The probability that a student chosen randomly from the class plays both basketball and baseball is 39%.
What is probability?
The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a proposition to be true. A number between 0 and 1 is the probability of an event, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
Given:
In a certain Algebra 2 class of 23 students, 11 of them play basketball and 13 of them play baseball.
There are 8 students who play neither sport.
Either (or both) sports = (23 - 8) = 15 students play
Both = [11 basketball and 13 baseball) - 15] = 9 must play both
Probability=9/23
Probability=0.39 or 39%
Hence, the probability that a student chosen randomly from the class plays both basketball and baseball is 39%.
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Solved Calculate the interest earned on a $4500 saving
The interest earned almost is $337.50 when a $4,500 type of saving account have earns 2.5% simple interest for almost 3 years.
Simple Interest = Principal x Interest Rate x Time/ 100
The principal of a loan or the initial deposit into a savings account serves as the foundation for simple interest. Simple interest does not compound, so the creditor only has to pay interest on the principal sum and the borrower never has to pay interest on the interest that has already accrued.
The principal, or initial amount of a loan, is used to compute simple interest. Compound interest is often referred to as "interest on interest" since it is computed using the main amount and the interest that has accrued over the course of previous periods.
Here Principal= 4500
Rate= 2.5%
Time= 3 years
Using Simple Interest
SI = ( P x R xT)/100
SI = (4500 x 2.5 x 3) /100
SI = 33750/100
SI = $337.50
Hence, the interest earned is $337.50
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Correct Question:
Calculate the interest earned on a $4,500 saving account that earns 2.5% simple interest over 3 years.
Simplify each expression
1. 8x+3y-x-2y
Suppose that the functions r and s are defined for all real numbers x as follows.
r(x)=x+5
s(x) = 4x+2
Write the expressions for (r*s) (x) and (r-s) (x) and evaluate (r+s)(1).
The values of the expression (1) (r*s)(x) is 4x²+22x+10 (2) (r-s)(x) is -3x +3 (3) (r+s)(1) is 5x +7
How to determine the values of the expressions?The given parameters that will help us to calculate the values are
r(x) = x+5
s(x) = 4x +2
(1) r*s(x) will be
(x+5)(4x+2)
Opening the brackets we have
4x²+2x+20x+10
= 4x²+22x+10
(2) (r-5)(x)
Putting the values of r and s
(x+5)- (4x+2)
Open the brackets to have
x+5-4x-2
Collecting like terms to get
-3x+3
(3) (r+s)(x)
By substitution we have
x+5+4x+2
⇒5x +7
In conclusion the values of the expressions are (1) (r*s)(x) is 4x²+22x+10 (2) (r-s)(x) is -3x +3 (3) (r+s)(1) is 5x +7
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Describe frequency, relative frequency, and cumulative relative frequency.
Frequency :
The frequency of a particular data is the number of times the particular data value occurs. We represent the value of frequency as f.
Relative frequency :
Relative frequency is the fraction or proportion times an answer occurs in the data set.
Relative frequency can be written in decimal, fraction and percent.
To find the relative frequency, divide the frequency by the total number of data values.
Cumulative frequency :
Cumulative frequency is the collection of all previous frequencies together.
Cumulative frequency is also called frequency of non-exceedance.
There are two types of Cumulative Frequency Curves (or Ogives) :
1. More than type Cumulative Frequency Curve.
2. Less than type Cumulative Frequency Curve.
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the national park service is interested in comparing the amount of money that visitors in two different national parks spend. they sample visitors on the same day in each of the two parks and then compare the mean dollar amounts spent from each sample. analysis for these data will be based on a design.
The answer is , Analysis for these data will be based on a Independent Two sample t-test design .
In the question ,
the national park service is comparing the amount of money spent by the visitors in two different national parks .
we know that the ,
Independent sample t-test is defined as statistical technique that can be used to analyze the mean comparison of two independent groups.
