Suppose x, y, z > 1 and integers, let :
p(x, y): x is a factor of y,
q(x, y, z): z = GCF(x, y), and
r(x): x is prime.
Check if the following argument is valid or not.
(∀x)(∃y)(p(x, y) ⇒ r(x)), (∀x)(∀y)(∀z)(¬q(x, y, z)), (∃x)(∀y)(p(x, y) ∨ r(x)).
Therefore, (∀y)(∃z)(∃x)q(x, y, z).

Answer:

0, -2.5

Step-by-step explanation:

First find the latitude coordinate (N-S)

=0

2nd find the longitude coordinate (W-E)

=-2.5

since it's between -3 and -2, we'll put a decimal 5 (.5)

The  vector-valued function is continuous at t=2,

are

A vector-valued function, is described as a mathematical function of one or more variables whose range is a set of multidimensional vectors or infinite-dimensional vectors.

We are required  to check if the limit of the function as t approaches 2 exists and is equal to the value of the function at t=2, in order to determine if the  vector-valued function is continuous at t=2.

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The cost for a new customer to rent a bay for 6 hours at Top Golf is $22, which includes a $10 player card fee and a $12 bay rental fee at $2 per hour.

Let's let "x" be the total cost for a new customer to rent a bay for 6 hours.

We know that there is a flat fee of $10 for the player card, and then an additional $2 per hour for the bay rental.

So, the equation for the cost "x" can be written as

x = 10 + 2(6)

The expression 2(6) represents the cost of the bay rental for 6 hours. We can simplify the expression by multiplying 2 and 6, which gives us

x = 10 + 12

Now, we can combine like terms to find the final cost

x = 22

Therefore, the cost for a new customer to rent a bay for 6 hours at Top Golf is $22.

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--The given question is incomplete, the complete question is given

" For a new customer top golf charges $10 for a player card and $2 per hour. Write and solve a linear equation to find the cost for a new customer to rent a bay for 6 hours."--

b) By basing on the findings in part (a), we rejected the null hypothesis. This implies that a Type I error – which is the mistake of disregarding a validly-true null supposition – could have potentially been made.

(c) Since the confidence interval holds both negative and positive values, we are not able to confirm that leastwise some dissimilarity might exist between these two proportions.

d) Raising the power of the test may be achievable by lessening the significance level.

In this state, it would indicate that we concluded that there exists a considerable divergence between the proportion of men and women intending to vote for Trump when factually there is no distinction.

Raising the power of the test may be achievable by lessening the significance level. Doing so will penalize us with being more lenient towards taking up the alternate assumption, consequently reducing the likelihood of having a Type II error.

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Note that the probabilities are given below.

a) the probability of a randomly selected catch being a mouse caught by Cyd

p(Catching a mount) x p(Cyd made the catch)

= 0.5x .2

= 0.1

b) the   probability of a bird not caught by Cyd is 0.5 x 0.8 = 0.4.

Thus

P(that a catch is a bird) x p(the Cyd didn't make the catch)

= 0.3 x 0.8

=0.24

c) The probability of a randomly selected catch being caught by Greg is 0.45

To calculate, we say

(0.5   x0.45) + (0.3 x 0.45) + (0.2 x .45)

= 0.45.

d)

P (mouse caught by Greg) = (0.45 x 0.5) / 1

= 0.225.

e) P(catch is a mouse caught by Ken and catch is a mouse)

= P(catch is a mouse | catch is made by Ken) x P(catch is made by Ken)

= 0.05 x 0.1

= 0.005

f)

P (catch made by Cyd | catch is a mouse)

= 0.1    x 0.2 / 0.5

= 0.04

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The quadratic polynomial with integer as coefficients that has four real roots including these conjugates is a² + b² - 2ab - 20a - 20b + 88 ≥ 0

One possible quartic polynomial with integer coefficients that has four real roots, including the conjugates 5+√3 and 5-√3, is:

(x - 5 - √3)(x - 5 + √3)(x - a)(x - b)

where a and b are the remaining two roots.

