Go step by step to reduce the radical

The argument "All cats are mammals. I am a mammal. Therefore, I am a cat" is fallacious and can be shown as such using set theory and a Venn diagram.

Let's represent the sets using a Venn diagram:

   -------------

   |    Mammals   |

   -------------

       /       \

      /         \

     /           \

----          ----

| Cats |        | You |

----          ----

In the Venn diagram, the circle labeled "Mammals" represents the set of all mammals, and the circle labeled "Cats" represents the set of all cats. The region where the circles overlap represents the set of mammals that are also cats.

According to the argument, "All cats are mammals," which means that the set of cats is entirely contained within the set of mammals. This relationship is correctly represented in the Venn diagram.

The argument also states, "I am a mammal," which means that you are part of the set of mammals. In the Venn diagram, your position would be within the circle labeled "Mammals" but outside the circle labeled "Cats."

The fallacy occurs when the argument concludes, "Therefore, I am a cat." This conclusion is not valid because being a mammal does not automatically make you a cat. The Venn diagram clearly shows that there is a region within the set of mammals that is not within the set of cats.

To summarize, the fallacy in the argument arises from incorrectly inferring that being a mammal automatically implies being a cat. The Venn diagram visually demonstrates that being a mammal is a broader category that encompasses various animals, including cats, but being a mammal alone does not make one a cat.

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Answer:

17/12

Step-by-step explanation:

Answer:

The formula for the volume of a cone is V = (1/3)πr^2h,

r is the base radius

h is the height.

Substituting the given values, we get:

V = (1/3)π(4 yards)^2(9 yards)

V = (1/3)π(16 yards^2)(9 yards)

V = (1/3)π(144 yards^3)

V = 48π cubic yards

Therefore, the volume of the cone is 48π cubic yards.

Answer:

5.50

Step-by-step explanation:

the 7 tells the 9 to round up and that will make the 4 turn into a 5 so it would end up being 5.50

Using translation concepts, the vertices of the rectangle after the translation about the origin by 180° will be as follows:

E'(-4,3), F'(7,-5) and G(-2,-8).

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

The rule for a rotation of 180º about the origin is:

(x,y) -> (-x,-y).

Hence, for triangle EFG, the vertices after the translation will be given as follows:

E'(-4,3), F'(7,-5) and G(-2,-8).

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Answer:

Step-by-step explanation:

Using compatible numbers and adjusting them helps us to perform mental math and make calculations faster. This method also helps us to estimate answers and check if the actual answer is reasonable or not.

To find sums, I would prefer to use the method of using compatible numbers and adjusting. The reason behind this is that it can help me to perform mental calculations and solve mathematical problems faster.What are compatible numbers?Compatible numbers are numbers that are close to the actual numbers, but are easier to work with mathematically. They are rounded numbers that make it easier to perform mental math. Once we have the answer, we can adjust it to get the correct answer.To solve an addition problem using compatible numbers, we choose numbers close to the actual numbers in the problem. For example, if we are adding 45 and 32, we can round the numbers to 50 and 30. Then we add 50 and 30 to get 80, which is the compatible number sum. But this is not the actual answer because we rounded the numbers, so we need to adjust. We subtract 5 from 50 and add 3 to 30 to get 45 and 33, respectively. Then we add the adjusted numbers (45 and 33) to get the correct answer, which is 78.Using compatible numbers and adjusting them helps us to perform mental math and make calculations faster. This method also helps us to estimate answers and check if the actual answer is reasonable or not.

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The expression (3.6 * 10^-5) / (1.8 * 10^2) can be calculated as = 2 * 10^-7

A canonical, normal, or standard form of a mathematical object is a conventional manner of presenting that item as a mathematical expression in mathematics and computer science. It is frequently the one that gives the simplest representation of an item and allows it to be identified in a unique fashion.

A quantity is said to be stated in standard form if it is written as the product of a power of ten and a number higher than or equal to one but less than ten (or scientific notation).

The expression (3.6 * 10^-5) / (1.8 * 10^2) can be calculated as follows:

=3.6 * 10^-5 / (1.8 * 10^2)

= (3.6 / 1.8) * (10^-5 / 10^2)

= 2 * 10^-7

Therefore, the answer in standard form is 2 * 10^-7.