In independent samples t-test, if we take two samples from same population, then mean of the two samples may be identical.
So , Analysis for these data will be based on a independent samples t-test design .
Therefore , the independent samples t-test design will be used for the analysis for the given data.
The given question is incomplete , the complete question is
The national park service is interested in comparing the amount of money that visitors in two different national parks spend. they sample visitors on the same day in each of the two parks and then compare the mean dollar amounts spent from each sample. Analysis for these data will be based on a design .
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12 in.
Intro
7 in.
Are the two spheres congruent?
O no, because they have the same diameter length
O no, because they have a different radius length
O yes, because they appear to look the same size
O yes, because they have the same volume
Done
The two spheres aren't congruent as B. no, because they have a different radius length
What is congruence?If two figures have the same shape but different sizes, they are similar. In particular, similar figures' similar lengths are proportional.
In geometry, two shapes or objects are said to be congruent if they have the same dimensions, or if one is the mirror image of the other. Congruent in geometry refers to being the same size and shape. Congruence can be used with figures, angles, and line segments.
Note that the complete information wasn't found but the correct option is B based on searches made.
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Answer:
no, because they have a different radius length
Step-by-step explanation:
we can only assume that 12 in and 7 in are the radius or diameter of the 2 spheres.
but it seems clear that whatever these 2 numbers really mean, they are some form of size information about the spheres.
and because they are different, that means that the sizes of the 2 spheres are different.
and therefore, they are not congruent.
congruent means that both compared objects would have to have to same form/shape, angles and overall size.
in other words, they are congruent, if you could place them really "on top of each other" (like holograms), and there would be no part anywhere of one object extruding from the other.
therefore, the first answer option does not make any sense at all. if the spheres would have the same diameter length, they would be congruent.
the third answer option does not make any scientific sense. we don't need to rely on the "looks", when we have precise measurement. and they tell us, that a complete "coverage" of each other of both spheres is not possible.
the fourth answer option is also nonsense, as with different size indicators (like radius or diameter lengths) they simply cannot have the same volume.
a) Battery life for a hand-held computer is normally distrbuted and has a population standard deviation of 3 hours. Suppose you need to estimate a confidence interval estimate at the 95% level of confidence for the mean life of these batteries. Determine the sample size required to have a margin of error of 0.253 hours. Round up to the nearest whole number.
b)The managers of a company are worried about the morale of their employees. In order to determine if a problem in this area exists, they decide to evaluate the attitudes of their employees with a standardized test. They select the Fortunato test of job satisfaction which has a known standard deviation of 24 points. They should sample employees if they want to estimate the mean score of the employees within 5 points with 90% confidence.
c) Suppose a department store wants to estimate the average age of the customers of its contemporary apparel department, correct to within 2 years, with level of confidence equal to 0.95. Management believes that the standard deviation is 8 years. The sample size they should take is .
(a) The required sample size is 1.96.
(b) Sample size = n = 89
(c) Sample size = n = 62
What is standard deviation?
The standard deviation in statistics is a measurement of how much a set of values can vary or be dispersed. A low standard deviation suggests that values are typically close to the set's mean, whereas a high standard deviation suggests that values are dispersed over a wider range.
(a) Population standard deviation = σ = 3
Margin of error = E = 0.253
At 95% confidence level the z is,
α = 1 - 95%
α = 1 - 0.95 = 0.05
α/2 = 0.025
Zα/2 = 1.96
sample size = n = [Zα/2* σ / E]^2
n = [1.96 * 3 / 0.253]2
n = 540.14
Sample size = n = 541
b) Population standard deviation = σ = 24
Margin of error = E = 5
sample size = n = [Zα/2* σ/ E] 2
n = [1.96 * 24 / 5]2
n = 88.51
Sample size = n = 89
c) Population standard deviation = σ = 8
Margin of error = E = 2
sample size = n = [Zα/2* σ / E] 2
n = [1.96 * 8 / 2]2
n = 61.46
Sample size = n = 62
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what is the value of x in the equation 2x โ 4 = 4x + 4?; 6(x โ 2) = 36 โ 10x?; 8p+2=4p-10; 3(x-2)=2x+6; 1/2w + 7 = 2w - 2
The value of x for an equation
1) 2x - 4 = 4x + 4 is x = -4
2) 6(x - 2) = 36 - 10x is x = 3
3) 3(x-2) = 2x + 6 is x = 12
In this question, we have been given an equation.
