Branden and Janna are analyzing the same conditional statement. Branden finds multiple examples that validate the conditional statement. Janna finds one example that satisfies the hypothesis of the conditional statement, but not the conclusion. Which must be true? The conditional statement is true. There are more examples that validate the statement than there are that do not. The conditional statement is true. There is at least one example that validates the statement. The conditional statement is false. There is at least one counterexample for the statement. The conditional statement is false. There must be exactly one example that validates the statement.

In step 4 and 5 he used prime factorization of 5 under cube root.

This was done in order to eliminate the cube root.

Prime factorization is a process of finding the prime factors of a given number. A prime factor is a factor of a number that is a prime number. The prime factorization of a number is the list of its prime factors, together with their multiplicities.

To find the prime factorization of a number, divide it by its smallest prime factor and write down the result as the product of the prime factor and the quotient. Continue this process with the quotient until quotient of 1 is obtained.  

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Answer:

đẹp trai quá đi

Step-by-step explanation:

Divide all numbers by prime factors

14 21 40 | 2

7 21 20 | 2

7 21 10 | 2

7 21 5 | 5

7 21 1 | 7

1 3 | 3

1 |

Now, multiply all this numbers to find the least common multiple

The least common multiple is 840

Answer:

For me, it always helps to break down equations like this. Divide it up into two separate parts.

4^2*4^2=x

4^2=16

Replace both 4^2 with 16

16*16=256

============================================

Explanation:

On that diagram, the unmarked angle above the (6x-8) is equal to (5x+12). This is because the unmarked angle and the angle marked with (5x+12) are corresponding angles. Corresponding angles must be congruent if you want line m to be parallel to line n.

From here we add up (5x+12) and (6x-8) and set that sum equal to 180. Solve for x

We get the following:

(5x+12)+(6x-8) = 180

5x+12+6x-8 = 180

(5x+6x)+(12-8) = 180

11x+4 = 180

11x = 180-4

11x = 176

x = 176/11

x = 16

In the given argument, "No swimmers fear water. Some bathers are swimmers.

Therefore, some bathers do not fear water," it is a deductive argument.

A deductive argument is an argument in which the premises provide complete and conclusive support for the conclusion. This means that if the premises are true, then the conclusion must also be true.

In this argument, the first premise is "No swimmers fear water," which is a universal negative statement. The second premise is "Some bathers are swimmers," which is a particular affirmative statement.

The conclusion "Therefore, some bathers do not fear water" follows logically from the two premises, and is a particular negative statement.

Therefore, it is a deductive argument.

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The odds ratio between race and political affiliation is 1.23 with a 95% confidence interval of (0.884, 1.795). The difference in proportions is -0.126 with a 95% confidence interval of (-0.206, -0.046). The relative risk is 1.45 with a 95% confidence interval of (1.454, 3.082).

In the study conducted in the United States on the association between race and political affiliation, the following 95% confidence intervals were calculated:

Odds Ratio:

Odds ratio = (103/11) / (341/405) = 1.23

Standard error (SE) of ln(OR) = √(1/103 + 1/11 + 1/341 + 1/405) = 0.316

z-value for a 95% confidence level (α/2 = 0.025) is 1.96

Lower limit of the confidence interval: ln(OR) - (1.96 * SE(ln(OR))) = ln(1.23) - (1.96 * 0.316) = -0.123

Upper limit of the confidence interval: ln(OR) + (1.96 * SE(ln(OR))) = ln(1.23) + (1.96 * 0.316) = 0.587

Therefore, the 95% confidence interval for the odds ratio is (e^-0.123, e^0.587) = (0.884, 1.795)

Difference in Proportions:

Difference in proportions = (103/454) - (341/746) = -0.126

Standard error (SE) of (p1 - p2) = √[(103/454) * (351/454) / 454 + (341/746) * (405/746) / 746] = 0.041

z-value for a 95% confidence level (α/2 = 0.025) is 1.96

Lower limit of the confidence interval: -0.126 - (1.96 * 0.041) = -0.206

Upper limit of the confidence interval: -0.126 + (1.96 * 0.041) = -0.046

Therefore, the 95% confidence interval for the difference in proportions is (-0.206, -0.046)

Relative Risk:

