If X1/12 = 491/24 then find the value of X.

(i) none of these ailments, 26

(ii) arthritis but neither of the other two ailments, 17

(iii) exactly one of these ailments, 102

(iv) arteriosclerosis and loss of hearing but not arthritis, 16

We can use a Venn diagram to solve this problem.

Let A, B, and C represent the events of having arthritis, arteriosclerosis, and loss of hearing, respectively. Then, the given information can be represented as:

A = 70

B = 60

C = 80

A ∩ B = 35

A ∩ C = 33

B ∩ C = 31

A ∩ B ∩ C = 15

Using these values, we can find the answers to the questions:

(i) The number of senior citizens with none of these ailments is the complement of the union of A, B, and C. That is:

n(A ∪ B ∪ C)' = n(S) - n(A ∪ B ∪ C)

                      = 200 - (70 + 60 + 80 - 35 - 33 - 31 + 15)

                      = 26

Therefore, 26 senior citizens had none of these ailments.

(ii) The number of senior citizens with arthritis but neither of the other two ailments is:

n(A) - n(A ∩ B) - n(A ∩ C) + n(A ∩ B ∩ C)' = 70 - 35 - 33 + 15

                                                                   = 17

Therefore, 17 senior citizens had arthritis but neither of the other two ailments.

(iii) The number of senior citizens with exactly one of these ailments is the sum of the complements of the intersections of the events. That is:

n(A' ∩ B ∩ C') + n(A ∩ B' ∩ C') + n(A' ∩ B' ∩ C) = (200 - 60 - 31 - 15 - 33) + (200 - 70 - 31 - 15 - 33) + (200 - 70 - 60 - 15 - 35) = 102

Therefore, 102 senior citizens had exactly one of these ailments.

(iv) The number of senior citizens with arteriosclerosis and loss of hearing but not arthritis is:

n(B ∩ C) - n(A ∩ B ∩ C) = 31 - 15 = 16

Therefore, 16 senior citizens had arteriosclerosis and loss of hearing but not arthritis.

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The equation of the line parallel to the given line is y + 4x = 22

The given line is y= -4x+1

Slope of the line = -4

Slope of the parallel line= -4

Equation of the line parallel to the given line which passes through C(6,4)

y - 6 = - 4 ( x - 4 )

y - 6 = -4x + 16

y + 4x = 22

Hence the equation of the parallel line is y + 4x = 22

One that stretches on all sides and has no width is referred to in geometry as a line. A straight line is, to put it simply, a line without bends. An non-curved line that extends to infinity on both sides is said to be straight.

The general equation for a straight line is y = mx + c, where m stands for the line's slope and c for its y-intercept. The most frequently used straight line equation is one that has to do with geometry.

The equation of a straight line can be written in a number of different ways, such as point-slope form, slope-intercept form, general form, standard form, etc.

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Answer:

the answer would be 43 degrees.

Step-by-step explanation:

60/100 * 75 & 0.60 * 75

60% can be rewritten as 0.60, and since 60/100=0.60, this expression is correct as well

The other two are incorrect because 0.60/100 would be 0.6%, and 60*75 would mean she is saving 6000%

a. The dimensions that should be used to make the gardens are length = 25 yards and breadth = 33.33 yards

b. The largest area possible will be 3333.33 yards²

Since the Two rectangular gardens are made from 200 yards of fencing, let

Since they have a common side which is the breadth of the rectangular area, the total length of fencing L' = 4L + 3B

Since L' = 200 yards,

4L + 3B = 200

Making L subject of the formula, we have

L = (200 - 3B)/4

Since the area of the two rectangular gardens is A = 2L × 2B = 4LB

Substituting L into A, we have

A = 4LB

= 4(200 - 3B)/4 × B

= 200B - 3B²

The dimensions that should be used to make the gardens are length = 25 yards and breadth = 33.33 yards

To find the value of B at which A is maximum, we differentiate A with respect to B and equate to zero.