we need to find the value of x in the equation 2x - 4 = 4x + 4;
6(x - 2) = 36 - 10x
and 3(x-2)=2x+6;
1) consider an equation 2x - 4 = 4x + 4
2x - 4x - 4 = 4x + 4 - 4x
-2x - 4 + 4 = 4 + 4
-2x = 8
x = -4
2) consider an equation, 6(x - 2) = 36 - 10x
6x - 12 = 36 - 10x
6x + 10x = 36 + 12
16x = 48
x = 48/16
x = 3
3) consider an equation 3(x - 2) = 2x + 6
3x - 6 = 2x + 6
3x - 2x = 6 + 6
x = 12
Therefore, the value of x for
a) 2x - 4 = 4x + 4 is x = -4
b) 6(x - 2) = 36 - 10x is x = 3
c) 3(x-2) = 2x + 6 is x = 12
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Solve the problem.
How much money needs to be invested now to get $2000 after 4 years at 8%
compounded quarterly? Express your answer to the nearest dollar.
A) $584
B) $1457
C) $1848
D) $2746
Answer:
A) $584
Step-by-step explanation:
Compounded quarterly means it is compounded 4 times a year.
This means that the amount its compounded 16 times during this period.
to compound the money you must multiply it by 1+ the rate its being compounded so here it is .08.
work: (584 * 1.08)= 630.72
630.72 *1.08= 681.1
... repeat until done 16 times and $2000 is reached.
14. Solve for t by factoring: t² - 2t - 15 =
Complete the equation describing how
x and y are related.
X
0 1 2 3 4
y -1 3 7 7 11
11 15
y = [? ]x + [ ]
Enter the answer that belongs in [?].
The equation of the linear relationship between x and y is: y = 4x - 1.
How to Write the Equation that Describes the Relationship between x and y?If we are given a table of values that shows the relation of x to y, to find the equation, find the value of the slope (m) and the value of the y-intercept (b), then plug their values into the equation, y = mx + b.
Given the table:
x 0 1 2 3 4
y -1 3 7 11 15
Using two points from the table, (0, -1) and (1, 3), find the slope (m):
Slope (m) = change in y / change in x = (-1 - 3) / (0 - 1)
Slope (m) = -4/-1
m = 4
The y-intercept (b) = -1 [this is the value of y when x = 0, as seen in the table]
Substitute m = 4 and b = -1 into the equation, y = mx + b:
y = 4x - 1
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My age this year is multiple of 8. My age next year is a multiple of 7. How old am I?
8x + 1 = 7
y - x = 1
y = 1 + x
sub 1 + x in eqtn i
8x + 1 = 7 { 1 + x }
8x + 1 = 7 + 7x
8x - 7 = 7 - 1
x = 6
y - 6 = 1
y = 1 + 6
y = 7
So,
8x = 8 x 6 = 48
7y = 7 x 7 = 49
My present years is 48
Next year i will be 49
What is multiple?Multiple can be defined as a number that is the product of a given number and some other natural number. For example when we multiply 7 × 3=21 or 8×3 =24
Therefore my present age is 48 and next year will be 49
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A projectile is fired straight up from ground level. After t seconds, its height above the ground is s feet, where s= - 161? + 112t. For what time period is the projectile at least 160 feet above the ground?
The time period the projectile at least 160 feet above the ground is 2 sec to 5sec.
What is time period?
