as a guest was sneaking away,the groundskeeper was 4 feet (48 inches) away and pushed an 84 inches ladder onto the suspect. They very top of the ladder hit the guest on the top of the head. Find the height of the guest in inches, then convert in feet. His weight is 207

By using the same logic and identity, we can also say that ¬(p∨¬q) is equivalent to q∧¬p.

a. To find the given series i.e.,  5∑n=0(9(2)n)−7(−3)nTo find 5∑n=0(9(2)n)−7(−3)n,

we need to find the first five terms of the series. The given series is,

5∑n=0(9(2)n)−7(−3)n5[(9(2)0)−7(−3)0] + [(9(2)1)−7(−3)1] + [(9(2)2)−7(−3)2] + [(9(2)3)−7(−3)3] + [(9(2)4)−7(−3)4]

After evaluating, we get:

5[(9*1) - 7*1] + [(9*2) - 7*(-3)] + [(9*4) - 7*9] + [(9*8) - 7*(-27)] + [(9*16) - 7*81]15 + 57 + 263 + 1089 + 4131= 5555b.

Given premises: p → q, ¬p → r, r → s.

We are to prove that ¬q → s. i.e.,

Premises: (p → q), (¬p → r), (r → s)

Conclusion: ¬q → s

To prove ¬q → s,

we need to assume ¬q and show that s follows.

Then we use the premises to derive s.

Proof:

1. ¬q        Assumption

2. ¬(¬q)    Double negation

3. p         Modus tollens 2,1 & p → q

4. ¬¬p      Double negation

5. ¬p        Modus ponens 4,3 (Conditional elimination)

6. r         Modus ponens 5,2 (Conditional elimination)

7. s         Modus ponens 6,3 (Conditional elimination)

8. ¬q → s     Conditional introduction (Implication)

Thus, ¬q → s is proven.

c. To show that ¬(p∨¬q) and q∧¬p are equivalent, we need to show that their negation is equivalent. i.e.,

we show that (p ∨ ¬q) ↔ ¬(q ∧ ¬p)Negation of (p ∨ ¬q) = ¬p ∧ q Negation of (q ∧ ¬p) = ¬q ∨ p

Thus, we are to show that (p ∨ ¬q) ↔ ¬(q ∧ ¬p) is equivalent to ¬p ∧ q ↔ ¬q ∨ p

Proof:

¬(q ∧ ¬p)  ≡  ¬q ∨ p       Negation of (q ∧ ¬p)(p ∨ ¬q)   ≡  ¬(q ∧ ¬p)  

De Morgan's laws ∴ (p ∨ ¬q) ≡ ¬q ∨ p

By using the same logic and identity, we can also say that ¬(p∨¬q) is equivalent to q∧¬p.

To know more about equivalent visit:

https://brainly.com/question/24207766

#SPJ11

a. The formula given is, ∑n=0(9(2)n)−7(−3)n. Let’s find out the first five terms of the given formula as follows:

First term at n = \(0:9(2)^0-7(-3)^0= 9 + 7= 16\)

Second term at n = \(1:9(2)^1-7(-3)^1= 18 + 21= 39\)

Third term at n = \(2:9(2)^2-7(-3)^2= 36 + 63= 99\)

Fourth term at n = \(3:9(2)^3-7(-3)^3= 72 + 189= 261\)

Fifth term at n = \(4:9(2)^4-7(-3)^4= 144 + 567= 711\)

Therefore, the first five terms of the given formula are: 16, 39, 99, 261, 711.

b. To prove that ¬q→s from p→q, ¬p→r, and r→s,

we need to use the law of contrapositive for p→q as follows:

¬q→¬p       (Contrapositive of p→q)¬p→r         (Given)

∴ ¬q→r        (Using transitivity of implication) r→s           (Given)

∴ ¬q→s        (Using transitivity of implication)

Therefore, ¬q→s is proved.

c. To show that ¬(p∨¬q) and q∧¬p are equivalent,

we need to use the De Morgan’s laws as follows:

¬(p∨¬q) ≡ ¬p∧q     (Using De Morgan’s law)      

≡ q∧¬p     (Commutative property of ∧)

Therefore, ¬(p∨¬q) and q∧¬p are equivalent.

