The point estimate for sales when advertising is $3000 is $5412.
Based on the given information, the estimated regression equation is Ŷ = 12 + 1.8x, where Ŷ is the estimated value of the dependent variable (sales), x is the value of the independent variable (advertising), and the constants 12 and 1.8 are the coefficients of the regression equation.
If advertising is $3000, then the point estimate for sales (in dollars) is the value of Ŷ when x = 3000. Substituting this value into the estimated regression equation, we get:
Ŷ = 12 + 1.8 * 3000 = 12 + 5400 = 5412
So, the required amount is $5412.
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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:
(a) Find the eigenvalues of Matrix A. (5 marks) (b) Find a corresponding eigenvector for each of the eigenvalues found in (a). (10 marks) (c) Use the above (a) and (b) results to solve the vector-matrix differential equation * = AX X(0) = 11 with the initial conditions
For the given matrix A ,(a) the eigen values are 0 and -3 . and the eigen vectors corresponding to the given eigen vectors are [tex]\left[\begin{array}{ccc}1 \\1 \\\end{array}\right][/tex] and [tex]\left[\begin{array}{ccc}2 \\1 \\\end{array}\right][/tex] .
In the question ,
it is given that ,
the matrix A is = [tex]\left[\begin{array}{ccc}-6&6\\-3&3\\\end{array}\right][/tex]
Part(a)
the eigen values of the matrix A can be found by the characteristic equation ,
|A - λI | = [tex]\left|\begin{array}{ccc}-6-\lambda &6\\-3&3-\lambda\\\end{array}\right|[/tex] = 0 ;
= -(6 + λ)(3 - λ) + 18
= λ² - 3λ + 6λ = 0
= λ² + 3λ = 0
So , λ = 0 and λ = -3 .
the eigen values are 0 and -3 .
Part(b)
for finding the eigen vectors ,
For eigen value λ = 0 , [A - λI]*X = 0
on solving [tex]\left[\begin{array}{ccc}-6&6\\-3&3\\\end{array}\right][/tex]*[tex]\left[\begin{array}{ccc}x_{1} \\x_{2} \\\end{array}\right][/tex] = 0 ,
we get x₁ = 1 and x₂ = 1 ,
the eigen vector corresponding to eigen value 0 is [tex]\left[\begin{array}{ccc}1 \\1 \\\end{array}\right][/tex] .
Similarly solving for eigen value λ = -3 ,
[tex]\left[\begin{array}{ccc}-3&6\\-3&6\\\end{array}\right][/tex]*[tex]\left[\begin{array}{ccc}x_{1} \\x_{2} \\\end{array}\right][/tex] = 0 ,
Solving further ,
we get , x₁ = 2 and x₂ = 1 ,
the eigen vector corresponding to eigen value -3 is [tex]\left[\begin{array}{ccc}2 \\1 \\\end{array}\right][/tex] .
Therefore , (a) the eigen values are 0 and -3 .
(b) the eigen vectors are [tex]\left[\begin{array}{ccc}1 \\1 \\\end{array}\right][/tex] and [tex]\left[\begin{array}{ccc}2 \\1 \\\end{array}\right][/tex] .
The given question is incomplete , the complete question is
The matrix is A = [tex]\left[\begin{array}{ccc}-6&6\\-3&3\\\end{array}\right][/tex] ,
(a) Find the eigenvalues of Matrix A .
(b) Find corresponding eigenvector for each of eigenvalues found in (a).
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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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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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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.
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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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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a new pizza chain applies constant pricing and asks customers to choose 6 toppings out of 15 options, allowing multiplicity in the topping choice. for instance, a person who wants a pizza with only mushrooms and olives can select 4 mushrooms and 2 olives. a) [20 pts) How many different types of pizza are possible? 1 b) (30 pts) How many different types of pizza are possible if we are heat-sensitive and the selection of jalapeno cannot exceed 3?
(a) 15⁶ many distinct pizza varieties are there.
(b) Given that we are heat-sensitive and that there can be no more than three types of jalapeno, 8108520 many different sorts of pizza are possible.
