For each equation, choose the statement that describes its solution.If applicable, give the solution.-6(u+1)=2(1-3u)-8

The prove that the modus ponens is a valid argument form in correct order is

The complete question is given below:

1. ~p V -(p = q) Vq = (Tp Vq) v-(Tp V q)

2. Since the disjunction of an expression and its negation is always true, Zp V q) v-(-p V q) is a tautology: This completes the proof:

3. ~(p ^ (p + 9)) Vq =-pV (p + 9) Vq 10

4. Using the rule p 7 q =7p V 4, we rewrite the given expression as 12

5. ~(p ^ (p = 4) Vq =-pv-Wpv 9)Vq

6. To prove the validity of the modus ponens, we need to show that (p 5 9) 5 4 is a tautology:

7. We now reorder and re-associate the terms of the last expression by using the associative and commutative laws and apply the rule p v q = 7pV q again: N

8. To prove the validity of the modus ponens; we need to show that (p ^ (p 7 74 is a tautology:

9. (p v q) - 4=-pv 9Vq

10. Using the rule p 4 q =7p ^ q, we rewrite the given expression as 13

11. By the domination law; the last expression is always true: This completes the proof: 11

12 Zp V-(p - 9) Vq = (~p V 9) ^ -(-p V9)

13. We now use one of the rules of De Morgan:

14. (p ^ (p = 9)) - q =-(p ^ (p = 9)) V q

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The correct answer is:

a = 43%

b = 88%

To determine the values of a and b in the relative frequency table, we need to analyze the information provided in the Venn diagram and the given table.

From the Venn diagram, we can gather the following information:

The circle labeled "satellite" has a value of 55.

The circle labeled "cable" has a value of 75.

The overlap between the two circles is labeled as 12.

Using this information, we can complete the table:

First column - "Satellite":

Entries: Satellite, Not satellite, Total

Total: 55 (as given in the Venn diagram)

Second column - "Cable":

Entries: Blank, 51%, Blank

To find the value for the "Cable" entry, we need to subtract the overlap (12) from the total number of cable users (75).

Cable: 75 - 12 = 63

Therefore, the entry becomes: Blank, 51%, Blank

Third column - "Not Cable":

Entries: a, b, Blank

To find the value for "a," we subtract the overlap (12) from the total number of satellite users (55).

a: 55 - 12 = 43

To find the value for "b," we subtract the overlap (12) from the total number of households (100).

b: 100 - 12 = 88

Therefore, the entries become: 43, 88, Blank

Fourth column - "Total":

Entries: Blank, Blank, 100%

The total number of households is given as 100% (as stated in the question).

Therefore, the values of a and b in the relative frequency table are:

a = 43% (rounded to the nearest percent)

b = 88% (rounded to the nearest percent)

Hence, the correct answer is:

a = 43%

b = 88%

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When it comes to interest, most Certificates of Deposit (CDs) will allow periodic interest payouts. So, correct option is B.

A CD is a type of savings account that allows you to earn a fixed interest rate on your deposit for a specific period of time, called the term. Typically, the longer the term of the CD, the higher the interest rate offered.

However, during the term of the CD, the funds are locked in, meaning that you cannot withdraw the principal without incurring a penalty.

While some CDs may allow for unlimited withdrawals of interest, this is not common, and may still come with restrictions or penalties. Loans against principal are also not typically allowed with CDs, as the funds are meant to be held for a set term.

Therefore, the most common option available for CD holders is to receive periodic interest payouts, which can be monthly, quarterly, or annually, depending on the terms of the CD. This allows the CD holder to earn interest on their deposit while still receiving some income during the term of the CD.

So, correct option is B.

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The cost of the 28 inches and 36 inches diagonal Smart TVs, based on the quadratic cost function are;

28 - inch diagonal; $134

36 - inch diagonal; $165

A quadratic function is a function of the form f(x) = a·x² + b·x + c, where a ≠ 0, and a, b, and c are numbers.