To know more about law of contrapositive visit:

https://brainly.com/question/17831746

#SPJ11

hi

Mary  has  1/4 to pick  red  and Frank 1/3 to pick purple  

both event at the same time :  1/4*1/3 =  1/12

Part A: The composite function that represents how many flowers Lily can expect to bloom over a certain number of weeks is given by f(s(w)) = 2s(w) + 30.

Part B: flowers

Part C:  2580 flowers

It is a function that is formed by combining two or more functions. It is created by taking the output of one function and using it as the input of another function.

Part A: The composite function that represents how many flowers Lily can expect to bloom over a certain number of weeks is given by f(s(w)) = 2s(w) + 30 where s(w) = 40w and w represents the number of weeks. This means that for any number of weeks w, the total number of flowers that will bloom is given by f(s(w)) = 2(40w) + 30.

Part B: The units of measurement for the composite function in Part A are flowers.

Part C: Evaluating the composite function in Part A for 35 weeks, we get f(s(w)) = 2(40*35) + 30 = 2550 + 30 = 2580 flowers. This means that if Lily plants 40 seeds per week for 35 weeks, she can expect 2580 flowers to bloom.

For more questions related to function

https://brainly.com/question/25638609

#SPJ1

Answer:

From the two graphs, I can see in the picture, I can tell that the left graph represents y=2x because the y-intercept is 0 and the slope is 2 because the line goes up two and over one (2/1) or just 2.

Step-by-step explanation:

Hope this helps

The number of wins is 68 ad losses is 26.

Let the number of losses = l

Therefore, the number of wins will be: = (2 × l) + 16 = 2l + 16

Total games = 94

Therefore we will add the equation

l + 16 + 2l = 94

3l + 16 = 94

3l = 94 - 16

3l = 78

Divide

l = 78/3

l = 26

Losses = 26

Number if wins = 2l + 16 = 2(26) + 16 = 52 + 16 = 68

Learn more about equations on:

brainly.com/question/13763238

#SPJ1

Answer:

1/7

Step-by-step explanation:

y = -7x - 1 so slope is -7

The slopes of two perpendicular lines are negative reciprocals of each other

so negative reciprocal of -7 is 1/7

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

\(y = \stackrel{\stackrel{m}{\downarrow }}{-7}x-1\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\)

thus a line perpendicular to that slope will have a slope of

\(\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{-7}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{-7}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{-7}\implies {\LARGE \begin{array}{llll} \cfrac{1}{7} \end{array}}}}\)

The statement "a) the mean of the sampling distribution of sample mean is always the same as that of x, the distribution from which the sample is taken" is not necessarily true.

While the mean of the sampling distribution of the sample mean is an unbiased estimator of the population mean, it is not always equal to the mean of the original distribution from which the sample is taken. This is because the sample mean will vary from sample to sample, and the sampling distribution will reflect this variability.

For example, if the population distribution is skewed or has outliers, the sampling distribution of the sample mean may be more symmetrical and have a different mean. However, as the sample size increases, the sampling distribution of the sample mean will approach a normal distribution with a mean equal to the population mean. This is known as the Central Limit Theorem.

Therefore, the incorrect statement is a).

Learn more about mean at

brainly.com/question/31101410

#SPJ4

Answer:

0.75 → 0.5 → 1/3(0.33) → 1/4(0.25)

To find an expression for a square matrix A satisfying A² = In, where In is the n x n identity matrix, we can consider a diagonal matrix D with the square root of the diagonal entries equal to 1 or -1. Let's denote the diagonal matrix D as D = diag(d1, d2, ..., dn), where di = ±1 for i = 1 to n. Then, the matrix A can be defined as A = D.

Examples for n = 3:

For the case n = 3, we can have the following examples:

A = diag(1, 1, 1)

A = diag(-1, -1, -1)

A = diag(1, -1, 1)

Question 21:

To give an example of a 2 x 2 matrix with non-zero entries that has no inverse, we can consider the matrix A as follows:

A = [[1, 1],

[2, 2]]

To check if A has an inverse, we can calculate its determinant. If the determinant is zero, then the matrix does not have an inverse. Calculating the determinant of A, we have:

det(A) = (12) - (12) = 0

Since the determinant is zero, the matrix A does not have an inverse.