The duration of time that a behavior lasts or a condition persists. Depending on the type of activity or situation under consideration, it may be measured in seconds or in millions of years.
Given function that represents height of the projectile above the ground is s feet is s = - 16t² + 112t.
To find the time period is the projectile at least 160 feet above the ground, make an inequality:
- 16t² + 112t ≥ 160
Subtract 160 from both sides:
- 16t² + 112t - 160 ≥ 0
Divide both sides by 16:
- t² + 7t - 10 ≥ 0
- t² + 2t + 5t - 10 ≥ 0
-t(t -2) + 5(t - 2) ≥ 0
(t - 2)( -t+ 5) ≥ 0
Either, t - 2 ≥ 0 → t ≥ 2
or, -t + 5 ≥ 0 → t ≤ 5
2 ≤ t ≤ 5
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One leg of a right triangle is 1 cm longer than the other leg. The hypotenuse measures 5 cm.
Part A: Find the perimeter of the triangle.
Part B: Find the area of a triangle
The perimeter of a triangle is: 12cm.
The area of triangle is: [tex]6 cm^2\\[/tex]
What are right angle properties?A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees or any one angle is a right angle.
Therefore, this triangle is sometimes called the right triangle or 90-degree triangle.
The characteristics a right-angle triangle possesses.
The right angle, or 90°, is always one angle.The hypotenuse is the side with the 90° angle opposite.The longest side is always the hypotenuse.The other two inner angles add up to 90 degrees.Base and perpendicular are the names of the other two sides that are close to the right angle.Right-angle triangles have an area equal to half of the product of their neighboring sides, or Right-angle triangle's area is equal to (1/2) × base × perpendicular.Let x be the one side of the triangle.
Then the other side will be x + 1 cm.
Hypotenuse is 5 cm.
Using right angled triangle property and (a + b)²=a²+b²+2ab
[tex]x^2 + (x+1)^2 = 5^2\\\implies x^2 + x^2 + 2x + 1 = 25\\\implies 2x^2 + 2x = 24\\\implies 2x^2 + 2x -24 = 0\\\implies x^2 + x -12 = 0\\[/tex]
Solving this equation:
x = -4 or x = 3
since the length of triangle can't be negative therefor x = 3.
which means sides are 3, 4 and 5
Perimeter = sum of all three side
Therefore, Perimeter = 3 + 4 + 5 = 12cm.
Area = (height * base)/2
Therefore, Area = [tex]3*4/2 = 12/2 = 6 cm^2[/tex]
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what is the value of n in the equation ? n = 0 n = 2 n = 4 n = 6; kate begins solving the equation 2/3(6x-3)=1/2(6x-4); what is the value of x in the equation ? 2 13; solve the equation. y + 3 = โy + 9 y = 1 y = 3 y = 6 y = 9; what value of x is in the solution set of 2x โ 3 > 11 โ 5x? โ3 0 2 4; what is the solution to the linear equation? + p = + p p = 1 p = 2 p = 8 p = 10; solve the equation. โ9x + 1 = โx + 17 x = โ8 x = โ2 x = 2 x = 8; which number line represents the solutions to โ2|x| = โ6?
1) The value of n is 2
2) The best interpretation of equation 2/3(6x – 3) =1/2 is the equation has one solution: x = 0
3) The solution to equation y + 3 = -y + 9 is y = 6
4) The value of x is 4
5) The solution to a linear equation 2/5 + p = 4/5 + 3/5p is p = 1
6) The solution to an equation - 9x + 1 = - x + 17 is x = -2
7) A number line represents the solutions to -2|x| = -6 is option 4
1) We have been given an equation 1/2(n-4) - 3 = 3 - (2n+3)
We need to find the value of n.