Given that,
A brand-new pizza restaurant offers 15 topping choices and consistent cost, allowing customers to select any six of them. For instance, a customer can choose 4 mushrooms and 2 olives if they just want mushrooms and olives on their pizza.
We have to find
a) How many distinct pizza varieties are there.
b) Given that we are heat-sensitive and that there can be no more than three types of jalapeno, how many different sorts of pizza are possible.
We know that,
(a) we have 6 places to fill form 15 options.
So, each place has 15 choice
Type of pizza possible=15⁶.
(b) No jalapeno used = 14⁶
1 jalapeno used = 14⁵
2 jalapeno used = 14⁴
3 jalapeno used = 14³
Total pizza = 14³+14⁴+14⁵+14⁶
Total pizza = 14³(1+14+14²+14³)
Total pizza = 8108520
Therefore,
(a) 15⁶ many distinct pizza varieties are there.
(b) Given that we are heat-sensitive and that there can be no more than three types of jalapeno, 8108520 many different sorts of pizza are possible.
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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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14. Solve for t by factoring: t² - 2t - 15 =
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.
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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The breaking strength of hockey stick shafts made of two different graphite-kevlar composites yields the following results (in Newtons):
For Composite 1 the average and the standard deviation of the 14 hockey sticks are respectively 487.42 Newtons and 11.528 Newtons.
For Composite 2 the average and the standard deviation of the 12 hockey sticks are respectively 466.76 Newtons and 7.193 Newtons.
Use a 5% significance level to test the claim that the standard deviation of the breaking strength of hockey stick shafts made of graphite-kevlar composite 1 is different from the standard deviation of the breaking strength of hockey stick shafts made of graphite-kevlar composite 2.
Procedure:?
We don't have claim to strength of composite B is smaller than the strength of composite B by at least 2 [N].
From the given data we calculate μ₁s₁ and μ₂s₂ mean and standard deviation of samples A and B respectively.
μ₁ = 464.7, s₁ = 13.42 composite A
μ₂ = 479.49, s₂ = 13.38 composite B
n₁ : n₂ < 30 then we will use t-table.
Null hypothesis H₀:μ₂-μ₁ ≥ 2
Alternative hypothesis Hₐ : μ₂ - μ₁ < 2
assuming CI 95%
α = 5% = 0.05
and degree of freedom is n₁ + n₂ - 2 = 9 + 9 - 2 = 16
then for the one tail t(c) = 1.746
now we will compute t(s),
t(s) = (μ₂ - μ₁ - 2)/ sp×√1/n₁ + 1/n₂
sp²= (n₁ - 1) × s₁² + (n₂ - 1) × s₂² / n₁ + n₂ - 2
= 8 × (13.42)² + 8 × (13.38)²/ 16
= (8 × 180.1 + 8 × 179) / 16
sp² = 179.55
sp = 13.40
Therefore
t(s) = (479.49 - 464.7 - 2)/ 13.40 ×√1/9+1/9
= 12.79 / 13.40 × 0.4714
= 12.79 / 6.32
t(s) = 2.02
t(s) > t(c)
t(s) is rejection region.
Therefore we reject H₀
so we don't have evidence to claim to strength pf composite B is smaller than the strength of composite B at least 2 [N].
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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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find the solution to the system of equations
Answer:
Step-by-step explanation:
Find the corner points of X (x,y) and Y(x,y)
Serena buys 15 shirts with five $100.00. She gets $22 change, What is the cost per shirt?
Answer:
98.53
Step-by-step explanation:
[tex]100 \times 5 = 1500 \\ 1500 - 22 = 1478 \\ 1478 \div 15 = 98.53[/tex]
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.
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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Problem 9. Find the exact sum of the infinite geometric sequence 5, 2,
8
5'25'**
Problem 10. The population size of a city was 79,000 in the year 1990 and is growing at a rate of 5% per year.
(a) What will the population be in 2003?
(b) In what year will the population be triple?