Relative risk = (103/454) / (341/746) = 1.45

Standard error (SE) of ln(RR) = √[(1/103) - (1/454) + (1/341) - (1/746)] = 0.266

z-value for a 95% confidence level (α/2 = 0.025) is 1.96

Lower limit of the confidence interval: ln(1.45) - (1.96 * 0.266) = 0.374

Upper limit of the confidence interval: ln(1.45) + (1.96 * 0.266) = 1.124

Therefore, the 95% confidence interval for the relative risk is (e^0.374, e^1.124) = (1.454, 3.082)

Thus, the 95% confidence interval for the odds ratio is (0.884, 1.795), the 95% confidence interval for the difference in proportions is (-0.206, -0.046), and the 95% confidence interval for the relative risk is (1.454, 3.082).

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a) Coordinates of the midpoint: (2,1)

b) Gradient of the line PQ = -2/3

c) n = 13

What is the midpoint  of a line segment?

The midpoint is defined as the point which divides the line segment into two equal halves.

Given P = (-1,3) , Q = (5,-1)

Coordinates of the midpoint are given by

X' = (X1+ X2)/2

Y' = (Y1+ Y2)/2

(X1,Y1 ) and (X2,Y2) are the endpoints of the line segment.

Putting the values in the above formula X' = (-1+5)/2 = 2

Y' = (3-1)/2 = 1

hence midpoint  = (2,1)

The Slope or Gradient of the line is given by = (Y2-Y1)/X2-X1)

= (-1-3)/(5-(-1))

= -4/6 = -2/3

Gradient = -2/3

Distance between 2 points is given by the formula

\(\sqrt{(x_{1}-x_{2}) ^{2}+(y_{1}-y_{2}) ^{2} }\)

\(\sqrt{(-1-5)^{2}+(3-(-1))^{2} }\)

\(\sqrt{6^{2}+4^{2} }\)

= \(2\sqrt{13}\)

hence n = 13

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Answer:

Step-by-step explanation:

The circumference:

If the circumference is doubled, it means the radius is doubled.

The area:

And the new area:

Correct choice is D

Answer:

Solution given:

area of a circle[A]=πr²

circumference of circle [C]=2πr

when circumference of circle is doubled

it becomes :4πr

Step-by-step explanation:

area directly proportional to circumference

πr²=2πr

when circumference is doubled

πr²=2(2πr)

so area

C. The area is 2 times the original circle

Answer:

x=-1, y=-2. (-1, -2).

Step-by-step explanation:

2x-5y=8

3x+5y=-13

----------------

5x=-5

x=-5/5

x=-1

2(-1)-5y=8

-2-5y=8

5y=-2-8

5y=-10

y=-10/5

y=-2

Answer:

the out put would be 49

Step-by-step explanation:

The statement ''the formula for finding the surface area of a cylinder is sa = πr2 πrh.'' is false because the formula for finding the surface area of a cylinder is given by: SA = 2πrh + 2πr^2 , where SA represents the surface area, r is the radius of the base, and h is the height of the cylinder.

The first term, 2πrh, represents the area of the curved surface of the cylinder (the lateral surface area), which is a rectangle that wraps around the cylinder. It is calculated by multiplying the height of the cylinder by the circumference of the base.

The second term, 2πr^2, represents the areas of the two circular bases of the cylinder.

By adding these two terms together, we obtain the total surface area of the cylinder.

Therefore, the correct formula for finding the surface area of a cylinder is SA = 2πrh + 2πr^2.

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the dimensions of the rectangle are L = 15 inches and W = 15 inches, and the minimum perimeter is:    P = 2L + 2W = 60 inches.

Let the length and width of the rectangle be L and W, respectively, so that the area of the rectangle is A = LW = 225. We want to find the dimensions of the rectangle with minimum perimeter P = 2L + 2W, and then find the minimum perimeter.

Using the given area, we can solve for one of the variables in terms of the other:

L = 225/W

Substituting this expression for L into the expression for the perimeter, we get:

P = 2(225/W) + 2W

Taking the derivative of P with respect to W and setting it equal to zero to find the minimum, we get:

\(dP/dW = -450/W^2 + 2 = 0\)

Solving for W, we get:

W^2 = 225

Since W must be positive (it is a length), we take the positive square root:

W = 15

Substituting this value of W back into the expression for L, we get:

L = 225/W = 15

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Answer:

The answer is 38 euros.