The cost of the Smart TV as a function of the diagonal length is C(d) = 0.322·d² - 16.776·d + 351.444

The above function indicates that the cost of a Smart TV that is 28 inches long is; C(28) = 0.322 × 28² - 16.776 × 28 + 351.444 ≈ 134

The cost of a Smart TV with a diagonal of 36 inches is therefore;

C(36) = 0.322 × 36² - 16.776 × 36 + 351.444 ≈ 165

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The two column proof showing that  ΔWXZ ≅ ΔYXZ is as shown below

From the given triangle, we see that;

Given: WX ≅ XY, XZ bisects WXY

Prove: ΔWXZ ≅ ΔYXZ

The two column proof for the above is as follows;

Statement 1;  WX ≅ XY, XZ bisects 2

Reason 1; Given

Statement 2: ∠WXZ ≅ YXZ

Reason 2; Angle bisector

Statement 3; XZ ≅ XZ

Reason 3: Reflexive property of congruence

Statement 4:  ΔWXZ  ≅ ΔYXZ

Reason 4:  SAS Congruence Postulate

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Answer:

180 gallons of water

Step-by-step explanation:

4×6×1=24

24×7.5=180

Hope this helps!

Answer:

\(x=-\dfrac{44}{7}\)

\(y=\dfrac{58}{7}\)

Step-by-step explanation:

Arrange the equations so that all the variables are in columns (x as the first column, y as the second, equals a number as the third):

-11x - 4y = 36

5x + 5y = -10

Define and edit Matrix A.  We need a 3 x 2 matrix.  Input the coefficients and constant:

\(\left[\begin{array}{ccc}-11&-4&36\\5&5&-10\end{array}\right]\)

Find rref function, enter matrix A:  rref([A])  (press enter)

This gives you:

\(\left[\begin{array}{ccc}1&0&-\frac{44}{7}\\0&1&\frac{58}{7}\end{array}\right]\)

which means:

\(x=-\dfrac{44}{7}\)

\(y=\dfrac{58}{7}\)

There is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.

To find the probability that a box of cereal is underfilled by 5 g or more, we need to calculate the probability of obtaining a weight measurement below 345 g.

First, we can standardize the problem by using the z-score formula:

z = (x - μ) / σ

Where:

x = the weight value we want to find the probability for (345 g in this case)

μ = the mean weight (350 g)

σ = the standard deviation (4 g)

Substituting the values into the formula:

z = (345 - 350) / 4 = -1.25

Next, we can find the probability associated with this z-score using a standard normal distribution table or a statistical calculator.

The probability of obtaining a z-score less than -1.25 is approximately 0.1056.

However, we are interested in the probability of underfilling by 5 g or more, which means we need to find the complement of this probability.

The probability of underfilling by 5 g or more is 1 - 0.1056 = 0.8944, or approximately 89.44%.

Therefore, there is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.

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The unit rate of change (slope) from 1996 to 2016 is -.025

What is Ratio?

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all. Any two different points on a line can be used to calculate the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula. A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, m = y/x, where m is the slope, can be used to express the change in the y coordinate with regard to the change in the x coordinate.

Take notice that tan = y/x.

The given problem is about the decrease of two variables, which represent years and represent video rental.

The ratio here refers to the slope of the linear decreasing behavior, where pairs are (1996,9) and (2016, 4).

The formula for the slope is

\(&m=\frac{y_2-y_1}{x_2-x_1}\)

So, In the given question, we have:

10 video rental locations in 1996;

So,  Assuming a constant decrease in the number of stores:

The slope or the unit rate of change from 1996 to 2016 is:

\(\begin{aligned}&m=\frac{y_2-y_1}{x_2-x_1}=\frac{4-9}{2016-1996}=\frac{-5}{20}=-\frac{1}{4} \\&m=-0.25\end{aligned}\)

So, The Value of the Slope is -0.25

This means that the linear relation decreases, with a constant ratio of 0.25, that is, video rental decreases one per 4-years periods.

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Answer:

The perimeter should be 49 centimeters

Step-by-step explanation:

You're just adding up the centimeters that are stated in the question and then just putting the number there in the answer

The solution is, in PRYZ square, the value of m∠YKZ = 90.