Expanding the first two factors using the difference of squares formula, we get:

(x - 5)² - 3

Expanding the last two factors, we get:

x² - (a + b)x + ab

Putting it all together, the quartic polynomial is:

a² + b² - 2ab - 20a - 20b + 88 ≥ 0

To ensure that a and b are also real, we can use the fact that the discriminant of a quadratic equation ax² + bx + c = 0 with real coefficients is b² - 4ac ≥ 0. Applying this to the quadratic factor in the above polynomial, we get:

(a + b)² - 4ab ≥ 0

Expanding and simplifying, we get:

a² + b² - 2ab - 20a - 20b + 88 ≥ 0

To simplify the problem, we can set a = b, since the polynomial is symmetric with respect to the roots. Then, the inequality becomes:

2a² - 40a + 88 ≥ 0

Dividing by 2 and factoring, we get:

(a - 10)² - 12 ≥ 0

This inequality is always true for real values of a, so we can choose any real value for a and set b = a to obtain a quartic polynomial with integer coefficients that has four real roots, including the conjugates 5+√3 and 5-√3.

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Answer:

b

Step-by-step explanation:

The triangles are not similar. Triangle EFG and Triangle QRS are not similar. ΔEFG not ~ ΔQRS

From the question, we are to determine if the given triangles are similar

From one of Triangle similarity theorems, AA (or AAA) or Angle-Angle Similarity theorem.

The Angle-Angle similarity theorem states that If any two angles of a triangle are equal to any two angles of another triangle, then the two triangles are similar to each other

In the given diagram,

In triangle EFG

m ∠E = 104°

m ∠F = 45°

m ∠G = 180° - (104° + 45°) = 31°

In triangle QRS

m ∠R = 100°

m ∠Q = 45°

m ∠S = 180° - (100° + 45°) = 35°

Since no two angles of one of the triangles are equal to any two angles of other triangle, the triangles are not similar

Hence,

ΔEFG not ~ ΔQRS

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The most accurate for a Zero-Based Budget is You put every dollar of your take-home pay into a budget category each month. Option A

Zero-based budgeting (ZBB) is simply defined as a method of budgeting having that all expenses must be checked for each new period.

The process of zero-based budgeting is one that begins from a zero account

Note that the budgets are carried out when it is needed for the upcoming period, regardless of whether the budget is less or greater than the previous one.

It is important to note the following;

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The critical value from the given data is 2.776.

Hypothesis Testing:

Step 1: State the null and alternative hypotheses.

Null Hypothesis (H0): The average number of units taken by students in PSY 190 is equal to the average number of units taken by Rio Hondo students.

Alternative Hypothesis (H1): The average number of units taken by students in PSY 190 is greater than the average number of units taken by Rio Hondo students.

Step 2: Calculate a test statistic.

To calculate a test statistic, we will use a one-sample t-test. The t-test will allow us to compare the average of the PSY 190 students to the average of all Rio Hondo students. The test statistic will be calculated as follows:

t = (x - μ) / (s/√n)

Where x is the sample mean, μ is the population mean, s is the sample standard deviation, and n is the sample size.

In this case, x = 10.6, μ = 9.1, s = 5.1, and n = 5.

Plugging these values into the equation, we get:

t = (10.6 - 9.1) / (5.1/√5) = 1.78

Step 3: Determine the critical value.

To determine the critical value, we need to determine the degrees of freedom, which is equal to n-1 = 4. We can then look up the critical value in a t-table with α = 0.05 and 4 degrees of freedom. The critical value is 2.776.

Step 4: Compare the test statistic to the critical value.

Since the test statistic (1.78) is less than the critical value (2.776), we fail to reject the null hypothesis.

Therefore, the critical value from the given data is 2.776.

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Answer:

Step-by-step explanation:

You want the number of day passes sold for $61 and weekend passes sold for $110 if 257 more day passes were sold, and sales totaled $307745.

Let w represent the number of weekend passes sold. Then w+257 is the number of day passes sold. The total revenue is ...

  61(w+257) +110(w) = 307745

Simplifying the equation, we have ...

  171w +15677 = 307745

  171w = 292068 . . . . . . . . subtract 15677

  w = 1708 . . . . . . . . . . . divide by 171

  w+257 = 1965 . . . day passes sold

1965 day passes and 1708 weekend passes were sold.

<95141404393>

There are 125 sheets in the sale package.

If a regular package of graph paper contains 100 sheets, then a package with 25% more sheets would contain:

100 + (25/100) x 100 = 100 + 25 = 125

So a package with 25% more sheets would contain 125 sheets.

During the sale, the store is offering a package with 25% more sheets for no additional cost.

This means that the sale package contains the same number of sheets as a regular package, plus an additional 25% of that same number of sheets.

To find the number of sheets in the sale package, we can set up an equation:

Number of sheets in sale package = Number of sheets in regular package + 25% of the Number of sheets in the regular package

or

Number of sheets in sale package = 100 + 0.25 x 100

Simplifying,

Number of sheets in the sale package = 100 + 25

Number of sheets in the sale package = 125

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Answer:

<HAG

Step-by-step explanation:
Two angles are adjacent when they have a common side and common vertex, and they do not overlap one another. In this case, <EAG, A is the vertex. <HAG has the same vertex, A, and it shares side AG.