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Answer: y= 2/5 * x - 6

Step-by-step explanation:

y intercept

y= 2/5 x+b putting in the point 5,4

y=2/5 5+ b

4=10+b

b= -6

Step-by-step explanation:

32.605    is it

The empirical rule states that in a normal distribution, 68% of the observations lie within 1 standard deviation from the mean, 95% of the observations lie within 2 standard deviations from the mean, and , 99.7% of the observations lie within 3 standard deviations from the mean.

a) -  Mean = U = 330 grams

standard deviation= \(\sigma=40 \: grams\)

As per the empirical rule, 68% of the observations lie within 1 standard deviation from the mean.

Let \(X_1\) and \(X_2\) be the 2 random value, between which 68% of the observations lie.

Mathematically,

\(X1=U-\sigma\)

\(X1\) = 330 - 40

\(X1\) =  290

Similarly,

\(X1=U-\sigma\)

\(X1\) = 330 + 40

\(X1\) = 370

Thus, about 68 % of organs will be between 290 and 370 grams in weight.

b) - In this, we need to find the percentage of organs weighing between 250 grams and 410 grams.

We can rewrite 250 as follows:

250= 330− 80 ⇒ 30−2(40) ⇒ 330−2(σ)

The above value (250) lies within 2 standard deviations from the mean.

Similarly,

We can rewrite 410 as follows:

410 = 330+80 ⇒ 330+2(40) ⇒ 330+2(σ)

The above value (410) lies within 2 standard deviations from the mean.\

As per the empirical rule, 95% of the observations lie within 2 standard deviations from the mean.

Thus, 95% of organs weighs between 250 grams and 410 grams.

c)-As we have calculated in part(b) that 95% of the organs lie within 250 and 410 grams.

So, area outside these values = Total area under curve - 95%

= 100 - 95 ⇒ 5%

So, 5% of the area lies outside the 250 and 410 grams range.

From the property of normal curve, we know that the area under the curve is divided into 2 equal parts.So, we divide the area- 5% into 2 equal parts which gives 2.5%.

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Answer:

55%

Step-by-step explanation:

33 is 55% of 60

and 11/20 = 33/60=0.55

Step-by-step explanation:

-5x+2y= 4         <==== Multiply entire equation by -3 to get:

15x-6y = -12  

2x+3y= 6          <====  Multiply entire equation by 2 to get :

4x+6y = 12    Add the two underlined equations to eliminate 'y'

19x = 0     so x = 0

sub in x = 0 into any of the equations to find:  y = 2

(0,2)

8x + 7 = -25

=>  8x = -25 - 7 = -32

=> x = -32/8 = -4

Answer:

-4=x

Step-by-step explanation:

8x+7(-7)=-25(-7)

8x(/8)=-32(/8)

-4=x

\(\\ \sf\longmapsto \dfrac{20}{3x-18}=\dfrac{15}{9}\)

\(\\ \sf\longmapsto 300=15(3x-18)\)

\(\\ \sf\longmapsto 300=45x-270\)

\(\\ \sf\longmapsto 45x=570\)

\(\\ \sf\longmapsto x\approx 13\)

Answer:

• from scale factors, big triangle : small triangle

\(\dashrightarrow \: { \tt{ \frac{24}{(24 - 9)} = \frac{(3x - 18) + 20}{20} }} \\ \\\dashrightarrow \: { \tt{20 \times 24 = (3x + 2) \times 15}} \\ \\ \dashrightarrow \: { \tt{480 = 45x + 30}} \\ \\ \dashrightarrow \: { \tt{45x = 450}} \\ \\ \dashrightarrow \: { \boxed{ \tt{x = 10}}}\)

• The missing length:

\( = { \tt{3x - 18}} \\ \\ = { \tt{3(10) - 18}} \\ \\ = { \tt{30 - 18}} \\ \\ \dashrightarrow \: { \boxed{ \boxed{ \tt{ \: \: missing \: length = 12 \: \: }}}}\)

The Taylor series approximation for y(0.5) is y(0.5) ≈ 0.9921875.