So, dA/dB = d(200B - 3B²)/dt

= 200 - 6B

Equating to zero, we have

dA/dB = 0

200 - 6B = 0

200 = 6B

B = 200/6

B = 33.33 yards

We need to determine if this value of B maximizes A. So, we differentiate A twice.

So, d²A/dB² = d(200 - 6B)/dB = -6 < 0. So, A is maximum at B = 200/6

Since L = (200 - 3B)/4

Substituting the value of B into the equation, we have

L = (200 - 3B)/4

L = (200 - 3 × 200/6)/4

L = (200 - 100)/4

L = 100/4

L = 25 yards

The dimensions that should be used to make the gardens are length = 25 yards and breadth = 33.33 yards

The largest area possible will be 3333.33 yards²

Since A = 4LB

Substituting the values of the variables into the equation, we have

A = 4LB

A = 4 × 25 × 200/6

A = 20000/6

A = 3333.33 yards²

So, the largest area possible will be 3333.33 yards²

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Answer:

To find the tens and units digit of the product, we only need to focus on the last two digits of the product.

First, we multiply 8 x 6, which gives us 48. So the units digit is 8 and we carry-over the 4 to the tens digit.

Next, we multiply 7 x 6, which gives us 42. We add the carry-over 4, which gives us 46. So the tens digit is 6 and we carry-over the 4.

Continuing with the multiplication, we get:

6 x 0 = 0 (no carry-over)

6 x 7 = 42 (carry-over 4)

6 x 2 = 12 (carry-over 1)

Adding the carry-over, we get:

4 + 4 + 1 = 9

Therefore, x+y= 8 + 6 = 14

This directly proportional relationship between p and q is written as p∝q  where that middle sign is the sign of proportionality. The value of y can be found as shown below.

Let there are two variables p and q

Then, p and q are said to be directly proportional to each other if

 p = kq

where k is some constant number called the constant of proportionality.

This directly proportional relationship between p and q is written as

 p∝ q  where that middle sign is the sign of proportionality.

In a directly proportional relationship, increasing one variable will increase another.

Now let m and n be two variables.

Then m and n are said to be inversely proportional to each other if

\(m = \dfrac{c}{n} \\\\ \text{or} \\\\ n = \dfrac{c}{m}\)

(both are equal)

where c is a constant number called the constant of proportionality.

This inversely proportional relationship is denoted by

\(m \propto \dfrac{1}{n} \\\\ \text{or} \\\\n \propto \dfrac{1}{m}\)

As visible, increasing one variable will decrease the other variable if both are inversely proportional.

1.) The relation can be written as,

y ∝ x

y = kx

27 = k × 3

k = 9

Value of y, when x=4 is,

y = 9 × 4 = 36

2.)  The relation can be written as,

y ∝ x²

y = k x²

160 = k × 4²

160 = k × 16

k = 10

Value of y, when x=6 is,

y = 10 × 36 = 360

3.) The relation can be written as,

y ∝ (1/x)

y = k/x

16 = k × (1/2)

k = 32

Value of y, when x=17 is,

y = 32 × (1/17) = 1.8823

4.)  The relation can be written as,

y ∝ (1/x²)

y = k(1/x²)

64 = k × (1/4²)

64 = k × (1/16)

k = 1024

Value of y, when x=7 is,

y = 1024 × (1/49) = 20.8979

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The number of different special pizzas possible is 3003.

To find this, you need to calculate the number of combinations of choosing 6 toppings from the 14 available. This can be represented using the combination formula, which is C(n, k) = n! / (k!(n-k)!), where n represents the total number of toppings (14) and k represents the number of toppings to choose (6).


1. Calculate factorial of n (14!): 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 87,178,291,200.
2. Calculate k! (6!): 6 x 5 x 4 x 3 x 2 x 1 = 720.
3. Calculate (n-k)! (8!): 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320.
4. Divide n! by (k!(n-k)!): 87,178,291,200 / (720 x 40,320) = 3003.

