Use the four implication rules to create proof for the following argument.

H ⊃ G

F ⊃ ~G

F /~H

On December 13, 2007, 56.65 dollars is worth 27.77 pounds.

On December 13, 2007, 163.23 pounds is worth  332.99 dollars.

The exchange rate of a currency is the rate at which one currency is exchanged for another currency. There are usually two pairs of currency in an exchange rate. The exchange rate given in these question is: 1 pound = 2.04 dollars. This means that 1 pound would buy 2.04 dollars.

In order to determine the value of pounds given the value of the dollars, this formula would be used:

Value in pounds = value of dollars / exchange rate

56.65 / 2.04 = 27.77 pounds

In order to determine the value of dollars given the value of pounds, multiply the given value of dollars by the exchange rate.

Value in dollars = value of pounds x exchange rate

163.23 x 2.04 = 332.99 dollars

A similar question was answered here: https://brainly.com/question/19437632?referrer=searchResults

The answer is option A. No, there is a good chance that 12 randomly selected adult male passengers will exceed the elevator capacity.

Probability that it is overloaded if 12 adult male passengers have a mean weight greater than 157 lb is 0.0229.Round to four decimal places as needed.Based on the calculations the elevator does not appear to be safe.The solution for the given problem is as follows:

Given that, the maximum capacity of the elevator is 1884 lb - 12 passengers.

We can write as below:

Maximum capacity per person=1884/12=157lb.

And, weights of males are normally distributed with a mean of 165 lb and a standard deviation of 32 lb.Thus, Z = (157-165) / (32 / √12) = -1.7321Then, P(Z > -1.7321) = 0.9586

Hence, the probability that it is overloaded if 12 adult male passengers have a mean weight greater than 157 lb is:P(Z > -1.7321) = 1 - P(Z < -1.7321) = 1 - 0.0229 = 0.9771 (rounded off to 4 decimal places).This probability is greater than 5% and therefore, the elevator does not appear to be safe.

To know more about randomly:

https://brainly.com/question/13319968

#SPJ11

Answer:

Add up the number of chocolate chips and then just search up waht is the median of ____.

Step-by-step explanation:

Hope this helped

Answer:

c=5.87g

Step-by-step explanation:

because you know c is total cost and g is grams. 5.87g would be the cost per gram multiplied by the number of grams you need.

Answer:

height = 2.5 ft , base = 8 ft

Step-by-step explanation:

the area (A) of a triangle is calculated as

A = \(\frac{1}{2}\) bh ( b is the base and h the height )

height = h then base = 2h + 3 and A = 10 , then

\(\frac{1}{2}\) h(h + 3) = 10 ( multiply both sides by 2 to clear the fraction )

h(h + 3) = 20 , that is

h² + 3h = 20 ( subtract 20 from both sides )

h² + 3h - 20 = 0 ← in standard form

(h + 4)(2h - 5) = 0 ← in factored form

equate each factor to zero and solve for h

h + 4 = 0 ⇒ h = - 4

2h - 5 = 0 ⇒ 2h = 5 ⇒ h = 2.5

but h > 0 , then h = 2.5

and 2h + 3 = 2(2.5) + 3 = 5 + 3 = 8

that is height = 2.5 ft and base = 8 ft

Answer:

The measure of the third angle of the triangle is 45°.

Step-by-step explanation:

What is a triangle?

A triangle is a polygon with 3 sides.

Given that, the measures of the two angles of a triangle are 50° and 85°.

Let the measure of the third angle be x.

Since the sum of the interior of a triangle is 180°, it follows,

50°+85°+x=180°

135° +x = 180°

x = 180° - 135°

x = 45°

Hence, the measure of the third angle of the triangle is 45°.

There are 1e-6 cubic meters in a cubic centimeter.

A centimeter is a metric unit of measurement used for measuring the length of an object. It is written as cm. It can also be defined as the unit of length in the International System of Units (SI), the current form of the metric system. It is equivalent to 1/100 meters.

A meter has 100 centimeters.

10 millimeters make one centimeter.

The centimeter can be written as cm.

While calculating the surface area of an object, the unit of measurement becomes cm².

While measuring the volume of an object, the unit of measurement becomes cm³.