The sum of the series is 25/3
The population in 2003 is 148966The population triples in 2013The sum of the seriesFrom the question, we have the following parameters that can be used in our computation:
5, 2, 4/5, ....
The sum of the series to infinity is
Sum = First term/1 - common ratio
In this, we have
First term = 5
common ratio = 2/5
So, we have
Sum = 5/(1 - 2/5)
Evaluate
Sum = 25/3
The population in 2003Here, we have
Initial population, a = 79000
Rate = 5%
An exponential function is represented as
P(x) = a *(1 + r)^x
So, we have
P(x) = 79000 *(1 + 5%)^x
In 2003. we have
x = 2003 - 1990 = 13
So, we have
P(13) = 79000 *(1 + 5%)^13
Evaluate
P(13) =148966
When the population triplesThis means that
P(x) = 3a
So, we have
3a = a *(1 + 5%)^x
This gives
3 = (1 + 5%)^x
Take the logarithm of both sides
x = log(3)/log(1 + 5%)
Evaluate
x = 23
So, the year is
Year = 1990 + 23 = 2013
Hence, the year is 2013
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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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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.
Assume that you plan to use a significance level of α = 0.05 to test the claim that p1 = p2, Use the given sample sizes and numbers of successes to find the pooled estimate overbar(p). Round your answer to the nearest thousandth.
n1 = 100 n2 = 100
x1 = 42 x2 = 45
A. 0.435
B. 0.305
C. 0.392
D. 0.479
Option c 0.932 is the correct option of the given statement.
Assume that you plan to use a significance level of α = 0.05 to test the claim that p1 = p2, Use the given sample sizes and numbers of successes to find the pooled estimate overbar(p)
n1 = 100 n2 = 100
x1 = 42 x2 = 45
"In mathematics, what are probabilities?On a linear scale from 0 (impossibility) to 1 (certainty), or as a percentage between 0 and 100%, the word "probability" is commonly used to refer to the likelihood that a specific event (or group of events) will take place. Statistics describes the examination of events subject to probability.
What does probability formula mean?The proportion of favorable outcomes to all possible outcomes serves as the basis for the formula used to determine an event's probability. Always between 0 and 1 are the possible outcomes. Probability = Number of Favorable Outcomes / Total Number of Outcomes is a general form of the probability formula.
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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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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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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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Which of the following describes a regular polygon? A. all sides are congruent
C. their sides are congruent
B. no sides are congruent
D. two sides are congruent
Answer: D) Two sides are congruent
Step-by-step explanation:
In a km race A beats B by 60m Or 7s. What is the time taken by A over the course
The time taken by A over the course is 109.3 s
How to determine the time taken by the course?The given parameters that will help us to solve the problem is
A beats B by 60m in 7s
Length of track = 1km
Distance by which A beats B = 60m
And the time by which A beats B is 7 seconds
Time taken by A over the course according to the problem is
A covers 60m in 7 secs
Let us consider the formula,
Speed = Distance / Time
The Speed of B= 60/7 m/s = 8.6 m/s
This implies that Time taken by B over the course = Distance / Speed
= 1000/8.6 = 116.3 s
According to the problem, if A reaches earlier , then time taken by A = (116.3 - 7) s = 109.3 s
In conclusion time taken by A over the course is 109.3 s .
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Which of the following describes a function?
A. 1,2,1,3,2,2,2,3
C. -1,6, 7,-1,-1,3 – 4,3
B. 2,3, 2,-3, 2,6 , 2.0
D. 1,2,2,3,3,4,4,5
Among the following relations, the Function is option D,{1,2,2,3,3,4,4,5}.
In simple words, a function is a relationship between inputs where each input is related to exactly one output. Functions are often defined by a formula that describes a combination of arithmetic operations
A function is uniquely represented by the set of all pairs (x, f (x)), called the graph of the function, a popular means of illustrating the function. To identify a function from a relation, we just have to see if any 'x' values are being repeated, if not, it is a function. If x values are repeated, and y values are different, then we have a relationship and not a function.
In the question, we can see that values 2,3, and 4 are repeating. This specifies that they are a function.
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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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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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