So, there are 3003 different special pizzas possible with 6 toppings from a choice of 14.

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According to the solution we have come to find that, The missing sides are t=ST=9 and s=RT=12.

what is right angle triangle?

A right angle triangle, also known as a right triangle, is a triangle that has one angle measuring 90 degrees, which is also known as a right angle. The side opposite to the right angle is called the hypotenuse, and the other two sides are called legs or catheti. The Pythagorean theorem, which states that the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse, is a fundamental property of right triangles. Right triangles are important in mathematics and physics, and they have many applications in geometry, trigonometry, and calculus.

We can use the fact that the two triangles are similar to set up a proportion and solve for the missing sides.

AB/RS = BC/ST = AC/RT

Substituting the given values:

5/RS = 3/9 = 4/s

Solving for RS:

RS = (5/3) * 9 = 15

Solving for RT:

RT = (4/5) * 15 = 12

Therefore, the missing sides are t=ST=9 and s=RT=12.

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Answer:

1. AC

2. BC

3. BA

Step-by-step explanation:

Answer:

Explanation:

A simple method to identify which is the smallest or largest is to look at the smallest angle given. Its opposite side will be the smallest side. Simply, look at the largest angle. The opposite side of that angle will be the largest side.

Answer: Luis’s, because he flipped the inequality sign when he subtracted

Step-by-step explanation:

Here is the complete question:

Amelia, Luis, Shauna, and Clarence used different approaches to solve the inequality

7.2b + 6.5 > 4.8b – 8.1.

Amelia started by subtracting 7.2b from both sides to get 6.5 > –2.4b – 8.1.

Luis started by subtracting 4.8b from both sides to get 2.4b + 6.5 < – 8.1.

Shauna started by subtracting 6.5 from both sides to get 7.2b > 4.8b – 14.6.

Clarence started by adding 8.1 to both sides to get 7.2b + 14.6 > 4.8b.

Which student’s first step was incorrect, and why?

a. Amelia’s, because the variable term must be isolated on the left side

b. Luis’s, because he flipped the inequality sign when he subtracted

c. Shauna’s, because she did not apply the subtraction property of equality properly.

d. Clarence’s, because the terms he added together were not like terms.

The inequality given is:

7.2b + 6.5 > 4.8b – 8.1.

We are informed that Luis started by subtracting 4.8b from both sides to get 2.4b + 6.5 < – 8.1.

If Luis started by subtracting 4.8b from both sides, he should get:

7.2b + 6.5 > 4.8b – 8.1.

7.2b + 6.5 - 4.8b > 4.8b – 8.1 - 4.8b

2.4b + 6.5 > - 8.1

But looking critically, we would realise that what Luis got us different as the inequality sign has been changed from greater than to less than and this is incorrect.

The inequality sign can only be flipped in case whereby there's a division or multiplication of a negative number from both sides.

Therefore, Luis’s first step was incorrect because he flipped the inequality sign when he subtracted.

In the given map, the approximate area of the Central Park is 450 blocks

Froom the question, we are to determine the approximate area of the central park.

The park is a rectangular park and the approximate area of the park can be calculated by using the formula for calculating the area of a rectangle.

If Central Park is about 50 blocks long by 9 blocks wide, we can find its approximate area by multiplying the length and width:

Area = Length x Width

Area = 50 x 9

Area = 450

Hence, the approximate area of Central Park is 450 blocks.

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In this question, it is required to calculate the rate of the cross-sectional area of the artery opening changing relative to the thickness of the fat deposit when the thickness of deposit is 2mm. We will use derivatives to solve this problem.

