve is always equal to 1 and is determined by the sample size and degrees of freedom.
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For each of the following research scenarios, decide whether the design uses a related sample. If the design uses a a sample, identify whether it uses matched subjects or repeated measures. Suzanne Thomas was interested in how alcoholics with social phobia compared to alcoholics without social phobia. She matched alcoholics without social phobia to those with social phobia on several variables, including age and gender. She then queried participants in each group about the seventy of their alcohol dependence. The design described Lorrin Koran has studied whether antidepressants are effective for treating kleptomania. Suppose that people with kleptomania typically score 72 on the Barratt Impulsiveness Scale. You want to see whether kleptomaniacs who are taking antidepressants score lower on the impulsiveness scale than the population average. The design described.........
The design described in the first scenario uses a related sample with matched subjects.
In the first scenario, Suzanne Thomas is interested in comparing alcoholics with social phobia to alcoholics without social phobia. She matches participants from both groups on several variables, such as age and gender, in order to create comparable groups. This indicates the use of matched subjects design, where participants in one group are matched with participants in another group based on certain criteria to create comparable groups for comparison. Suzanne Thomas then collects data on the severity of alcohol dependence from each group. Therefore, the design described in the first scenario uses a related sample with matched subjects.
In the second scenario, the design described does not involve the use of a related sample. It is mentioned that the researcher wants to compare kleptomaniacs who are taking antidepressants to the population average, without matching or pairing participants.
Therefore, the design in the second scenario does not involve the use of a related sample.
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A cube of side 5 is built with black and white cubes of side 1, so that the cubes next to each other have different colors and the corner cubes are black, as shown in the figure. How many white cubes were used?
Answer: 62
Step-by-step explanation:
top row has 12
the next row has 1 more =13
and it alternates
12+13+12+13+12=62
Help please and thank you!
Answer:
height = 9 in
Step-by-step explanation:
The formula for volume (V) of a rectangular prism is V = lwh, where l is the length, w is the width, and h is the height
In the question, we're given the volume and in the diagram, we're given the length (8.5 in.) and the width (2 in.). We can solve for l by plugging in our volume, length, and width into the formula and solving for x (the length):
[tex]153=(8.5)(2)x\\153=17x\\9=x[/tex]
When would you use a pictograph?
more than one answer
A. if the data is numerical
B. to compare change over time
C. to save space for a large set of data
D. if the data is categorical
Answer:
The answer to your problem is, D. If the data is categorical
Step-by-step explanation:
What a pictograph is:
Remember that a pictographs are less useful for comparing change over time or for presenting large sets of numerical data, as they can become cluttered and difficult to read.
Here is a little example, if you want to show how the population of a city has changed over the years, a line graph or a bar graph would be a better choice than a pictograph
Thus the answer to your problem is, D. If the data is categorical
Which statement best describes the expression fraction 1 over 2 x (14 − 6) x 6 + 4? (2 points)
Find half the product of 6 and 4, then subtract the difference between 14 and 6.
Find half the difference of 14 and 6, multiply by 6, then add 4.
Find the product of 14 and 6, add the product of 6 and 4, then divide by 2.
Find the product of 6 and 4, subtract the difference between 14 and 6, then multiply by fraction 1 over 2
The correct statement is "Find half the difference of 14 and 6, multiply by 6, then add 4".
What is the solution of the expression?The solution of the fraction expression is calculated as follows;
1/[2 x (14 - 6) x 6 + 4]
To solve the above expression, we will apply the rule of BODMAS as shown below;
The difference of 14 and 6 = 14 - 6 = 8
The next is to divide 8 by 2
= 8/2
= 4
The next step is to multily the result by 6
= 4 x 6
= 24
The final step is to add 4 to it;
= 24 + 4
= 28
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Use the 240 values sorted in the frequency table to find the test statistic x².