To learn more about expression visit: brainly.com/question/29176690

#SPJ11

tan 36° can be written as cot 54°, which simplifies to (√3 + 1) / (√3 - 1).

The tangent of 36° can be expressed in terms of its cofunction, which is the cotangent. The cotangent of an angle is equal to the reciprocal of the tangent of that angle. Therefore, we can rewrite tan 36° as cot (90° - 36°).

Now, cot (90° - 36°) can be simplified further. The angle 90° - 36° is equal to 54°. So, we have cot 54°.

The cotangent of 54° can be determined using the unit circle or trigonometric identities. In this case, the exact answer for cot 54° is (√3 + 1) / (√3 - 1).

Hence, tan 36° can be written as cot 54°, which simplifies to (√3 + 1) / (√3 - 1).

Learn more about trigonometric identities here:

https://brainly.com/question/24377281

#SPJ11

The treatment mean square can be calculated by dividing the sum of squares for treatment by the degrees of freedom for treatment. In this case, the sum of squares for treatment is 1,122 and the degrees of freedom for treatment is 2. Therefore, the treatment mean square is 1,122/2 = 561. Therefore, the correct answer is: 561.

Based on the ANOVA table you've provided, you're interested in determining the treatment mean square. The treatment mean square (also called mean square between) is calculated by dividing the treatment sum of squares by the treatment degrees of freedom (df). Unfortunately, the ANOVA table appears to be incomplete, and I am unable to give you the specific numbers for the calculations.

However, I can guide you on how to calculate the treatment mean square. Once you have the treatment sum of squares and treatment df, simply follow this formula:

Treatment Mean Square = Treatment Sum of Squares / Treatment df

After applying this formula, you'll be able to choose the correct answer from the multiple-choice options you've mentioned: 71.6, 71.8, 561, or 537.

The treatment mean square can be calculated by dividing the sum of squares for treatment by the degrees of freedom for treatment. In this case, the sum of squares for treatment is 1,122 and the degrees of freedom for treatment is 2. Therefore, the treatment mean square is 1,122/2 = 561. Therefore, the correct answer is: 561.

To learn more about Mean Square, click here:

brainly.com/question/30403276

#SPJ11

Answer:

828.6667

Step-by-step explanation:

Answer:

Step-by-step explanation:

The temperature starts at 50 and increases because the slope is positive.

A computer manipulates data, doing arithmetic or logical operations on it. Computers are electronic devices that can input, store, process, and output data. They are capable of performing complex operations and calculations at a very high speed and accuracy.

The manipulation of data is a core function of a computer and is achieved through the use of specialized hardware and software. The central processing unit (CPU) of a computer is responsible for executing instructions and manipulating data. It consists of arithmetic logic units (ALUs) that perform arithmetic operations such as addition, subtraction, multiplication, and division, and logical operations such as AND, OR, NOT, and XOR. The CPU also contains registers, which are small, fast storage locations used to hold data temporarily during processing. Computer software, such as operating systems and applications, provide a means for users to manipulate data through a user interface. The software sends instructions to the CPU to perform various operations on the data, and then outputs the result to the user. Common software applications that manipulate data include spreadsheets, word processors, and database management systems. Overall, the ability to manipulate data is a crucial aspect of computing. It enables users to perform tasks such as data analysis, modeling, and simulation, which are essential in various fields such as science, engineering, and finance. As Computers continue to evolve, their capabilities for data manipulation will also improve, leading to even more advanced applications and technologies.

Learn more about Computers here

https://brainly.com/question/30049556

#SPJ11

The new function with the slope multiplied by -9 and the y-value of the y-intercept increased by 2 units would be represented by graph y.

Multiplying the slope by -9 means that the steepness of the line will be increased and it will slope downwards towards the right. Increasing the y-value of the y-intercept by 2 units means that the line will be shifted upwards by 2 units.

Looking at the four graphs, we can see that graph y has a steeper slope than the original function, and its y-intercept is 2 units higher. Graphs w, x, and z do not have the same characteristics as the new function, therefore they cannot represent the new function.

Thus, the best graph that represents the new function is graph y.