Thus, There are 1e-6 cubic meters in a cubic centimeter.

To know more about centimeter visit: brainly.com/question/19098836

#SPJ4

Answer:

x > 15/4

x < 17/2

Step-by-step explanation:

1/4< (2x - 7)/2

1/4 < x - 7/2

1/4 + 7/2 < x

x > 15/4

(2x - 7) / 2 < 5

x - 7/2 < 5

x < 5 + 7/2

x < 17/2

According to the division property of equality, if both sides of an equation are divided by a common real integer that is not zero, the quotients remain equal.

Commutative property, associative property, distributive property, and identity property are the four number properties. Only the algebraic operations addition, subtraction, multiplication, and division are linked with number characteristics.

The four key terminology used in the division process are dividend, divisor, quotient and remainder. Dividend Divisor = Quotient + Remainder is the formula for dividing two numbers.

Commutative property, associative property, distributive property, and identity property are the four number properties. Only the algebraic operations addition, subtraction, multiplication, and division are linked with number characteristics.

For more questions on Division

https://brainly.com/question/28119824

#SPJ4

The distance from the entrance which is located at (-3,7) to the garden at points (3,-2) is \(3\sqrt{13}\).

First, let us understand the distance formula:

The distance formula is the measurement of the distance between 2 points. It calculates the straight line distance between the given points.

The distance formula is given by:

Distance = \(\sqrt{(a-c)^2+(b-d)^2}\)

Where A(a, b) and B(c, d) are the coordinates.

We are given;

The park entrance is located at (-3, 7).

Another point at (3, -2).

We need to find the distance from the entrance to the garden at another given point.

Substitute the given values in the distance formula, we will get;

Distance = \(\sqrt{(a-c)^2+(b-d)^2}\)

Distance = \(\sqrt{(-3-3)^2+(7-(-2))^2}\)

Distance = \(\sqrt{(6)^2+(9)^2}\)

Distance = \(\sqrt{36+81}\)

Distance = \(\sqrt{117}\)

Distance = \(3\sqrt{13}\)

So, the distance between the given points is \(3\sqrt{13}\).

Thus, the distance from the entrance which is located at (-3,7) to the garden at points (3,-2) is \(3\sqrt{13}\).

To learn more about distance formula visit:

https://brainly.com/question/28956738

#SPJ1

Caelan must spend a total cost of $ 17 for 10 bowling games.

The total cost consists in the sum of a fixed cost, represented by rent of shoes, and a variable cost, represented by the number of bowling games, whose model is presented below:

c' = c + r · n

Where:

First, construct the system of equations related to Kai and Jack:

Kai

c + 3 · r = 6.50

Jack

c + 5 · r = 9.50

Second, solve the system of linear equations by numerical methods:

(c, r) = (2, 1.5)

Third, write the resulting function:

c' = 2 + 1.5 · n

Fourth, evaluate the function for the situation of Caelan:

17 = 2 + 1.5 · n

1.5 · n = 15

n = 10

Caelan rents 10 bowling games for $ 17.

To learn more on linear variation models: https://brainly.com/question/25048707

#SPJ1

This result shows that the eigenvalues of A^2 are the squares of the eigenvalues of A, and the eigenvectors of A and A^2 are the same

Let λ be the eigenvalue associated with eigenvector v of matrix A. Then by definition, we have:

Av = λv

Now consider the matrix A^2. We can write A^2 as the product A * A, so we have:

A^2 v = A(Av) = A(λv) = λ(Av)

Note that Av = λv, so we have:

A^2 v = λ(Av) = λ(λv) = λ^2 v

This shows that v is an eigenvector of A^2 with associated eigenvalue λ^2. To see why, note that we have shown that A^2 v is a scalar multiple of v, with the scalar being λ^2. This means that v is an eigenvector of A^2 with associated eigenvalue λ^2.

Therefore, we have shown that if v is an eigenvector of A with associated eigenvalue λ, then v is an eigenvector of A^2 with associated eigenvalue λ^2.

To summarize:

If Av = λv, then A^2 v = λ^2 v.

So, v is an eigenvector of A^2 with associated eigenvalue λ^2.