To apply the Taylor series up to the fourth derivative to approximate y(1) for the given ODE, we can follow these steps:

Write out the Taylor series expansion for y(x+h) around x=0 up to the fourth derivative:

y(x+h) = y(x) + hy'(x) + (h^2/2)y''(x) + (h^3/6)y'''(x) + (h^4/24)y''''(x) + O(h^5)

Substitute the given ODE, y' + cos(x)y = 0, into the Taylor series expansion:

y(x+h) = y(x) - h*cos(x)*y(x) - (h^2/2)*y''(x) - (h^3/6)*y'''(x) - (h^4/24)*y''''(x) + O(h^5)

Differentiate the ODE to obtain expressions for y''(x), y'''(x), and y''''(x) in terms of y(x) and its derivatives:

y''(x) = -cos(x)*y'(x) - sin(x)*y(x)

y'''(x) = -cos(x)y''(x) - 2sin(x)*y'(x) - cos(x)*y(x)

y''''(x) = -cos(x)y'''(x) - 3sin(x)y''(x) - 3cos(x)*y'(x) + sin(x)*y(x)

Substitute these expressions into the Taylor series expansion:

y(x+h) = y(x) - h*cos(x)y(x) - (h^2/2)(-cos(x)*y'(x) - sin(x)y(x)) - (h^3/6)(-cos(x)y''(x) - 2sin(x)*y'(x) - cos(x)y(x)) - (h^4/24)(-cos(x)y'''(x) - 3sin(x)y''(x) - 3cos(x)*y'(x) + sin(x)*y(x)) + O(h^5)

Evaluate the expression at x=0, y(0)=1, and h=0.5 to obtain an approximation for y(0.5):

y(0.5) = 1 - (0.5cos(0)1) - (0.25(-cos(0)0 - sin(0)1)) - (0.125(-cos(0)(-cos(0)0 - sin(0)1) - 2sin(0)0)) - (0.0625(-cos(0)(-cos(0)(-cos(0)0 - sin(0)1) - 3sin(0)(-cos(0)0 - sin(0)1)) - 3sin(0)(-cos(0)*0 - sin(0)*1) - sin(0)*1))

Simplify the expression:

y(0.5) = 1 - 0.50 - 0.1251 - 0.031250 - 0.0078125(-1) = 0.9921875

Therefore, the Taylor series approximation for y(0.5) is y(0.5) ≈ 0.9921875.

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Take the difference in y coordinates and divide that by the difference in the x coordinates. That's the slope, sometimes called the "rise over run"  For a straight line or a linear function the slope is a constant

(6-10)(7,10) = 2/3 = slope

the line is

y-h = m(x-k) where m=2/3 and (k,h) = (10,10) or either point

to get y-10 = (2/3)(x-10)

3y -30 = 2x-20

2x-3y = -10

or use (k,h) as (7,8)

y-8 = (2/3)(x-7)

3y-24 = 2x-14

2x-3y = -10

or if you write it in y=mx + b form

it's y=(2/3)x + 10/3  where 10/3 is the y-intercept and 2/3 = slope

In this form, take the derivative of (2/3)x + 10/3

to get y' = 2/3,  the derivative is the slope

Answer:

whole number, integer and rational

Step-by-step explanation:

squareroot of 25 equals 5, which is a whole number, integer and rational

The value of determinant of the matrix det (AB) is 15.

Given matrices A and B are 3 by 3 matrices with

det (A) = 3 and

det (b) = 5.

We need to find the value of det (AB).

Writing the given matrices into the augmented matrix form gives [A | I] and [B | I] respectively.

By multiplying A and B, we get AB. Similarly, by multiplying I and I, we get I. We can then write AB into an augmented matrix form as [AB | I].

Therefore, we can solve the augmented matrix [AB | I] by row reducing [A | I] and [B | I] simultaneously using elementary row operations as shown below.


The determinant of AB can be calculated as det(AB) = det(A) × det(B)

= 3 × 5

= 15.

Conclusion: The value of det (AB) is 15.

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We need to find the value of determinant det(AB), using the formula: det(AB) = det(A)det(B)

=> det(AB) = 3 × 5

=> det(AB) = 15.

Hence, the value of det(AB) is 15.

The given matrices are A and B. Here, we need to determine the value of det(AB). To calculate the determinant of the product of two matrices, we can follow this rule:

det(AB) = det(A)det(B).

Given that: det(A) = 3

det(B) = 5

Now, let C = AB be the matrix product. Then,

det(C) = det(AB).

To evaluate det(C), we have to compute C first. We can use the following method to solve the augmented matrix by elementary row operations.

Given matrices A and B are: Matrix A and B:

[A|B] = [3 0 0|1 0 1] [0 3 0|0 1 1] [0 0 3|1 1 0][A|B]

= [3 0 0|1 0 1] [0 3 0|0 1 1] [0 0 3|1 1 0].