For more questions like Function click the link below:

https://brainly.com/question/21145944

#SPJ11

Answer:

The first one is 1 the second one is 1/16 = 0.0625

Step-by-step explanation:

Answer:

Step-by-step explanation(A):

\(a^{-b}=\frac{1}{a^b}\\\frac{1}{4^2}\\4^2=16\\\frac{1}{16}\\= 0.0625\)

Step-by-step explanation(BA):

\(7 \div 7 = 1\)

when dealing with an exponent of 0, your answer essentially is always 1, so divide the number by itself.

Step-by-step explanation(BB):

\(a^0=1,\: \:a\ne \:0\)

Answer: (A)

Step-by-step explanation: I hope this helps!

The total cost of the computer is $645.00. The total cost of the computer can be calculated by adding the cost of the computer and the sales tax. The sales tax rate is 7.5%, which means that for every $100 of the cost of the computer, $7.50 is added for sales tax.

To find out how much sales tax is added to the cost of the computer, we can multiply $600 by 0.075, which gives us $45. Therefore, the total cost of the computer is $600 + $45 = $645.00. So, the correct answer is $645.00.

To calculate the total cost of the computer including the sales tax, first find the sales tax amount by multiplying the cost of the computer ($600.00) by the sales tax rate (7.5%). $600.00 * 0.075 = $45.00 Now, add the sales tax amount to the original cost of the computer: $600.00 + $45.00 = $645.00 The total cost of the computer, including the 7.5% sales tax, is $645.00.

To know more about computer visit:

https://brainly.com/question/21247697

#SPJ11

The total cost of the computer would be $645.00. To calculate this, you would need to add the sales tax rate of 7.5% to the original cost of the computer, which is $600.00. To find out how much the sales tax is, you can multiply the original cost of the computer by the sales tax rate.
So, 7.5% of $600.00 is:
($600.00 x 7.5%) / 100 = $45.00
Then, to find out the total cost of the computer, you can add the sales tax amount to the original cost of the computer:
$600.00 + $45.00 = $645.00

Therefore, the total cost of the computer is $645.00.

To know more about sales tax rate visit:

https://brainly.com/question/29751934

#SPJ11

Answer:

x=

\( \frac{5}{4} \)

Step-by-step explanation:

hope u understand,have a good day

Michelle would need to shoot an additional 40 free throws to have a shooting percentage of 90%.

Let's denote the number of additional free throws that Michelle needs to make as "x." Since she has made 14 out of her 20 free throws this season, her current shooting percentage is:

Current shooting percentage = (Number of made free throws / Total number of attempted free throws) * 100

                        = (14 / 20) * 100

                        = 70%

To find the number of additional free throws she needs to shoot to achieve a shooting percentage of 90%, we set up the following equation:

(14 + x) / (20 + x) = 90/100

We can now solve this equation to find the value of x:

(14 + x) / (20 + x) = 0.9

Cross-multiplying gives:

0.9 * (20 + x) = 14 + x

18 + 0.9x = 14 + x

0.9x - x = 14 - 18

-0.1x = -4

Dividing both sides by -0.1 gives:

x = 40

Therefore, Michelle would need to shoot an additional 40 free throws to have a shooting percentage of 90%.

To learn more about percentage click here:

brainly.com/question/23270628

#SPJ11

π/16 is the area enclosed by the curve r= sin(4θ)

The given curve is polar curve and hence the area of the polar curve is given by:

Let A be the area of the curve so,

A = \(\int\limits^b_a {\frac{1}{2}r^2 } \, d\theta\)

where a and b is the boundary at which r=0

so after equation r=0

sin(4θ) =0

=> sin(4θ) =0

=> 4θ = 0,π

=> θ = 0, π/4

so a=0 , b= π/4

now  

  A =  \(\int\limits^b_a {\frac{1}{2}r^2 } \, d\theta\)   ------(i)

so   \(r^2\) = (sin(4θ))^2

=>   \(sin^2\)( 4θ )

ans we know that

cos(2α) = 1 -  \(2sin^2\)2 α

so     \(sin^2\)= (1- cos(8θ) )/2

putting the value of r in the equation (i) we get :-

A = \(\int\limits^b_a {\frac{1}{4} *(1-cos8\theta) } \, d\theta\)

=> 1/4*  \(\int\limits^b_a {(1-cos8\theta) } \, d\theta\)

here a=0 and b=π/4

after putting the value and solving the integral

A = π/16

so A is the area enclosed by r=sin(4θ) is π/16

To know more about polar curve click on below link:

brainly.com/question/1094340#

#SPJ4

Using the quotient rule for differentiation we obtain: the correct answer as option (b) (sin(3t) – 3t cos (3t))/54.