This result shows that the eigenvalues of A^2 are the squares of the eigenvalues of A, and the eigenvectors of A and A^2 are the same

To know more about eigenvectors refer here

https://brainly.com/question/31013028#

#SPJ11

ABC needs money to buy a new car.

a) ABC can borrow approximately $20500.99 from his friend initially

b) Assuming a payment growth rate of 0.75, ABC can borrow approximately $50139.09

a) To calculate how much ABC can borrow from his friend initially, we can use the present value formula for an annuity:

PV = PMT * [(1 - (1 + r)^(-n)) / r]

Where PV is the present value, PMT is the annual payment, r is the interest rate, and n is the number of years.

In this case, ABC will make annual payments of $5000 in the first year and $8000 for the next four years, with a 7% compounded interest rate.

Calculating the present value:

PV = 5000 * [(1 - (1 + 0.07)^(-5)) / 0.07]

PV ≈ $20500.99

Therefore, ABC can borrow approximately $20500.99 from his friend initially.

b) If ABC's salary is estimated to increase at a rate of 0.75, we need to adjust the annual payments accordingly. The new payment schedule will be $5000 in the first year, $5000 * 1.75 in the second year, $5000 * (1.75)^2 in the third year, and so on.

Using the adjusted payment schedule, we can calculate the present value:

PV = 5000 * [(1 - (1 + 0.07)^(-5)) / 0.07] + (5000 * 1.75) * [(1 - (1 + 0.07)^(-4)) / 0.07]

PV ≈ $50139.09

Therefore, ABC can borrow approximately $50139.09 from his friend initially, considering the estimated salary increase.

To learn more about compound interest visit:

https://brainly.com/question/3989769

#SPJ11

The frequency of oranges in the classroom can be calculated as follows:Frequency of oranges in the classroom = Total number of oranges / Total number of fruits= 16/42 = 0.3809 (rounded to 4 decimal places)Thus, the frequency of oranges in the classroom is approximately 0.3809.

To determine the frequency of oranges in the classroom, we need to calculate the proportion of students who brought oranges out of the total number of students.

First, let's calculate the total number of students:

Total students = Number of students with 2 apples + Number of students with 1 apple and 1 orange + Number of students with 2 oranges

Total students = 9 + 4 + 8 = 21

Next, let's calculate the number of students who brought oranges:

Number of students with oranges = Number of students with 1 apple and 1 orange + Number of students with 2 oranges

Number of students with oranges = 4 + 8 = 12

Finally, we can calculate the frequency of oranges:

Frequency of oranges = Number of students with oranges / Total students

Frequency of oranges = 12 / 21 ≈ 0.5714 (rounded to 4 decimal places)

Therefore, the frequency of oranges in the classroom is approximately 0.5714.

To know more about Frequency,Visit:

https://brainly.com/question/254161

#SPJ11

To determine the frequency of oranges in the classroom, it is important to add up the total number of fruits brought to the classroom. The given information is as follows:

2 Apples: 9 students

1 Apple and 1 Orange: 4 students

2 Oranges: 8 students

Thus, the frequency of oranges in the classroom is approximately 0.2105.

Total number of fruits = 2(9) + 1(4) + 2(8)

= 18 + 4 + 16

= 38 fruit in total

So, total number fruits are 38.

Frequency of oranges = Number of oranges / Total number of fruits

There are 8 oranges brought to class, so the frequency of oranges is:

8 / 38 ≈ 0.2105 (rounded to 4 decimal places)

Hence, the frequency of oranges in the classroom is approximately 0.2105.

To know more about frequency visit

https://brainly.com/question/5102661

#SPJ11

40, 3600/90 =40, is the  complete problem  where 40, 36, and 9 are the, missing numbers.

The problem we dealing with here is related to Algebra which is meant as the department of mathematics that makes a difference in the representation of problems or circumstances within the frame of numerical expressions. It includes factors like x, y, z, and mathematical operations like addition, subtraction, multiplication, and division to create an important numerical expression.

Here we are  asked to  use the digits 9, 6, and 3 in order to solve the problem. Since we know  that we  get 40 when 3600 is divided by 90,

3,600 / 90 = 40

So the number 40 means the result and followed by 3600 and 90.