1/2(n - 4) - 3 = 3 - (2n+3)
1/2(n - 4) = -2n + 3
n - 4 = -4n + 6
5n = 10
n = 2
2) In this question Kate begins solving the equation 2/3(6x – 3) =1/2 as:
2/3(6x – 3) = 1/2(6x – 4)
4x – 2 = 3x – 2
4x = 3x
We need to find the best interpretation of this equation.
4x - 3x = 0
x=0
Thus, the best interpretation of this equation is the equation has one solution: x = 0
3) In this question we need to solve an equation y + 3 = -y + 9
y + y = 9 + 3
2y = 12
y = 6
4) In this question we need to find the value of x for an inequality 2x - 3 > 11 - 5x
2x - 3 > 11 - 5x
2x + 5x > 11 + 3
7x > 14
x > 2
As x > 2, the value of x is 4.
5) We need to find the solution to a given linear equation.
Consider a linear equation,
2/5 + p = 4/5 + 3/5p
p - 3/5p = 4/5 - 2/5
2/5p = 2/5
p = 1
Thus, the solution to a given linear equation is p = 1
6) In this question, we need to solve an equation - 9x + 1 = - x + 17
- 9x + x + 1 = - x + 17 + x
-8x = 17 - 1
-8x = 16
x = 16/(-8)
x = -2
7) In this question, we have been given an equation -2|x| = -6
Divide both sides by -2.
|x| = 3
The absolute value of x is 3. It means the value if is either 3 or -3.
In the given figure the blue dot represent the solutions of the given equation.
Only option 4 represent the solution at x=3 and x=-3.
Therefore the correct option is 4.
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Given questions are incomplete.
1) Find the complete question in attachment.
2) Kate begins solving the equation 2/3(6x – 3) =1/2 (6x – 4). Her work is correct and is shown below. 2/3(6x – 3) = 1/2(6x – 4) 4x – 2 = 3x – 2 When she adds 2 to both sides, the equation 4x = 3x results. Which is the best interpretation of this equation? The equation has infinite solutions. The equation has one solution: x = 0. The equation has one solution: x = 4/3. The equation has no solution.
3) Solve the equation. y + 3 = -y + 9
y = 1, y = 3, y = 6, y = 9
4) What value of x is in the solution set of 2x - 3 > 11 - 5x?
-3, 0, 2, 4
5) To better understand the problem see the attached figure.
6) Solve the equation. - 9x + 1 = - x + 17
x = -8, x = -2, x = 2, x = 8
7) Which number line represents the solutions to –2|x| = –6?
Find the options are in the attached figure.
Can anyone help me with geometry
By analytic geometry, the resulting expression for the value t in the geometric system formed by two parallel lines is t = b + n.
How to derive an expression associate to the slope of two parallel lines
In this question we find the case of two parallel lines, in which we are asked to derive an equation to replace the value t seen in the figure. By analytic geometry, two lines are parallel when they have the same slope. Slope is defined by the following formula:
m = Δy / Δx
Where:
Δx - Change in the independent variable.Δy - Change in the dependent variable.m - SlopeThe slope of each line is described below:
Line j
m = (t - a - n) / (x₂ - x₁)
Line k
m' = (b - a) / (x₂ - x₁)
Then, we eliminate m, m' and (x₂ - x₁) by assumption of parallelism:
t - a - n = b - a
t - n = b
t = b + n
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A ball is launched directly in the air at a speed of 60 feet per second from a platform located 20 feet in the air. The motion of the
ball can be modeled using the function
where t is time in seconds and is the height of the ball. What is the maximum height of the ball?
The maximum height will be 141.5 feet.
What is quadratic equation
it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form. A non-zero term (a 0) for the coefficient of x2 is a prerequisite for an equation to be a quadratic equation. The x2 term is written first, then the x term, and finally the constant term is written when constructing a quadratic equation in standard form. In most cases, the numerical values of letters a, b, and c are expressed as integral values rather than fractions or decimals.
The function will be f(t) = -16t² + 60t + 20
at ground f(t) = 0
So, 4t² - 15t - 5 = 0
t = (15+√305) / 8
t = 4.05sec.