A.236.000
B.6.500
C.0.698
D.541.625
Answer: B. 6.500
Step-by-step explanation: I just took the quiz.
a car's wheels are 24 in. in diameter. how far (in mi) will the car travel if its wheels revolve 10,000 times without slipping? (round your answer to two decimal places). incorrect: your answer is incorrect. mi
The car will travel approximately 11.829 if its wheels revolve 10,000 times without slipping.
First, we need to find the circumference of the wheel, which is given by the formula:
circumference = pi x diameter
where pi is approximately equal to 3.14.
So, the circumference of the wheel = 3.14 x 24 = 75.36 inches.
Next, we need to find the distance traveled by the car in one revolution of the wheel, which is equal to the circumference of the wheel.
Distance traveled by the car in one revolution of the wheel = 75.36 inches = 0.0011829 miles (1 inch = 0.000015783 miles).
Therefore, the distance traveled by the car in 10,000 revolutions of the wheel = 0.0011829 x 10,000 = 11.829 miles.
Rounding this answer to two decimal places, we get the final answer as approximately 11.829.
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suppose that the distribution for total amounts spent by students vacationing for a week in florida is normally distributed with a mean of 650 and a standard deviation of 120 . suppose you take a simple random sample (srs) of 20 students from this distribution. what is the probability that a srs of 20 students will spend an average of between 600 and 700 dollars? round to five decimal places.
The probability that a srs of 20 students will spend an average of between 600 and 700 dollars is 0.92081.
We need to find the probability that a simple random sample of 20 students will spend an average of between 600 and 700 dollars.
To solve this problem, we will use the central limit theorem, which states that the sampling distribution of the sample means will be approximately normally distributed with a mean of μ and a standard deviation of σ/√(n), where n is the sample size.
Thus, the mean of the sampling distribution is μ = 650 and the standard deviation is σ/sqrt(n) = 120/√(20) = 26.83.
We need to find the probability that the sample mean falls between 600 and 700 dollars. Let x be the sample mean. Then:
Z1 = (600 - μ) / (σ / √(n)) = (600 - 650) / (120 / √t(20)) = -1.77
Z2 = (700 - μ) / (σ / √(n)) = (700 - 650) / (120 / √(20)) = 1.77
Using a standard normal distribution table or calculator, we can find the area under the standard normal distribution curve between these two Z-scores as:
P(-1.77 < Z < 1.77) = 0.9208
Therefore, the probability that a simple random sample of 20 students will spend an average of between 600 and 700 dollars is 0.9208, or approximately 0.92081 when rounded to five decimal places.
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A soccer dome shaped like a hemisphere has a volume of 450,000 m^3. What is the area of its field? Use 3. 14 for pi
As per the given values, the area of the hemisphere is 45065.41 m³
Volume = 450000 m³
Calculating the volume of the hemisphere -
Volume = 2/3 πr³
Substituting the values -
450,000 =2/3 x 3.14 x r³
Solving for r³
r³ = 450000 x 3/(2 x 3.14)
r³ = 214968.1
r = √214968.1
r = 59.9
Calculating the area of the hemisphere -
Area = 4πr²
Substituting the values -
Area = 4 x 3.14 x (59.9)²
= 12.56 x (59.9)²
= 45065.41
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yesterday, eric had m baseball cards. today, he got 10 more. using m , write an expression for the total number of baseball cards he has now. as an equation
Answer:
m+10
Step-by-step explanation:
We know that yesterday, eric had m baseball cards. Thus, we can denote that the total number of baseball cards he had yesterday is m.
We know that he got 10 more today. Since he is receiving more, he is adding to his collection. Since he is getting more, we have to add 10 to how many baseball cards he used to have. He used to have m baseball cards, so today he has m+10 baseball cards.
This is the answer as we cannot combine 10 and m. Since m is a variable with no set value as of now, and 10 is a constant number that has no variable, they are not like terms and cannot be added. So the answer is m+10 baseball cards.
I hope this helped.
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