We can see that the coefficient matrix is an identity matrix. So, we can directly evaluate the determinant of A to be 3.

det(A) = 3.

Therefore, det(AB) = det(A)det(B)

= 3 × 5

= 15.

Conclusion: Therefore, the value of det(AB) is 15.

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Answer:

7>x

Step-by-step explanation:

First get X on one side by adding 37 to both sides

-2 > 5x - 37

+37       +37

35> 5x

now dive both sides by GCF (5)

35/5> 5x/5

7>x

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Answer:

\(x<7\)

Step-by-step explanation:

\(-2>5x-37\)

Switch sides:

\(5x-37<-2\)

Add 37 to both sides:

\(5x-37+37<-2+37\)

\(5x<35\)

Divide 5 to both sides:

\(\frac{5x}{5}<\frac{35}{5}\)

\(x<7\)

Answer:

Step-by-step explanation:

To the nearest tenth, the bag of flour weighs approximately 5.5 pounds.

To convert kilograms to pounds,  use the conversion factor: 1 kilogram ≈ 2.20462 pounds.

Given that the bag of flour weighs 2.5 kilograms,  calculate its weight in pounds as follows:

Weight in pounds = Weight in kilograms × Conversion factor

Weight in pounds = 2.5 kg × 2.20462 (approximately)

Weight in pounds ≈ 5.51155 pounds

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Answer:

i think its b not 100% sure. hope i helped you

Answer:

b. 4X+22

Step-by-step explanation:

4(x + 5) + 2

= 4x + 20 + 2

= 4x + 22

Answer: D. (8, 4)

Step-by-step explanation:

Answer: 62

Step-by-step explanation:

top row has 12

the next row has 1 more =13

and it alternates

12+13+12+13+12=62

Answer:

The answer is

Step-by-step explanation:

The midpoint M of two endpoints of a line segment can be found by using the formula

\(M = ( \frac{x1 + x2}{2} , \: \frac{y1 + y2}{2} )\)

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(2,−7),(10,1)

The midpoint is

\(M = ( \frac{2 + 10}{2} , \: \frac{ - 7 + 1}{2} ) \\ = ( \frac{12}{2} \: , \: - \frac{6}{2} )\)

We have the final answer as

Hope this helps you

Answer:

9.987 × 10^-3

Step-by-step explanation:

Answer:

Weird question.

Step-by-step explanation:

2.915 = 2.9 (to the nearest tenth)

2.915 = 3 (to the nearest one)

Their difference = 3 - 2.9 = 0.1

Hope you understand.

And I hope that I've answered your questions.

Answer:

s = 4

Step-by-step explanation:

The equation for the line of best fit for the data is p=25s+40.

Where p is no. of points and s is no. fo strikes

We need to find the number of strikes made by a bowler with 140 points.

Put p = 140

p=25s+40

140 = 25s+40

Subtract 40 to both sides,

140-40 = 25s+40-40

100 = 25s

⇒ s = 4

So, there are 4 strikes made by a bowler with 140 points.

The truth table for the statement is

r     s     ¬r    s ∧ ¬r

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

T     T     F     F  

T     F     F     F  

F     T     T     T

F     F     T     F

From the question, we have the following parameters that can be used in our computation:

s ∧ ¬r

To construct the truth table, we make use of the following notations

s, r and ¬r

The truth table for the statement s ∧ ¬r is then represented as follows:

r     s     ¬r    s ∧ ¬r

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

T     T     F     F  

T     F     F     F  

F     T     T     T

F     F     T     F

The condition for ∧ is that it is true if both statements are true

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Answer:

Step-by-step explanation:

it would be 15.12 and you would save5.88

| c - 7 | 《 17

- 17 《 c - 7 《 17

add sides 7

- 17 + 7 《 c - 7 + 7《 17 + 7

simplification

- 10 《 c《 24

Answer:

c - 7 ≤ 17

c ≤ 24

Step-by-step explanation:

The difference of c and 7 can be written as c - 7 or 7 - c.

Now, since c - 7 is less than or equal to 17, you need to add ≤ to imply that it's less than or equal to 17.

As always, write the 17 on the other side. Now you have an inequality.

If you just need the equation, it's c - 7 ≤ 17.

But if you want to solve for c, it would be c ≤ 24.

(bring the like terms together and isolate c.)