Here is the solution:Let's take, A be the cross-sectional area of the artery, r be the radius of the artery, and t be the thickness of the fat deposit. Therefore, the radius of the artery can be given as r = 5mm, and the thickness of the fat deposit is given as t = 2mm.The cross-sectional area of the artery A can be given as follows:A = π(r-t)²Now, differentiate both sides of the above equation with respect to t.

dA/dt = d/dt (π(r-t)²) = 2π(r-t)(-1) Therefore, dA/dt = -2π(r-t)After substituting the values, we have r = 5mm and t = 2mm.dA/dt = -2π(5-2) = -6πmm²/mmHence, the rate of the cross-sectional area of the artery opening changing relative to the thickness of the fat deposit when the thickness of deposit is 2 mm is -6π mm²/mm.

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Answer:

the 2nd one

Step-by-step explanation:

Answer:

its the blue circle

Step-by-step explanation:

Therefore, the dimensions of the rectangle are width = 2 m and length = 1 m.

Let's denote the width of the rectangle as w and the length as L.

According to the given information, we have two conditions:

The length of the rectangle is 3 m less than twice the width:

L = 2w - 3

The area of the rectangle is 14 m²:

A = L * w = 14

We can substitute the expression for L from the first condition into the second condition to solve for w:

(2w - 3) * w = 14

Expanding and rearranging the equation:

2w² - 3w - 14 = 0

Now, we can solve this quadratic equation for w using factoring, completing the square, or the quadratic formula.

In this case, the equation can be factored:

(2w + 7)(w - 2) = 0

Setting each factor equal to zero:

2w + 7 = 0 or w - 2 = 0

Solving for w:

2w = -7 or w = 2

w = -7/2 or w = 2

Since the width cannot be negative, we discard w = -7/2.

Therefore, the width of the rectangle is w = 2 m.

Now, we can substitute this value of w back into the expression for L from the first condition to find the length:

L = 2w - 3

L = 2 * 2 - 3

L = 1

Therefore, the dimensions of the rectangle are width = 2 m and length = 1 m.

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\(364 \times 3\)

\(= 1092\)

The difference between the two investments after 35yrs is $4700 and  Bank of America is offering higher interest than 5/3rd banks.

Most interest is compounded semiannually, quarterly, or monthly. Continuous compounding assumes that interest is compounded indefinitely and reentered on the balance sheet. The continuous compounding formula takes into account four variables.

For the given question,

5/3rd bank offers continuous interest:

For continuous interest, A = P\(e^{rt}\)

where,

P = the initial amount

A = the final amount

r = the rate of interest

t = time

e is a mathematical constant where e ≈ 2.7183.

A = 10000 × \(2.71^{0.042*35}\)

A =  10000 × 4.04

A = $40400 approximately

Interest = Amount - Principle

Interest = 40400 - 10,000

Interest = $30400

Bank of America offers compound interest:

For compound interest:

\(A = P(1 + \frac{r}{n})^{nt}\)

A = 10000 × 4.51

A = $45100

Interest = Amount - Principle

Interest = 45100 - 10,000

Interest = $35100

The above calculation explains Bank of America is offering higher interest than 5/3rd bank by $35100 - $30400 = $4700

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 The probabilities associated with each value of Y are as follows: Calculation of probabilities:Let the random variable Y represent the number of radar sets that detect a particular aircraft.

The probability that one radar detects the airplane = 0.98 (the probability of not failing to detect the airplane)The probability that all three radars detect the airplane is:0.98 * 0.98 * 0.98 = 0.941192The probability that two radars detect the airplane, and one radar fails:0.98 * 0.98 * 0.02 = 0.019208The probability that one radar detects the airplane and two radars fail:0.98 * 0.02 * 0.98 = 0.019208

The probability that all radars fail:0.02 * 0.02 * 0.02 = 0.000008Therefore, the probabilities associated with each value of Y are: For Y = 0: P(Y=0) = 0.000008For Y = 1: P(Y=1) = 0.019208 + 0.019208 + 0.019208 = 0.057624For Y = 2: P(Y=2) = 0.019208

For Y = 3: P(Y=3) = 0.941192

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Answer:

x+1=12

hope it will help you

The base radius, r, and height H of the cylinder indicates that the equation that represents the volume of each of the two inscribed cones of the cylinder is \(V = \dfrac{\pi \cdot r^2\cdot H}{6}\)

The volume of a cone is the product of pi, the square of the base radius of the cone, the height of the cone divided by 3.

