Can anyone help me solve this problem step by step?

By using the truth table The correct options are (a) The row where both p and q are true, but r is false and (c) The row where p, q and r are all false.

Given, (p ^ r) -> ~(q v p)

Creating truth table:

=> p ^ r will return true if both the values of p and r are true else will return false.

=> q v p will return true if at least one of the values of q or p is true else will return false.

=>~(q v p) will return true if the truth value of q v p is false else will return false.

=>(p ^ r) -> ~(q v p) will return false if truth value of p ^ r is true and truth value of ~(q v p) is false else will return true.

p    q    r      (p ^ r)     (q v p)         ~(q v p)     (p ^ r) -> ~(q v p)

F    F    F         F            F                   T                   T

F    F    T         F            F                   T                   T

F    T    F         F            T                    F                  T

F    T    T         F            T                    F                  T

T    F    F         F            T                    F                  T

T    F    T         T            T                    F                  F

T    T    F         F            T                    F                  T

T    T    T         T            T                    F                  F

=> Option (a) is correct because according to the row number 7 where p = q = T and r = F, the result = T

=> Option (b) is wrong because according to row number 6, where p = q = T and q = F, the result = F

=>Option (c) is correct because according to row number 1, where p = q = r = F the result = T

=>Option (d) is wrong because according to the row number 8 where p = q = r = T the result = F

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The least number of square pieces that Monica can cut from a rectangular cake without wasting any cake is 15 pieces, each 7 inches on a side.

Monica wants to cut a cake into identical square pieces without wasting any cake. To find the least number of square pieces that can be cut from a rectangular cake, we need to find the greatest common divisor (GCD) of the lengths of the sides.

In this case, the GCD of 21 and 35 is 7. This means that we can cut the cake into 7-inch square pieces, and there will be no waste. The number of pieces can be found by dividing each side of the rectangular cake by the side length of the square pieces.

For the 21-inch side, the number of pieces is

21 / 7 = 3

For the 35-inch side, the number of pieces is

35 / 7 = 5

Therefore, the total number of pieces that can be cut from the rectangular cake is

3 * 5 = 15.

In conclusion, the least number of square pieces that Monica can cut from a rectangular cake without wasting any cake is 15 pieces, each 7 inches on a side.

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The minimum amount of glass used for the exterior  615340.84 m ²

We must calculate the lateral area which is given by:

A = (1/2) * pb * Ap

Where,

pb: perimeter of the base

Ap: Apotema

Calculating the apothem we have:

Ap = root ((646/2) ^ 2 + (350) ^ 2)

Ap = 476.27 feet

Calculating the perimeter of the base we have:

pb = 4 * (646)

pb = 2584 feet

Substituting values:

A = (1/2) * pb * Ap

A = (1/2) * (2584) * (476.27)

A = 615340.84 m ^ 2

The minimum amount of glass used for the exterior is:

A = 615340.84 m ²

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Correct question:

The luxor hotel in las vegas is a square base pyramid that is 646 feet wide at the base and 350 feet tall. if the outer walls of the hotel are covered in glass, what was the minimum amount of glass used for the exterior?

Variance is a useful tool for gaining a deeper understanding of a dataset beyond just the mean.

Variance is a measure of how far the individual values in a set of data are from the average value.

The variance is calculated by first finding the difference between each value in the dataset and the mean, squaring these differences, and then averaging the squared differences.

The result is a non-negative number that indicates how far, on average, each value deviates from the mean. If the variance is small, it means that most of the values are close to the mean, while a large variance indicates that the values are widely spread out.

One important use of variance is in statistical inference, where it is used to make predictions about a population based on a sample of data. Variance also plays a role in hypothesis testing, where it is used to determine whether the differences between two sets of data are statistically significant.

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A shape must cross a line in order to be reflected.

Because a reflection across BA will map ABC to ABD, the true statement is (c).

A translation only moves a shape up, down, or from side to side; it has no effect on how it appears. An illustration of a transformation is translation. A transformation is a technique for moving or repositioning a shape.

here, we have,

Sides AC and AD of both triangles are congruent

Sides BD and BC of both triangles are congruent

The triangles share a common side AB

This means that a reflection over line AB will map both triangles.

Hence, the true statement is (c)

The complete question is given below.