Answer:

Given system of linear equations are

2x+3y+3z=5

x−2y+z=−4

3x−y−2z=3.

Represent it in matrix form

⎣

⎢

⎢

⎡

2

1

3

3

−2

−1

3

1

−2

⎦

⎥

⎥

⎤

⎣

⎢

⎢

⎡

x

y

z

⎦

⎥

⎥

⎤

=

⎣

⎢

⎢

⎡

5

−4

3

⎦

⎥

⎥

⎤

which is in the form of AX=B

A=

⎣

⎢

⎢

⎡

2

1

3

3

−2

−1

3

1

−2

⎦

⎥

⎥

⎤

∣A∣=10+15+15=40



=0

∴ A

−1

exists

To find adjoint of A

A

11

=5,A

12

=5,A

13

=5

A

21

=3,A

22

=−13,A

23

=11

A

31

=9,A

32

=1,A

33

=−7

Adj(A)=co-factor

⎣

⎢

⎢

⎡

5

3

9

5

−13

1

5

11

−7

⎦

⎥

⎥

⎤

=

⎣

⎢

⎢

⎡

5

5

5

3

−13

11

9

1

−7

⎦

⎥

⎥

⎤

A

−1

=

∣A∣

1

Adj(A)

=

40

1

⎣

⎢

⎢

⎡

5

5

5

3

−13

11

9

1

−7

⎦

⎥

⎥

⎤

X=A

−1

B

=

40

1

⎣

⎢

⎢

⎡

5

5

5

3

−13

11

9

1

−7

⎦

⎥

⎥

⎤

⎣

⎢

⎢

⎡

5

−4

3

⎦

⎥

⎥

⎤

X=

40

1

⎣

⎢

⎢

⎡

25−12+27

25+52+3

25−44−21

⎦

⎥

⎥

⎤

X=

40

1

⎣

⎢

⎢

⎡

40

80

−40

⎦

⎥

⎥

⎤

⎣

⎢

⎢

⎡

x

y

z

⎦

⎥

⎥

⎤

=

⎣

⎢

⎢

⎡

1

2

−1

⎦

⎥

⎥

⎤

Hence, x=1,y=2 and z=−1

The solution to the system of equations is

x = 3

y = 2

z = 2

To solve for x, y, and z, we can use the elimination method or substitution method. Here, we will use the elimination method.

First, we will eliminate y from the equations by multiplying the first equation by 3 and the second equation by 1, and then adding them:

(3) (2x – y + 3z = 10)

6x – 3y + 9z = 30

(1) (x + 3y – 2z = 5)

x + 3y – 2z = 5

Adding the two equations gives:

7x + 7z = 35

Simplifying, we get

x + z = 5 (Equation 1)

Next, we will eliminate y again by multiplying the second equation by 2 and the third equation by 3, and then adding them:

(2) (x + 3y – 2z = 5)

2x + 6y – 4z = 10

(3) (3x – 2y + 4z = 12)

9x – 6y + 12z = 36

Adding the two equations gives:

11x + 8z = 46

Substituting x + z = 5 from Equation 1 into the above equation, we get:

11(x + z) + 8z = 46

11x + 19z = 46

Solving for z, we get:

z = 2

Substituting z = 2 into x + z = 5 from Equation 1, we get:

x + 2 = 5

x = 3

Finally, substituting x = 3 and z = 2 into any of the original equations, we can solve for y:

2x – y + 3z = 10

2(3) – y + 3(2) = 10

6 – y + 6 = 10

y = 2

Therefore, the solution to the system of equations is:

x = 3

y = 2

z = 2

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The solid formed when the right triangle is rotated around the side length of 5 is two cones with a radius of 1.5 units and a height of 1.8 units and 3.2 units.

The volume of the smaller cone is approximately 3.82 cubic units, and the surface area is approximately 20.94 square units.

The volume of the larger cone is approximately 6.04 cubic units, and the surface area is approximately 20.94 square units.

We have,

When the right triangle is rotated around the side length of 5, it forms two cones with different heights and radii.

Now,

r = base / 2 = 3 / 2 = 1.5 units

h = height = 4 units

Using the Pythagorean theorem,

l = √(1.5² + 4²) = √(18.25) ≈ 4.27 units

The first cone has a radius of 1.5 units and a height of 1.8 units (5 - 4.27)

The second cone has a radius of 1.5 units and a height of 3.2 units (5 - 1.8).