A square is a regular quadrilateral, which means that it has four equal sides and four equal angles. It can also be defined as a rectangle with two equal-length adjacent sides.

here, we have,

Remember that

In a Square

All sides are equal

Diagonals bisect each other perpendicularly

so

Find out KY

In the right triangle RYK

Applying the Pythagorean Theorem

RY^2=RK^2+KY^2

substitute given values

13^2=5^2+KY^2

KY^2=13^2-5^2

KY^2=144

KY=12

Find out PK

Remember that

Diagonals bisect each other perpendicularly

that means

PK=KY=12

Remember that

Diagonals bisect each other perpendicularly

so, that means

m∠YKZ = 90

Hence, The solution is, in PRYZ square, the value of m∠YKZ = 90.

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A circle is 360 degrees so 360 = b + 96 + 209

360 = b + 305

b = 55 degrees.

If the train travels at an average speed of 50 Km/h, it would be late by 10 minutes.

Speed is simply referred to as distance traveled per unit time.

It is expressed as:

Speed = distance / time

Given that the train running between two stations 50 Km apart arrives on time if it travels at an average speed of 60 km/h.

The time taken by the train to travel 50 km at an average speed of 60 km/h can be calculated using the formula:

Speed = distance / time

time = distance / speed

time = 50 km / 60 km/h

time = 5/6 hour

Next, if the train travels at an average speed of 50 km/h, the time taken to cover the same distance of 50 km would be:

Speed = distance / time

time = distance / speed

time = 50 km / 50 km/h

time = 1 hour

Now, the difference in time between the two scenarios would be:

time difference = 1 hour - 5/6 hour

time = 1/6 hour

Convert to minutes

time = 1/6 × 60

time = 10 minutes

Therefore, the train would be late by 10 minutes.

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Answer:

$5.30

Step-by-step explanation:

If she plans to tip the 20%. Then the amount of tip will be $5.3.

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

Charissa is eating out with friends, and it is her turn to pay the gratuity. The bill for the food is $26.50.

If she plans to tip the 20%. Then the amount of tip is given as,

Amount of tip = 20% of $26.50

Amount of tip = 0.20 x 26.50

Amount of tip = $5.3

If she plans to tip the 20%. Then the amount of tip will be $5.3.

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Answer:

1

Hope that helps.

Answer:

1

Step-by-step explanation:

16/16=1

Hope this helps, if you have any questions, feel free to ask

Have a good day! :)

Answer:

thanks !!

Step-by-step explanation: have a wonderful day :)

Answer:

Thank you!!

Step-by-step explanation:

Have a great day:)

The system has the following solution: \(x_1=-4,\ x_2=3,\ x_3=1\). The vector xequals can be used to represent the answer.

A statement in mathematics demonstrating the equality of two expressions is called an equation. Two phrases with the same value are normally separated by the equals sign (=). Finding the area of a circle and predicting planetary motion are only two examples of the many practical issues that equations are used to address.

The linear system's augmented matrix, which is determined by the matrix equation A x = b is given by:

Aequals

\(\left[\begin{array}{ccc}1&-3&4\\2&-3&2\\-3&3&4\\-7&15&-4\end{array}\right]\)

Part 2:

Aequals

Write the system's solution as a vector after solving it.

We can use Gaussian Elimination to solve this system.

Step 1:

\(\left[\begin{array}{ccc}1&1&0\\2&-1&1\\-3&0&1\\-7&8&3\end{array}\right]\)

Step 2:

Aequals

\(\left[\begin{array}{ccc}1&0&0\\0&1&0\\3&1&0\\-4&3&1\end{array}\right]\)

The system's solution is \(x_1=-4,\ x_2=3,\ x_3=1\). The vector xequals represents the answer.

The matrix is,

\(\left[\begin{array}{ccc}-4\\3\\1\end{array}\right]\)

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The graph of the given function is attached.

Given is a function for the rainfall in 5 months in inches.

We need to display the data,

So, as we can see that the data is not showing any proportion or pattern,

So, it can be displayed as a line chart.

Hence the chart is attached for the function.

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a) The claim is given as follows:

\(\mu < 122\)

b) The null and the alternative hypothesis are given as follows:

The claim in this problem is given as follows:

The mean systolic blood pressure of all healthy adults is less than 122 mm Hg.