Is there a rigid transformation that maps triangle ABC to triangle ABD? If so, which transformation?

yes, because a translation to the right will map ΔABC to ΔABD

yes, because a rotation about point B will map ΔABC to ΔABD

yes, because a reflection across BA will map ΔABC to ΔABD

no, because no rigid transformation will map ΔABC to ΔABD

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The probability of the value of p(a ∩ bc ) is 1/54

Probability is a mathematical measure of how likely an event is to occur.

Given that p(a ∪ b) = 2/3, which means the probability of either event a or event b happening is 2/3, we can find the probability of a and b happening simultaneously using the formula for conditional probability.

=> p(a ∩ b) = p(a | b) * p(b) = 1/12,

where p(a | b) is the probability of event a happening given that event b has already happened. We can use this information to find p(b) as follows:

=> p(b) = p(a ∩ b) / p(a | b) = 1/12 / p(a | b)

We also know that p(b ∩ ac) = 1/3, which means the probability of both events b and ac happening is 1/3. We can use this information to find p(b) and p(a | b).

=> p(b) = p(b ∩ ac) / p(ac | b) = 1/3 / p(ac | b)

Finally, using the formula for conditional probability, we can find p(a ∩ bc) as follows:

p(a ∩ bc) = p(a | bc) * p(bc) = p(a | b) * p(b | bc) * p(bc) = p(a | b) * p(b) * p(bc | b) * p(bc)

p(a ∩ bc) = 2/3 * 1/12 *1/3 = 1/54

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Each month, you must pay $400 toward the balances on these two credit cards. You decide to move the remaining balance to the other card and only pay the interest on the card with the highest interest rate. Fill out the following two tables to help you respond to questions 1-3.

In its most basic form, interest is computed as a percentage of the principle. The interest you would pay, for instance, would only be 5% of $100 if you borrowed $100 from a friend and agreed to reimburse it with 5% interest: $100(0.05) = $5.

Card Name (APR %) Existing Balance Credit Limit

MarK2 (6.5%) $475.00 $3,000.00

Bee4 (10.1%) $1,311.48 $2,500.00

Savings vs. Debt Portfolio

You must pay off these two credit cards with $400 each month. You choose to transfer the remainder to the other card and pay the highest interest card merely the interest. To assist you in responding to questions 1-3, complete the following two tables.

Higher-Interest Card (Payoff Option)

Month 1 2 3 4 5 6 7 8 9 10

Principal 1311.48 1074.82 814.26 527.38 211.53      

Interest accrued 132.46 108.56 82.24 53.27 21.36      

Payment (on due date) 369.12 369.12 369.12 369.12 232.89      

End-of-month balance 1074.82 814.26 527.38 211.53 0      

Lower-Interest Card

Month 1 2 3 4 5 6 7 8 9 10

Principal 475 475 475 475 475 338.77    

Interest accrued 30.88 30.88 30.88 30.88 30.88 22.02    

Payment (on due date) 30.88 30.88 30.88 30.88 167.11 360.79  

End-of-month balance 475 475 475 475 338.77 0    

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The value of the energy E when m=6kg and v=2ms-1​ is;  E = 12 Joules

We are told that the energy E is possessed by a moving object that varies directly as the mass of m and the square of velocity V. Thus, this can be expressed as;

E = kmV²

Where k is the constant of variation

Thus,  when m= 8kg, v=5ms-1 and e =100 joules, we have;

100 = k * 8 * 5²

k = 100/(8 * 5²)

k = 0.5

Thus, when m=6kg and v=2ms-1​, we have;

E = 0.5 * 6 * 2²

E = 12 Joules

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1. After 32 minutes the two pools will have the same amount of water.
2. 2,280 liters of water will be in each pool when they have the same amount.

Let's call the time in minutes when the two pools have the same amount of water "t". Getting into variables here.

At time t, the first pool will have 1272 + 31.5t liters of water, and the second pool will have 1600 + 21.25t liters of water.

For the two pools to have the same amount of water, we need:

1272 + 31.5t = 1600 + 21.25t

10.25t = 328

t = 32 minutes

I underlined all the answers if you don't want to read the entire thing, lol.