Now,

The volume of a cone.

V = (1/3)πr^2h

The surface area of a cone.

A = πrl + πr^2

For the first cone:

V = (1/3)π(1.5)²(1.8) = 3.82 cubic units

A = π(1.5)(4.27) + π(1.5)² = 20.94 square units

For the second cone:

V = (1/3)π(1.5)²(3.2) = 6.04 cubic units

A = π(1.5)(4.27) + π(1.5)² = 20.94 square units

Thus,

The solid formed when the right triangle is rotated around the side length of 5 is two cones with a radius of 1.5 units and a height of 1.8 units and 3.2 units.

The volume of the smaller cone is approximately 3.82 cubic units, and the surface area is approximately 20.94 square units.

The volume of the larger cone is approximately 6.04 cubic units, and the surface area is approximately 20.94 square units.

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Answer:

To find the area of the rectangle BCDE, we can use the formula:

Area = length x width

First, we need to find the length and width of the rectangle.

The length of the rectangle is the distance between points B and C, which can be calculated using the distance formula:

distance BC = sqrt((x2 - x1)^2 + (y2 - y1)^2)

= sqrt((-6 - (-9))^2 + (-8 - (-4))^2)

= sqrt(3^2 + (-4)^2)

= sqrt(9 + 16)

= sqrt(25)

= 5

The width of the rectangle is the distance between points C and D:

distance CD = sqrt((x2 - x1)^2 + (y2 - y1)^2)

= sqrt((10 - (-6))^2 + (4 - (-8))^2)

= sqrt(16^2 + 12^2)

= sqrt(256 + 144)

= sqrt(400)

= 20

Since BCDE is a rectangle, the length and width are perpendicular. Therefore, the area of the rectangle can be calculated by multiplying the length and width:

Area = length x width = 5 x 20 = 100

Therefore, the area of BCDE is 100 square units.

Step-by-step explanation:

Answer: C. V ≈ 635.2 cm^3.

Explanation: The formula for the volume of a cone is V = (1/3)πr^2h, where r is the radius and h is the height (or slant height in this case).

Using the given values, we have:

V = (1/3)π(4.25 cm)^2(12 cm)

V ≈ 635.2 cm^3 (rounded to the nearest tenth)

Therefore, the answer is C. V ≈ 635.2 cm^3.

a) The probability that the student was female is 43/76

b) The probability that the student was female AND got a "C" is 9/38

c) The probability that the student was female OR got a "C" is 45/76

We have,

             A   B   C  

Male     16  15  2  33

Female 14  11  18  43

Total     30 26 20 76

a) The probability that the student was female

= 43/76

b) The probability that the student was female AND got a "C"

= 18/76

= 9/38

c) The probability that the student was female OR got a "C"

= 43 /76 + 20/76 - 18/76

= 45/76

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The test score for Jason will be 55% for answering 11 questions right.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that Jason is taking a multiple-choice test with a total of 20 points available. Each question is worth exactly 1 point.

The test score will be calculated as,

[tex]\text{Test score} =\dfrac{\text{Total questions - wrong answers}}{\text{Total questions}} \times100[/tex]

[tex]\text{Test Score}=\huge \text[\dfrac{(20-9)}{20}\huge \text] \times100[/tex]

[tex]\text{Test Score}=0.55\times100[/tex]

[tex]\text{Test Score}=0.55\%[/tex]

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The rectangular coordinates from the polar coordinates are: (-4√2, -4√2)

The steps to  to convert polar coordinates to rectangular coordinates are:

Step 1: Find the x -coordinate for the rectangular coordinate form of the point by using the equation x = r cos(θ)

Step 2: Find the y -coordinate for the rectangular coordinate form of the point by using the equation y = rsin(θ)

Step 3: Write the rectangular coordinates as (x,y) using the results from steps 1 and 2.

We are given the polar coordinates as (8, 225°)

Thus:

x-coordinate of rectangular coordinate = 8 cos 225 = -4√2

y-coordinate of rectangular coordinate = 8 sin 225 = -4√2

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Answer:

down your esophagus into your stomach

Step-by-step explanation:

After you swallow, peristalsis pushes the food down your esophagus into your stomach. Stomach. Glands in your stomach lining make stomach acid and enzymes that break down food. Muscles of your stomach mix the food with these digestive juices.