The maximum height will be in 2.025 sec = 60 * 2.025 = 121.5 feet. + 20feet.
Hence the maximum height will be 141.5 feet.
Hence the value of k is 0.33.
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The amount of work done in a certain amount of time is called?
By the information provided in the question, we can say that , Power is the measure of how much work can be done in a given amount of time.
What is work?Work in physics is the energy that is transferred to or from an item when a force is applied along a displacement. In its simplest form, it equals the product of the force's magnitude and the distance travelled for a constant force directed in the direction of motion.
Power measures how quickly labor is completed or energy is used. It is equal to the work completed divided by the time required to do the task. The Watt (W), which is a unit of power, is equivalent to a Joule per second (J/s).
Power is the measure of how much work can be done in a given length of time.
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Mineko had a piece of material that was 3/5 yard long. She cut 1/3 yard off the material to make a pillow. How much material does she have left?
The material that she has left after the cut of 1/2 yard of the material is 2/5 yards left
While I show you how to solve this problem, I would like to highlight some of the words and how they convert into a mathematical equation.
"She cut 1/3 yard off the material."
This means you multiply whatever you are starting with by 1/3.
So in this case Mineko begins with 3/5 yards.
So,
3/5 • 1/3 = 1/5
She used 1/5 yard to make the pillow.
This will translate to Mineko having left
Therefore 3/5-1/5
She has 2/5 yards left.
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determine whether the following statement about sample mean is true or not. with the correct sampling method, you expect to obtain a sample mean exactly the same as the population mean.
whether the sample mean statement is accurate. It is False to expect to acquire a sample mean that is exactly the same as the population mean using the appropriate sampling technique.
The sample mean is an estimate of the population mean, based on a sample of data taken from the population. Since the sample is only a subset of the population, it is unlikely that the sample mean will be exactly equal to the population mean. The larger the sample size, the more closely the sample mean will approximate the population mean. However, it is still not expected to be the same as the population mean, since the sample itself is a limited subset of the population and may not accurately represent the population as a whole.
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Solve
81 = 8(2x + 8) + x
Answer:
The value of x that satisfies the equation 81 = 8(2x + 8) + x is x = 1.125.
Step-by-step explanation:
To solve for x in the equation 81 = 8(2x + 8) + x, you can first distribute the 8 on the right side of the equation to obtain 81 = 16x + 64 + x. Then, you can combine like terms on the right side of the equation by adding the two x terms and the constants to get 82 = 16x + 64. Next, you can subtract 64 from both sides of the equation to isolate the x term, which gives 18 = 16x. Finally, you can divide both sides of the equation by 16 to solve for x, resulting in x = 1.125.
n least squares regression, the residuals e1, e2, . . . , en will always have a zero mean. group starts. True or false
The residuals e1, e2,..., en will always have a zero mean in least squares regression. fake group starts
False. The residuals may not have a zero mean, depending on the data used in the regression.
Least squares regression is a type of linear regression that is used to determine the best fit line for a given set of data points. The residuals in this type of regression are the differences between the actual values of the data points and the predicted values of the data points based on the model. While the sum of the residuals should be zero, the mean of the residuals may not necessarily be zero, depending on the data used in the regression.
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given a segment ab, construct the point p on the segment that divides it into two segments such that the shorter is to the longer as the longer is to the whole
A segment ab, construct the point p on the segment that divides it into two segments such that the shorter is to the longer as the longer is to the whole .
Given :
given a segment ab, construct the point p on the segment that divides it into two segments such that the shorter is to the longer as the longer is to the whole .
You are asked to construct P such that :
PB / AP = AP / AB
This ratio is the reciprocal of the Golden Ratio.