Question 1: So, 32 minutes after starting, the two pools will have the same amount of water.
Question 2: The amount of water in each pool will be:

1272 + 31.5 * 32 = 1600 + 21.25 * 32 = 1600 + 680 = 2,280 liters.

For the function f(x) = tan(x) , the option that cannot be an Asymptote is (a) x = 5π .

An Asymptote is a straight line or curve that a graph approaches but never touches as the input values become larger or smaller.

In mathematical terms, as x approaches positive or negative infinity, the value of the function approaches a fixed constant value or the value of an asymptote.

The function is f(x) = tan(x) ,

the tangent function do not have any horizontal asymptote , and

the vertical asymptotes of tangent function is multiple of π/2 .

the asymptotes of a tangent function are x = π/2 + πn .

From the formula , we can say that it is not possible for the tangent function to have an integer asymptote .

Therefore , (a) x = 5π is not an asymptote of f(x) = tan(x)  .

The given question is incomplete , the complete question is

Which of the following is NOT an asymptote of the function f(x) = tan(x) ?

(a) x = 5π

(b) x = -4.5π

(c) x = -0.5π

(d) x = -3.5π  .

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Answer:

The answer could be x * 33 + 30.

Step-by-step explanation:

In this expression, the parentheses indicate that 14 and 19 are to be added together first, which equals 33. The expression x * 33 means that 33 is being multiplied by x. Finally, 30 is being added to this product. So both expressions represent the same mathematical operation.

Here's how to check our answer:

First, we simplify the expression inside the parentheses:

x(33) + 30

Next, we multiply x and 33:

x * 33 + 30

Finally, we add 30 to the product of x and 33:

x * 33 + 30

So, the expression x * 33 + 30 is equivalent to the expression x(14 + 19) + 30.

I would greatly appreciate Brainliest.
Have a nice day.

x(14+19)+ 30 =

     33   +  30

33x+30

One possible solution is to define f(x) as the average of g(x) and h(x), which would be: f(x) = (g(x) + h(x)) / 2

The function g(x) = 1x^2 - 4x + 5 and the function h(x) = 2x^2 - 8x + 10x^2 - 4x + 6 are quadratic functions. To find a function f(x) that satisfies the inequality g(x) ≤ f(x) ≤ h(x) for all x >= 0, we need to find a function that lies between these two functions for all x >= 0.

One possible solution is to define f(x) as the average of g(x) and h(x), which would be: f(x) = (g(x) + h(x)) / 2

The intuition behind this choice is that if f(x) is the average of g(x) and h(x), it should be located between these two functions for all x >= 0. To confirm this, we can graph g(x), h(x), and f(x) on the same coordinate plane and see if they satisfy the inequality.

It's important to note that this solution is just one possible choice and there may be other functions that satisfy the inequality g(x) ≤ f(x) ≤ h(x) for all x >= 0.

Therefore, One possible solution is to define f(x) as the average of g(x) and h(x), which would be: f(x) = (g(x) + h(x)) / 2

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The number of color sequences possible when removing five balls one at a time depends on the number of different colors the balls have.

If there are C different colors, the number of color sequences possible is C^5 (C raised to the power of 5), since for each ball you remove, you have C options for its color.

The number of combinations of colors possible when removing five balls one at a time is given by the binomial coefficient "C choose 5", which represents the number of ways to choose 5 balls out of C different balls, ignoring the order in which they are chosen.

The binomial coefficient can be calculated as:

C choose 5 = C! / (5! * (C-5)!).

Here, "!" denotes the factorial symbol, which is the product of all positive integers up to that number (e.g. 5! = 5 * 4 * 3 * 2 * 1 = 120).

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Any pair of real numbers or algebraic expressions that are equivalent by the symbols ‘<’, ‘>’, ‘≤’ or ‘≥’ constitute an inequality.

A mathematical concept used to compare quantities is inequality. By highlighting the area that the inequality pertains to, we can graph the inequality on a number line.

Let's examine the number line graphing of inequality. Look at the illustration below, which shows the following disparities on a number line:

x ≥ 5, x > 5, x ≤ 5, and x < 5.

It should be noticed that if the inequality indicates that a certain number is included, we mark a filled circle on that specific number; nevertheless, if the inequality indicates that a certain number is excluded, we mark an empty circle on the number.