Step-by-step explanation:

The y-intercept of the line represented by the equation is; 60.

It follows from the task content that the y-intercept of the line represented by the equation is to be determined.

On this note, we must recall that the y-intercept of an equation is the value of y when x = 0.

Therefore, we have;

-60 (0) + 2y - 120 = 0

2y = 120

y = 60.

Hence, the y-intercept of the line represented by the equation is; 60.

Consequently, it can be inferred that the Ernesto is wrong in his evaluation of the y-intercept as 30.

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The number of bags of fiber stuffing needed to fill the cones is 52 bags.

Given:

Height (h) = 10 inches

Radius (r) = 4 inches

To calculate the number of bags of fiber stuffing needed to fill the ice cream cones, we first need to calculate the volume of a single cone ( cone + hemisphere) using its height and radius.

The volume of a cone can be calculated using the formula:

= (1/3) πr²h

The volume of a hemisphere can be calculated using the formula:

= (2/3) πr³

Substituting these values into the formula, we can find the volume of a single cone:

V = (1/3) π × 4² × 10 + (2/3)π × 4³

V = 167.5 + 134.04

V = 301.54

V ≈ 167.5516 cubic inches (rounded to 4 decimal places)

Now, to determine the number of bags of fiber stuffing needed, we divide the total volume of the cones by the volume that can be filled by a single bag of fiber stuffing:

Number of bags = Total volume of cones / Volume filled by a single bag

Total volume of cones = Volume of a single cone x Number of cones

Total volume of cones = 167.5516 cubic inches x 125 cones

Total volume of cones ≈ 37692.66 cubic inches (rounded to 2 decimal places)

Number of bags = 37692.66 cubic inches / 720 cubic inches (per bag)

Number of bags ≈ 52 (rounded to nearest whole number)

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Answer: The length is 15 feet.

Step-by-step explanation:

But, the problem is asking for the length...

t3(x)  = f(a) + f'(a)(x-a) + (1/2)f''(a)(x-a)^2 + (1/6)f'''(a)(x-a)^3.

To find t3(x) we need to find the coefficient of polynomials by using the formula for nth degree taylor polynomial.

what is taylor polynomials?

This are approximations of a function, which become generally better as n increases. It is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point.

using the nth degree taylor polynomial formula:

tn(x) = f(a) + f'(a)(x-a) + f''(a)(x-a)^2/2! + f'''(a)(x-a)^3/3! + ...... + f^(n)(a)(x-a)^n/n!

where f^(n)(a) is the nth derivative of f evaluated at x=a.

By calculating we get t3(x) as

t3(x) = f(a) + f'(a)(x-a) + f''(a)(x-a)^2/2! + f'''(a)(x-a)^3/3!

       = f(a) + f'(a)(x-a) + (1/2)f''(a)(x-a)^2 + (1/6)f'''(a)(x-a)^3.

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The time it takes for an orchestra to perform a symphony is not dependent on the number of players. Therefore, the number of players does not directly affect the duration of the performance. In this case, it took the 120-player orchestra 40 minutes to play Beethoven's 9th Symphony.

Assuming that the tempo and performance style remain constant, it is reasonable to assume that a 60-player orchestra would also take 40 minutes to perform the same symphony. The time it takes to play a symphony is primarily determined by the composer's tempo markings and the musicians' interpretation of those markings. Therefore, reducing the number of players does not necessarily mean a shorter performance time.

In summary, the number of players in an orchestra does not determine the time it takes to perform a symphony. The performance time is influenced by factors such as the composer's tempo markings and the musicians' interpretation. Hence, a 60-player orchestra would likely take the same amount of time, approximately 40 minutes, to play Beethoven's 9th Symphony.

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Answer:

254.34 m²

Step-by-step explanation:

The formula used to find the area of a circle is π · r².
The radius of a circle is half of it's diameter.
Using the given values, we can solve:

3.14 · 9²

3.14 · 81

= 254.34 m²

hope this helps!

Answer:

Area = 254.469004940773 m²

Step-by-step explanation:

formula : (area of a circle)

Area = π × r²

where r is the radius of the circle

\(\large \text r = \frac{\large \text Diameter \ of \ the \ circle }{2} = \frac{18}{2} =9\ m\)

then

Area = π × 9²

        = π × 81

        = 254.469004940773 m²

The value of F(1) is 0.0137.