( AP )^2 = PB * AB
( AP )^2 = PB * ( AP + BP )
( AP )^2 = PB ( AP ) + ( BP )^2
Divide by PB^2 on both sides
ф^2 = ф + 1
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Choose one of the proofs below and use one of the indirect proof techniques (reductio ad absurdum or conditional proof) presented in Chapter 8 to demonstrate the validity of the argument. The proofs below may use any of the rules of inference or replacement rules given in Chapter 8. (G • P) ? K, E ? Z, ~P ? ~ Z, G ? (E v L), therefore, (G • ~L) ? K (S v T) v E, S ? (F • ~G), A ? W, T ? ~W, therefore, (~E • A) ? ~G (S v T) v (U v W), therefore, (U v T) v (S v W) ~Q ? (L ? F), Q ? ~A, F ? B, L, therefore, ~A v B ~S ? (F ? L), F ? (L ? P), therefore, ~S ? (F ? P) In mathematics, it is very common for there to be multiple ways to solve a given a problem; the same can be said of logic. There is often a variety of ways to perform a natural deduction. In your peer responses, make suggestions for an alternate proof. Consider the following questions when constructing your response: If the proof was done using RAA, could it be done using CP? What about vice versa? Will a direct proof work for any of these? Can the proof be performed more efficiently by using different equivalence rules?
One of the proofs below and use one of the indirect proof techniques presented in Chapter 8 to demonstrate the validity of the argument .
Given :
The proofs below may use any of the rules of inference or replacement rules given in Chapter 8.
( G � P ) → K, E → Z, ~P → ~ Z, G → ( E v L ), therefore, ( G � ~L ) → K
( S v T ) ↔ ~E, S → ( F � ~G ), A → W, T → ~W, therefore, ( ~E � A ) → ~G
( S v T ) v ( U v W ), therefore, ( U v T ) v ( S v W )
~Q → ( L → F ), Q → ~A, F → B, L, therefore, ~A v B
~S → ( F → L ), F → ( L → P ), therefore, ~S → ( F → P )
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find the derivative dy, dx for y equals the quotient of the quantity x cubed minus 5 times x and the quantity x squared minus 1. . (4 points)
Answer:
minus 5 times x and the quantity x squared minus 1.
Step-by-step explanation:
Equations are given whose graphs enclose a region. Find the area of the region. (Give an exact answer. Do not round.) f(x) = x2; g(x) = â 1 5 (5 + x); x = 0; x = 3
The equations are given whose graphs enclose a region. when the area of the region is 301.5
The given function is f(x) and g(x), we need to calculate the area.
A = ₐ∫ᵇ (f(x) + g(x)) dx
A = ₀∫³ (x² + 15(x + 5)) dx
A = ₀∫³ (x²dx + ₀∫³15(x + 5)) dx
A = (x³/3) + 15x²/2 + 75x
A = ₀[x³/3]³ + ₀[15x²/2 + 75x]³
A = [(3 - 0)³/3] + [15(3 - 0)²/2 + 75(3 - 0)]
A = 27/3 + 15(9/2) + 75(3)
A = 9 + 15(4.5) + 7
A = 76.5 + 225
A = 301.5
Therefore, the equations are given whose graphs enclose a region. when the area of the region is 301.5
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A P-value of 1.018943E-06 is calculated on a hypothesis test with a significance level set at 0.01. Which of the following is the correct conclusion for the test?
a. Claim the null hypothesis is true
b. Claim the alternative hypothesis is true
c. Reject the null hypothesis
d. Fail to reject the null hypothesis
"Fail to reject the null hypothesis" is the correct conclusion for the test.
We have given that,
a P-value of 1.018943 is calculated on a hypothesis test with significance level set at 0.01.
That means p-value is greater that significance level.
And we know that if p-value is greater than significance level then the effect is statistically not significant. There is no enough evidence to reject the null hypothesis.
A p-value greater than 0.01 means that deviation from the null hypothesis is not statistically significant, and the null hypothesis is not rejected.