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Answer:

unlikely

Step-by-step explanation:

25% of the cookies are chocolate chip, so the other 75% would be oatmeal raisin and sugar cookies. 0.25 is equal to 25%, so it is unlikely you will get a chocolate chip cookie.

The amount of money that she has to pay per month, next year in rent will be $736.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

Lian currently pays 640 per month to rent her apartment she has been told by her landlord that her rent will be increasing by 15% next year.

Then the amount is given as,

A = $640 x (1 + 0.15)

A = $640 x 1.15

A = $736

The amount of money that she has to pay per month, next year in rent will be $736.

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Answer: D. 2w + 2(2w+3) = 96

Step-by-step explanation:

Perimeter = 2l + 2w

l = 2w + 3

Plug l into the perimeter equation

Perimeter = 2w + 2(2w+3)

Perimeter = 96

96 = 2w + 2(2w+3)

If you want to simplify, w = 22.5

The helix r(t) = (cos(πt/2), sin(πt/2), t) intersects the sphere x² + y² + z² = 2 in two points and the angle of intersection at every point is 0°.

Let's assume that the central axis of the helix is z

Given r(t) = (cos(πt/2), sin(πt/2), t)

Put this point in the sphere equation

cos²(πt/2) + sin²(πt/2) + t² = 2

                                 1 + t² = 2

                                      t² = 1

                                       t = +1, -1

Now, let f = x² + y² + z² - 2

Δf = (fx, fy, fz)

Δf = (2x, 2y, 2z)

At (cos(πt/2), sin(πt/2), t), Δf = (2cos(πt/2), 2sin(πt/2), 2t)

Angle of intersection at t = 1

Δf = (0, 2, 2) and r = (0, 1, 1)

Using dot product:

                           cosθ = (0, 2, 2).(0, 1, 1)/ √(2² + 2²) √(1² + 1²)

                           cosθ = 1

                                 θ = 0°

Angle of intersection at t = -1

Δf = (0, -2, -2) and r = (0,-1, -1)

Using dot product:

                           cosθ = (0, -2, 2-).(0, -1, -1)/ √((-2)² + (-2)²) √((-1)² + (-1)²)

                           cosθ = 1

                                 θ = 0°

Hence, the angle of intersection at every point is 0°

The given question is incomplete. The complete question is

"The helix r(t) = (cos(πt/2), sin(πt/2), t) intersects the sphere x² + y² + z² = 2 in two points. Find the angle of intersection at each point."

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The Shipping Company Cost, y=$(5.75+0.31x) is a linear function that determines the cost of shipping based on weight.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here, we have,

A shipping company charges a $5.75 handling fee in addition to $0.31 per pound to ship a package.

Using X for the weight in pounds and for the cost of shipping in dollars

Let the number of pounds being shipped=x

Shipping Company charges $5.75 plus an additional $0.31 per pound to ship a package.

Shipping Company Cost =  $5.75 + ($0.31 X Number of Pounds)

Shipping Company Cost,  y=$(5.75+0.31x)

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You first have to find 5% of 200,000gbp in order to find the value of the house for the year 2015.

200,000 x 5/100 = 10,000

Therefore by 2015 the house's value was= 200,000 + 10,000= 210,000

however, you cannot keep adding 10,000 thrice over to find the value of the house for the year 2017 as the amount the value increases by each year will change as it is a percentage difference

value for 2016,

210,000x5/100=10,500

Therefore by 2016 the house's value was= 210,000 + 10,500= 220,500

value for 2017,

220,500x5/100=11,025

Therefore by 2017 the house's value was= 220,500 + 11,025= 231,525gbp

Answer:

You first have to find 5% of 200,000gbp in order to find the value of the house for the year 2015.

200,000 x 5/100 = 10,000

200,000+10,000+10,000+10,000=231510

Amount it has increased: 11,025

Step-by-step explanation:

The number of ways in which the prizes are allocated is 67,525.

Combinations are the various ways in which objects from a set may be selected, generally without replacement, to form subsets.