Mathematically, the formula for the volume of a cone, V, is presented as follows;

\(V = \dfrac{\pi \cdot r^2\cdot h}{3}\)

The base radius of each cone are the same (cones inscribed in the same cylinder)

Whereby the height of each cone is h, we get;

h + h = H

2·h = H

h = H/2

The volume of each cone is therefore;

\(V = \dfrac{\pi \cdot r^2\times \frac{H}{2} }{3} = \dfrac{\pi \cdot r^2}{3} \times \dfrac{H}{2} = \dfrac{\pi \cdot r^2\cdot H}{6}\)

The equation that represents the volume of each cone is therefore;

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Answer:

Answer is A btw hope it helped

Step-by-step explanation:

Answer:

n (AnB) = 4 elements......

Answer:

The answer to this interesting riddle is Zebra.

Answer:

93.33

Step-by-step explanation:

You just multiply the $100 by the change rate to get the new currency

Answer:

107.15 :)

Step-by-step explanation:

You are traveling to Japan and need Japanese Yen (JPY)

We need to convert $100 USD to JPY

If conversion rate is $1USD = 0.9333JPY

The value of $1 USD is 0.9333 JPY

Let in $100 USD get x JPY

 100/.9333

=107.15

Answer:

Let's start by using algebra to solve the problem.

Let x be the total number of entries at the fair.

Given that 60% of the entries are livestock, we can write:

0.6x = number of livestock entries

Of those livestock entries, 70% are sold at the auction, which means:

0.7(0.6x) = 130

Simplifying the second equation, we get:

0.42x = 130

Solving for x, we can divide both sides by 0.42:

x = 309.52

Since we can't have a fractional number of entries, we can round up to the nearest whole number, giving us:

x = 310

Therefore, there were a total of 310 entries at the fair.

Step-by-step explanation:

Answer:

The correct option is;

1, 6, 11, 15

Step-by-step explanation:

The given information are;

The function that defines the terms of the sequence is f(n) = f(n - 1) + 5

Where;

n = The number of the term

For n = 1, we have, f(1) = -4

The first four terms are therefore;

f(2) = f(2 - 1) + 5 = f(1) + 5 = - 4 + 5 = 1

f(3) = f(3 - 1) + 5 = f(2) + 5 = 1 + 5 = 6

f(4) = f(4 - 1) + 5 = f(3) + 5 = 6 + 5 = 11

f(5) = f(5 - 1) + 5 = f(4) + 5 = 11 + 5 = 15

The first four terms are; 1, 6, 11, 15

Answer:

I would rename the trapezoid. I would rename it a semi-hexagon, because it is basically half of a hexagon.

The expression with a variables is 7x²y when x  is 3 and y is 9 is 567.

Given that,

The expression with a variables is 7x²y.

We have to find the value when x  is 3 and y is 9.

Any thing that has multiple possible values is considered a variable. What does that mean, then? A variable is anything that could possibly change. Age, for example, might be considered a variable because it might signify different things to different people or to the same person at different periods. A person's nationality can function similarly by having a value assigned to it.

By substituting in the expression we get,

7(3)²(9)

7×9×9

567

Therefore, the expression of variables 7x²y when x  is 3 and y is 9 is 567.

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Answer:

The rate of change would be y^2-y^1/x^2-x^1. So in this cause the answer is 10.5/3.

Step-by-step explanation:

I said it.

Answer:

x= 2/3 or -8/3

Step-by-step explanation:

(3x+3)^2 = 9x^2 +18x+9

therefore

9x^2 +18x+9 = 25

subtract 25 on both sides

9x^2 +18x-16 = 0

9(x^2+2x) - 16

or  substitute into the quadratic formula and you get

x= 2/3 or -8/3