To know more about algebra refer to the link  https://brainly.com/question/16936619?referrer=searchResults.

#SPJ1

According to the given information 62% of its original price was a dress sold.

A % is a quantity or ratio that, in mathematics, representing a portion of one hundred. A non - dimensional connection between two numbers can be represented in a variety of ways, such as through ratios, fractions, as well as decimals. The sign "%" is frequently put after the number to indicate percentages.

Each dress price = $76

If Original price = $200

Formula = (price difference/ original price)100

Prince deference = 200-76 = $124

In percentage :

\(\left(\frac{124}{200}\right) \times 100\)

= 12400/200

= 62%

Thus the final answer is 62% .

To know more about percentage visit:

https://brainly.com/question/24120406

#SPJ1

Answer:

multiply the first equation by -2, then add them

Step-by-step explanation:

7x+4y=-4         *-2 7x+4y=-4 *-2 = -14x-8y=8

5x+8y=28

-14x-8y=8                       x=-4, y=6

-9x=36

x=-4

7(-4)+4y=-4

-28+4y=-4

4y=24

y=6

Concurrent line segments are those that cross at least three other line segments at the same location.

Concurrent line segments are those that cross at least three other line segments at the same location. In geometry, if two lines intersect at a single point in a plane or higher-dimensional space, they are said to be concurrent. In contrast to parallel lines, they exist. Concurrent lines are those that cross more than one line at the same time through a single point in a plane. The point of concurrency is a location that each of those lines shares. Triangles provide another example where this concurrency characteristic can be observed.

Here,

Concurrent line segments are those where three or more line segments cross each other at the same location.

To know more about concurrent lines,

https://brainly.com/question/23843106

#SPJ4

Answer:

04x=24

Step-by-step explanation:

04x=24

divide both sides by 4 to let x stand alone

04x÷4=24÷4

x=6

Answer:

Okay so what you need to understand first is that this is a line right?

So, ask yourself if you know how to graph this line.

If you do graph it, and because this line has a < less than sign it means you shade down but it also means that any point directly on the line won't be a solution because the line is dashed!

There can be many solutions to this line, but only in the solution area/shaded region. This in on the lower right side of the diagonal line that is crossing from almost 2 x-axis to -4 y- axis on the line!

If you would've shown me the list of ordered pairs I would've been able to select the correct ones.

Answer:

(4,-2) and (5,1)  I took the test

Step-by-step explanation:

Answer:

x=u+k

Step-by-step explanation:

Answer:

x = k+u

Step-by-step explanation:

u = x - k

+k       +k

u + k = x

Hope this helps!

If the marbles of the same color are indistinguishable, the boy can arrange the marbles in a line in 66,660 different ways.

If the marbles of the same color are indistinguishable, we can treat them as identical objects. In this case, we can use combinations to calculate the number of ways the boy can arrange the marbles.

The total number of marbles is 2 red + 6 yellow + 4 green = 12 marbles.

To calculate the number of ways to arrange these marbles in a line, we can use the concept of permutations with repetition. The formula for permutations with repetition is:

P(n; r1, r2, ..., rk) = n! / (r1! * r2! * ... * rk!)

where n is the total number of objects and r1, r2, ..., rk represent the repetition factors for each object.

In this case, the number of ways to arrange the marbles would be:

P(12; 2, 6, 4) = 12! / (2! * 6! * 4!)

Calculating this expression:

P(12; 2, 6, 4) = (12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / (2 * 1 * 6 * 5 * 4 * 3 * 2 * 1 * 4 * 3 * 2 * 1)

Simplifying:

P(12; 2, 6, 4) = 66,660

Therefore, if the marbles of the same color are indistinguishable, the boy can arrange the marbles in a line in 66,660 different ways.

To learn more about expression visit;

https://brainly.com/question/28170201

#SPJ11

To determine if the bolts vary by more than the required variance, we can conduct a hypothesis test. The null hypothesis (H₀) states that the variance of the bolts is equal to or less than the required variance (σ² ≤ 0.025), while the alternative hypothesis (H₁) states that the variance is greater than the required variance (σ² > 0.025).