Given that

Number of customers = 75

Number of prizes = 3

And, the value of the gift card = $10

Based on the above information,

The number of ways in which the prizes are allocated is shown below:

=⁷⁵C₃

=[tex]\frac{75!}{(3!*(75-3)!}[/tex]

After solving this the number of ways that came is 67,525

Hence, the number of ways in which the prizes are allocated is 67,525

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If Jim's credit card statement shows a previous balance of $937.20, and he made a payment of $730 and add a new transaction of $502, if his credit card Annual Percentage Rate (APR) is 15%, then his new balance is $1699.20.

To calculate the new balance, the following steps were taken:

Add the previous balance ($937.20) to the new transaction amount ($502.00) to find the current balance before finance charges

$937.20 + $502.00 = $1439.20

Calculate the finance charges by dividing the annual percentage rate (APR) which is 15% by the number of billing periods in a year (usually 12) and then multiplying the result by the average daily balance.

finance charges = (15% / 12 months) × $1439.20

finance charges = $17.49

Add the finance charges to the current balance before finance charges to find the new balance:

$1439.20 + $17.49 = $1656.69

Finally, subtract the payment amount ($730) from the new balance ($1656.69) to find the updated balance:

$1656.69 - $730 = $1699.20.

Therefore, Jim's new balance is $1699.20.

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The cumulative frequency is the running total of the frequency; each value in the cumulative frequency column is the sum of the previous and current frequency values.

From the data on the number of children, the following can be calculated:

Table of Frequency:

No. of Children | Frequency 0 | 1 2 | 2 3 | 2 4 | 2 5 | 1

Table of Relative Frequency:

Children | Frequency | Relative Frequency 0 | 1 | 1/9 2 | 2 | 2/9 3 | 2 | 2/9 4 | 2 | 2/9 5 | 1 | 1/9

Table of Cumulative Frequency:

Child Count | Frequency | Cumulative Frequency

0 | 1 | 1 \s2 | 2 | 3 \s3 | 2 | 5 \s4 | 2 | 7 \s5 | 1 | 8

Because the cumulative frequency is the frequency's running total, each value in the cumulative frequency column is the sum of the previous and current values in the frequency column.

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When 5 winners are randomly selected, the probability that they are all men is 0.0045

Among the contestants in a competition are 45 women and 25 men.

Total persons are = 45+25 = 70

When one winner is chosen, there are 69 people left, when second winner is chosen there are 68 people left and so on.

So, the probability that they are all men is given by:

25/70 *24/69 * 23/68 * 22/67 * 21/66 = 0.0045

Therefore, when 5 winners are randomly selected, the probability that they are all men is 0.0045-

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A heptagon is a seven-sided polygon. It is also sometimes called a septagon, though this usage mixes a Latin prefix sept- (derived from septua-, meaning "seven") with the Greek suffix -gon (from gonia, meaning "angle"), and is therefore not recommended.

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Let's call the amount of sugar needed to make 200 grams of 15% sugar syrup "s".

From the information given, we know that 15% of the syrup is sugar, so 200 grams * 15% = 200 grams * 0.15 = 30 grams of the syrup is sugar.

Therefore, the amount of sugar needed is equal to 30 grams, or s = 30 grams.

The range of the graph is -4 ≤ y ≤ 2.

Option C is the correct answer.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

A coordinate plane with a segment going from the point (-3, 2) to (0, 1) and another segment going from the point (0, 1) to (5, -4).

This means,

(-3, 2) to (5, -4)

The range of the graph is the y-coordinate.

So,

-4 to 2

This can be written as,

-4 ≤ y ≤ 2

Thus,

The range is -4 ≤ y ≤ 2.

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The exponential function for the given  data will be y = 5 * [tex]e^{2*7}[/tex]

What is exponential?

The exponential is an example of a mathematical function that is useful in determining if something is increasing or decreasing exponentially is the exponential function. As implied by its name, an exponential function uses exponents. But take note that an exponential function does not have a variable as its exponent and a constant as its base (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function).

Given population is = 5(now)

The time = 7years

r = 2

Exponential growth equation:

N₁ = No e¹t

Where,

N= Population density after time t

N+= Population density at time zero

r = Intrinsic rate of natural increase

e = Base of natural logarithms (2.71828)

So the exponential expression will be y = 5 * [tex]e^{rt}[/tex]

y = 5 * [tex]e^{2*7}[/tex]

Hence, The exponential function for the given  data will be y = 5 * [tex]e^{2*7}[/tex]

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