Symbolically, the claim is given as follows:

\(\mu < 122\).

As:

At the null hypothesis, it is tested if there is not enough evidence to conclude that the claim is true, that is, not enough evidence to conclude that the mean systolic blood pressure of all healthy adults is less than 122 mm Hg, hence:

\(H_0: \mu \geq 122\).

At the alternative hypothesis, it is tested if there is enough evidence to conclude that the claim is true, that is, enough evidence to conclude that the mean systolic blood pressure of all healthy adults is less than 122 mm Hg, hence:

\(H_1: \mu < 122\).

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Answer: w=6

Step-by-step explanation: 1. Simplify. Distribute the -4 to the w and the -3. -4*w is -4w and -4*-3 is +12, so your left with 3w-4w+12=6.

2. simplify again. 3w-4w is -w.

3. -w+12=6. Subtract w to both sides, so its -w=-6. The negatives cancel out, so w just equals 6.

Step-by-step explanation:

follow the steps to get answer

Answer:

Q = (1, -5)

Step-by-step explanation:

Reflection over x-axis (x,y) → (x,-y)

B = (1,5)

Q = (1,-5)

71 poles are needed to fence the rectangular field.

What are the dimensions of the rectangle?

A rectangle is a two-dimensional shape with four sides that has opposite sides that are parallel and equal in length. The length and width of a rectangle are its dimensions. The sides that are equal in length are called the "long sides" or "length," and the sides that are shorter are called the "short sides" or "width."

The total length of the fence required to enclose the rectangular field is the sum of the lengths of all four sides. To find this, we multiply the length and width of the field and then add twice:

Total length = 2 * (63.9m + 104.6m) = 2 * 168.5m

Next, we need to determine the number of poles required to fence the rectangular field. To do this, we divide the total length by the maximum distance between poles (2.4m):

Number of poles = Total length / 2.4m

= 168.5m / 2.4m

= 70.21 poles

Since we can't have a fractional number of poles, we round up to the nearest whole number. This means that we need at least 71 poles to fence the rectangular field.

Hence 71 poles are needed to fence the rectangular field.

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Step-by-step explanation:

We have to find the distance the jogger must travel each minute. The distance covered in one minute is:

d= 3528/1800= 1.96 m

Therefore, the distance covered in one minute, or 60 seconds is:

dt= 1.96 × 60 = 117.6 m

The solution needed is, dt=588/5 = 117 (3/5) m

Carlos's score in his first game was 14.

Addition in maths, a process of combining two or more numbers.

Given that, Carlos scored a total of 60 points in his last three basketball games. be improved in each game by scoring 6 more points than in the previous game.

Let the first score be x,

x+x+6x+6+6=60

3x+18 = 60

3x = 42

x = 14

Hence, Carlos's score in his first game was 14.

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2 is the coefficient  

Answer:

To locate the number 8 and its opposite on the number line, we can use the given number line:

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

Number 8 is located to the right of zero. Its opposite can be found by moving an equal distance to the left of zero. Since the number line is symmetric about zero, the opposite of 8 would be -8.

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

↑ ↑

So, the opposite of 8 is -8. They are related to zero as equal distances on opposite sides of zero on the number line.

Now, let's address exercises 2-3:

a. To locate the opposite of 9, we need to move an equal distance to the left of zero. The opposite of 9 is -9.

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

↑

b. To locate the opposite of -2, we need to move an equal distance to the right of zero. The opposite of -2 is 2.

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

↑

c. To locate the opposite of 4, we need to move an equal distance to the left of zero. The opposite of 4 is -4.

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

↑

So, the opposites of the given numbers are:

9 → -9

-2 → 2

4 → -4

They are related to zero as equal distances on opposite sides of zero on the number line.

Step-by-step explanation:

Answer: 26 years old

Step-by-step explanation:

Since Scott is four more than double the age of Todd, start by taking away four from Scott's age.

56-4=52

Then take half of that because that would be double of Todd's age

52/2=26

Todd is 26 years old.

Answer:

Before a variable there is no coefficient.

There is an invisible 1 infront bc there is no real number. so the 1 appears.