High p-value indicates that your evidence is not strong enough to suggest an effect exist in the population. An effect might exist but it's possible that the effect size is too small, that sample size is too small or there is too much variability for the hypothesis test to detect it.
Therefore "Fail to reject the null hypothesis" is the correct conclusion for the given test.
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The vertex form of the quadratic function f (x) = x² + 8x + 7 is
f(x)= a(x-h)² + k.
What is the value of a?
What is the value of h?
What is the value of k?
Answer:
Step-by-step explanation:
The vertex form of a quadratic function is given by the equation f(x) = a(x - h)² + k, where (h, k) is the coordinates of the vertex of the parabola, and a is a constant coefficient.
To find the values of a, h, and k for the given quadratic function f(x) = x² + 8x + 7, we can first use the formula for the x-coordinate of the vertex of a quadratic function, which is given by h = -b / 2a. In this case, the quadratic function is f(x) = x² + 8x + 7, so b = 8 and a = 1. Plugging these values into the formula, we get:
h = -8 / 2(1) = -4
Therefore, the value of h is -4.
Next, we can use the formula for the y-coordinate of the vertex of a quadratic function, which is given by k = f(h) = a(h - h)² + k. In this case, we know that the value of h is -4, and we can plug this value into the original quadratic function to get the value of k:
k = f(-4) = (-4)² + 8(-4) + 7 = 16 - 32 + 7 = -9
Therefore, the value of k is -9.
Finally, we can use the equation f(x) = a(x - h)² + k to find the value of a. Since we know that the coordinates of the vertex are (-4, -9) and the equation of the quadratic function is f(x) = x² + 8x + 7, we can plug these values into the equation to solve for a:
f(x) = a(x - h)² + k
x² + 8x + 7 = a(x - (-4))² + (-9)
We can then distribute the squared term and simplify the equation to get:
x² + 8x + 7 = a(x² - 8x + 16) + (-9)
x² + 8x + 7 = a(x²) - 8a(x) + 16a + (-9)
We can then collect like terms to get:
x² + 8x + 7 = a(x²) - 8ax + 16a - 9
Comparing the coefficients of the x², x, and constant terms on both sides of the equation, we can see that a = 1.
Therefore, the values of a, h, and k for the given quadratic function f(x) = x² + 8x + 7 are a = 1, h = -4, and k = -9.
list the quantum numbers associated with all of the 5d orbitals, and indicate how many 5d orbitals exist in the sentences below.
The correct sentences here are n = 5, l = 2, ml = -2 , -1, 0 , +1 , +2. The 5 integer values for ml signify that there are 5 5d orbitals.
In the given question we have to list the quantum numbers associated with all of the 5d orbitals, and indicate how many 5d orbitals exist in the sentences below.
As we know that;
Quantum numbers are the collection of numbers used to represent the location and energy of an electron in an atom. The primary, azimuthal, magnetic, and spin quantum numbers are the four types of quantum numbers.
There are four different quantum numbers , principal , azimuthal , magnetic and magnetic spin quantum numbers . The correct sentences here are :
n = 5
l = 2
ml = -2 , -1, 0 , +1 , +2
The 5 integer values for ml signify that there are 5 5d orbitals.
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Suppose four treatments are being compared with an ANOVA F test at the 5% level for equality of means. There are 6 replicate within each treatment. How many confidence intervals or hypothesis tests would need to be done to make significance statements for each pair-wise comparison? O 2 O 4 O 6O 8O 15
Six (6) confidence intervals or hypothesis tests would need to be done to make significant statements for each pair-wise comparison.
In an ANOVA F test, the null hypothesis is that the means of all the treatments are equal, and the alternative hypothesis is that at least two of the means are different. If the null hypothesis is rejected at the 5% significance level, this means that the differences between the means are statistically significant and the treatments can be considered different.
Since there are four treatments, there are 6 possible pairs of treatments. These tests would determine whether the means of each pair of treatments are significantly different from each other.
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