Next, we need to determine the critical value(s) of the test statistic. Since we are testing for variance, we will use the chi-square distribution. For a one-tailed test with α = 0.01 and 14 degrees of freedom (n-1), the critical value is 27.488.

Now, we can compare the test statistic to the critical value. The test statistic is calculated as (n-1) * s² / σ², where n is the sample size (15), s² is the sample variance (0.1587²), and σ² is the required variance (0.025).

If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the bolts vary by more than the required variance. Otherwise, we fail to reject the null hypothesis.

To learn more about Hypothesis test - brainly.com/question/29996729

#SPJ11

To determine if the bolts vary by more than the required variance, we can conduct a hypothesis test. The null hypothesis (H₀) states that the variance of the bolts is equal to or less than the required variance (σ² ≤ 0.025), while the alternative hypothesis (H₁) states that the variance is greater than the required variance (σ² > 0.025).

Next, we need to determine the critical value(s) of the test statistic. Since we are testing for variance, we will use the chi-square distribution. For a one-tailed test with α = 0.01 and 14 degrees of freedom (n-1), the critical value is 27.488.

Now, we can compare the test statistic to the critical value. The test statistic is calculated as (n-1) * s² / σ², where n is the sample size (15), s² is the sample variance (0.1587²), and σ² is the required variance (0.025).

If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the bolts vary by more than the required variance. Otherwise, we fail to reject the null hypothesis.

To learn more about Hypothesis test - brainly.com/question/29996729

#SPJ11

Using the graph we will see that line q can be written as:

y = (-1/2)*x + 3

Remember that the general linear equation is written as:

y = a*x +b

Where a is the slope and b is the y-intercept.

We know that if the line passes through two points (x₁, y₁) and (x₂, y₂) then the slope is:

a = (y₂ - y₁)/(x₂ - x₁)

Using the graph we can identify the two points (0, 3) and (2, 2), then the slope is:

a = (2 - 3)/(2 - 0) = -1/2

And the y-intercept is y = 3, then the linear equation is:

y = (-1/2)*x + 3

Learn more about linear equations at:

https://brainly.com/question/1884491

#SPJ1

Answer:

y = 26

Step-by-step explanation:

48 = (1/2)(70 + y)

70 + y = 96

y = 26

Let:

x = number we want to find

the sum of a number and 6 is multiplied by 5:

(x + 6)*5

the result is the same as 7 times the number increased by 16. So:

(x + 6)*5 = 7x + 16

Let's solve for x:

Use distributive property on the left hand side:

5x + 30 = 7x + 16

Subtract 5x from both sides:

5x + 30 - 5x = 7x + 16 - 5x

30 = 2x + 16

Subtract 16 from both sides:

30 - 16 = 2x + 16 - 16

14 = 2x

Divide both sides by 2:

14/2 = 2x/2

7 = x

Answer:

The sum of the infinite geometric series can be found using the formula S = a / (1 - r), where 'a' is the first term and 'r' is the common ratio. In this case, the first term 'a' is 16 and the common ratio 'r' is 1/21. Substituting these values into the formula, we have:

S = 16 / (1 - 1/21)

To simplify the expression, we need to find a common denominator:

S = 16 / (21/21 - 1/21)

  = 16 / (20/21)

  = 16 * (21/20)

  = 336/20

  = 16.8

Therefore, the sum of the infinite geometric series 16(1/21)^k is equal to 16.8.

In more detail, we can observe that the given series is a geometric series with a common ratio of 1/21. This means that each term is obtained by multiplying the previous term by 1/21. The first term of the series is 16.

To find the sum of an infinite geometric series, we can use the formula S = a / (1 - r), where 'a' is the first term and 'r' is the common ratio. Substituting the given values into the formula, we get:

S = 16 / (1 - 1/21)

To simplify the expression, we need to find a common denominator for the denominator:

S = 16 / (21/21 - 1/21)

  = 16 / (20/21)

Now, to divide by a fraction, we can multiply by its reciprocal:

S = 16 * (21/20)

  = 336/20

  = 16.8

Hence, the sum of the infinite geometric series 16(1/21)^k is equal to 16.8.

Learn more about series here:

brainly.com/question/12707471

#SPJ11