The problem provided is: Question 2

Given that a) 1 b) cos(7) - 7 sin(7) c) cos(7) d) 7 x F(x) = [ f³₁0 e) 00 t cos(7 t) dt, find F(1).

For finding the value of F(1), we have to evaluate the definite integral given below: ∫₀¹ t cos 7t dt

Now, integrate the above integral by parts, taking t as the first function and cos 7t dt as the second function.

u = t and v = 1/7 sin 7tdu/dt = 1 and dv/dt = cos 7t∫₀¹ t cos 7t dt = [ t (1/7 sin 7t)]₀¹ - ∫₀¹ 1/7 sin 7t dt∫₀¹ t cos 7t dt = 0 - [1/49 cos 7t]₀¹= 0 - (1/49 cos 7) + 1/49

Now, let's put this value in the expression for F(x)F(x) = 7 ∫₀¹ t cos 7t dt= 7 (0 - 1/49 cos 7 + 1/49)= 7/49 - 7/49 cos 7So, F(1) = 7/49 - 7/49 cos 7 = 0.0649 - 0.0512 = 0.0137.

Therefore, the value of F(1) is 0.0137.

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Answer:

Step-by-step explanation:

Assuming that the Skateboard is $180, and you are asking for the price when it is 30% off.

180 * .70 = $126

Another way of solving the question is finding 10 % of 180, which is 18. And you are looking for 30% less, so 18 * 3 = 54, which is 30% of 180.

180 - 54 = 126

The number of students in each bus is 21

Given data

Total number of students on the trip = 172

25 students traveled in cars

7 buses were filled

let the number students on each bus be x

number of students on the bus is gotten by

172 - 25 = 147

so 147 students travelled by bus and the total number of buses is 7.

to get the number of students in each bus we solve as follows

147 / 7 = 21

Hence each bus contains 21 students.

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Answer:

Step-by-step explanation:

1. the words the author uses in the poem.

2. the way the author uses the pictures to describe the poem.

Answer:

x = 1.146 and x =7.854

Step-by-step explanation:

Use the quadratic formula

x = -b ± √b² -4ac

2a

-(-9) ±√81-36

2

9 ± √45

2

The mean and variance of the reward of the runner-up is 7/3 and Variance is 89/9

What is Variance?

Variance is the anticipated squared variation of a random variable from its population mean or sample mean in probability theory and statistics. Variance serves as a proxy for dispersion, or the degree to which a set of numbers deviates from their mean.

Here, a=0 and b=12. So,

f(x) = 1 / (12 - 0)

     = 1/12

A runner receives $10 if he or she is between 0 and 1 minute behind the leader. The corresponding probability is stated as

\(\int\limits^1_0 {1/12} \, dx\)=1/12(\(x^1_{0}\))

             = 1/12

A runner receives $6 if he or she is between one and three minutes behind the leader. The corresponding probability is stated as

\(\int\limits^3_1 {1/12} \, dx\) = 1/12(\(x^3_{1}\))

               = 1/6

A runner receives $2 if he or she is between three and six minutes behind the leader. The corresponding probability is stated as

\(\int\limits^6_3 {1/12} \, dx\) = 1/12(\(x^6_{3}\))

               = 1/4

A runner receives nothing if he or she is more than six minutes behind the leader. The corresponding probability is stated as

12

∫ 1/12 dx = 1/12 (\(x^{12}_6\))

6

             = 1/2

We can produce the following table:

X P(X)  X(P(X) X^2 P(X)

10 1/12   5/6         25\3

6 1/6         1     6

2 1/4      1/2  1

0 1/2      0     0

Sum: 1      E(X)=7/3  E(X^2)=46/3

Thus the expected value of X is given as

E(X) = 7/3

The variance is given as

σ² = E(X)² - [E(X)]²

    = 46/3 - (7/3)²

 σ²   = 89/9

Hence, Mean of the reward runner up is 7/3 and Variance is 89/9

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Answer

root 354

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

(√19 -√7)(√19 +√7)

( a +b)( a -b) = a²-b²

(√19)² -(√7)² = 19 -7 = 12

Answer:

3+3+3+3+3+3+3+3+3=27

Step-by-step explanation:

just add it together.