The given function is c(t) = (cos(3t) - 3t)/sqrt(9 + t^2).

Let us use the quotient rule for differentiation to find the derivative of c(t).

Let f(t) = cos(3t) - 3t and g(t) = (9 + t^2)^0.5.

Then, we get;

f'(t) = -3sin(3t) - 3, and g'(t) = t/(9 + t^2)^0.5.

∴ c'(t) = [(g(t) * f'(t)) - (f(t) * g'(t))]/[g(t)]^2

= {[(9 + t^2)^0.5 * [-3sin(3t) - 3]] - [(cos(3t) - 3t) * (t/(9 + t^2)^0.5)]}/[9 + t^2]

∴ c'(t) = (3t cos(3t) - sin(3t))/sqrt(9 + t^2)^3.

Hence, the answer is (sin(3t) – 3t cos (3t))/54.

To know more about quotient rule refer here:

https://brainly.com/question/30278964#

#SPJ11

Answer:

end behavior

Step-by-step explanation:

Answer:

the unit price that required is $30.60

Step-by-step explanation:

The computation of the unit price that required is shown below

For one mile, the cost is

= taxi ride cost ÷ distance covered

= $50.40 ÷ 56

= $0.90

Now for the cost of 34 mile taxi ride

= Unit cost × distance covered

= $0.90 × 34 mile

= $30.60

hence, the unit price that required is $30.60

We simply applied the above formula so that the correct cost could come

The same is to be considered

Ashley used 8/25 of the spool for her project.

To determine the fraction of the spool that Ashley used for her project, we need to multiply the fraction of the spool she had (4/5) by the fraction she used (2/5):

(4/5) * (2/5) = 8/25

Know more about fraction here:

https://brainly.com/question/10354322

#SPJ11

The point of diminishing returns is (20.98, 21247.3).

The point of diminishing returns occurs when the marginal cost of producing an extra unit of output exceeds the marginal revenue generated from selling that unit. Mathematically, it is the point at which the derivative of the production function equals zero and the second derivative is negative.

Given the polynomial function N(x) of degree 3, we can find the point of diminishing returns by finding the critical points where the first derivative equals zero and evaluating the second derivative at those points.

The derivative of N(x) is N'(x) = -18x² + 360x + 2250. To find the critical points, we set N'(x) = 0:

0 = -18x² + 360x + 2250

Dividing by -18 simplifies the equation:

0 = x² - 20x - 125

Using the quadratic formula, we find the solutions to the equation:

x₁,₂ = (20 ± √(20² - 4(1)(-125))) / 2(1)

x₁,₂ = 10 ± 5√5

Thus, the two critical points of N(x) are at x = 10 - 5√5 and x = 10 + 5√5.

To determine the point of diminishing returns, we evaluate the second derivative N''(x) = -36x + 360 at these critical points:

N''(10 - 5√5) = -36(10 - 5√5) + 360 ≈ -264.8

N''(10 + 5√5) = -36(10 + 5√5) + 360 ≈ 144.8

From the evaluations, we find that N''(10 + 5√5) is negative while N''(10 - 5√5) is positive. Therefore, the point of diminishing returns corresponds to x = 10 + 5√5.

To find the corresponding y-coordinate (N(10 + 5√5)), we can substitute the value of x into the original function N(x).

Hence, the point of diminishing returns is approximately (20.98, 21247.3).

Learn more about diminishing returns

https://brainly.com/question/30766008

#SPJ11

Using the mean concept, it is found that LeBron scored 10 more points per game on his last two games than on his first two.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.

For his first two games, he scored 20 + 15 = 35 points, hence the mean is:

35/2 = 17.5 points per game.

For his last two games, he scored 25 + 30 = 55 points, hence the mean is:

55/2 = 27.5 points per game.

The difference is:

27.5 - 17.5 = 10.

On average, LeBron scored 10 more points per game on his last two games than on his first two.

More can be learned about the mean of a data-set at https://brainly.com/question/24628525

#SPJ1