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{13\% of 50}}{\left( \cfrac{13}{100} \right)50}\implies 6.5[/tex]

Answer: 6.5

Step-by-step explanation: You can find the percent of a number by multiplying the two together such as 50(0.13). This will give you the answer of 6.5.

The equation that could be used to find the distance that the tornado traveled is: log d = 0.7

We are told that The wind speed near the center of a tornado is represented by the equation S = 93 log d + 65,

where:

d is the distance, in miles, that the tornado travels.

S is the wind speed, in miles per hour.

When S = 130, we have:

130 = 93 log d + 65

93 log d = 130 - 65

93 log d = 65

log d = 65/93

log d = 0.7

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- To purchase a new car in 4 years and expect the car to cost ​$76,000, you need to calculate how much money you need to deposit each month in a bank account that offers a guaranteed APR of 4.5%.

- You can use a formula called PMT to calculate the monthly deposit amount. PMT stands for payment and it is the amount of money you need to pay or deposit each period to achieve a certain future value.

- The formula for PMT is: PMT = ( FV * r) / [ ( (1+r)^n) - 1] where FV is the future value, r is the interest rate per period, and n is the number of periods.

- In your case, FV is $76,000, r is 0.045/12 (because the interest rate is 4.5% per year and there are 12 months in a year), and n is 4*12 (because you want to save for 4 years and there are 12 months in a year).

- Plugging these values into the formula, you get: PMT = (76000 * 0.00375) / [ ( (1+0.00375)^48) - 1] = 1449.72

- This means you should deposit $1449.72 each month to end up with $76,000 in 4 years.

I hope this helps you solve your problem.

Answer:

THE ANSWER OF 7×4=28 !!!!!!!

Answer:

The nearest tenth, Container A is about 46.3% full after the pumping is complete.

Step-by-step explanation:

To solve this problem, we need to find the volume of water in Container A and compare it to the volume of Container B.

The volume of water in Container A can be found using the formula for the volume of a cylinder:

V_A = πr^2h = π(6^2)(9) = 324π cubic feet

The volume of Container B can also be found using the same formula:

V_B = πr^2h = π(5^2)(12) = 300π cubic feet

After the water is pumped from Container A to Container B, Container B will be completely full, which means it will contain 300π cubic feet of water. To find the height of the water level in Container A, we need to find the height of the cylinder that would contain 300π cubic feet if it had a radius of 6 feet:

V_A' = πr^2h' = 300π

h' = 300/(36π) = 25/6 feet

So the height of the water level in Container A is 25/6 feet. Since the height of Container A is 9 feet, the percent of Container A that is full is:

(25/6) / 9 * 100% ≈ 46.3%

Therefore, to the nearest tenth, Container A is about 46.3% full after the pumping is complete.

The strongest classification of the quadrilateral with the given vertices is rhombus.

The vertices of the quadrilateral is given as,

E(5, 4), F(9, 2), G(5, 0) and H(1, 2).

Find the adjacent sides EF and FG whether they are equal.

Using the distance formula,

EF = √(9 - 5)² + (2 - 4)²  = √(16 + 4) = √20

FG = √(5 - 9)² + (0 - 2)² = √(16 + 4) = √20

Adjacent sides are equal.

So they are either square or rhombus.

Find the lengths of the diagonals whether they are equal.

EG = √(5 - 5)² + (0 - 4)²  = √(0 + 16) = 4

FH = √(1 - 9)² + (2 - 2)²  = √(64 + 0) = 8

Diagonals are not equal.

So it is a rhombus.

Hence the quadrilateral is a rhombus.

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The system of equations in the context of this problem is given as follows:

The solution is given as follows:

h = 35, c = 55.

The variables used for the system of equations are given as follows:

Considering the Monday's earnings, the equation is given as follows:

5h + 3c = 340.

Considering the Wednesday's earnings, the equation is given as follows:

2h + 6c = 400.

Hence the system is:

Simplifying the second equation by 2, we have that:

h + 3c = 200.

Subtracting the first equation by the second, we can obtain the value of h as follows:

4h = 140

h = 140/4

h = 35.

Hence the value of c is given as follows:

c = (200 - 35)/3

c = 55.

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The seller will owe the buyer an amount of $2,933.40.

To be able to compute the owed amount, first, we have to compute the daily rate per day which is shown below:

= Rent received / number of days in a month

= $4,400 / 30 days

= 146.67 per day

Data:

Number of days in a month = 30 days

Landlord received a rent on December 10

The remaining days would be =  30 days - 10 days = 20 days

Now, the owed amount would be calculated as:

= Remaining days × per day rate

= 20 days × 146.67

= $2,933.40

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