If a²=b+c,b² = c+a and c² = a +b, prove that: (1/a+1)+(1/b+1)+(1/c+1)=1​

Without any data, we cannot determine the variance and standard deviation for the number of patients arriving at a hospital with flu-like symptoms between 12:00pm and 12:20pm.

To determine the variance and standard deviation for the number of patients arriving at a hospital with flu-like symptoms between 12:00pm and 12:20pm, we would need to know some data about the number of patients arriving during this time period. Without this data, we cannot calculate the variance and standard deviation.

If we were given a sample of data for the number of patients arriving during this time period, we could calculate the sample variance and sample standard deviation using the following formulas:

Sample variance = [(Σx²) - (Σx)² / n] / (n - 1)

Sample standard deviation = √(sample variance)

where Σx² is the sum of the squares of the deviations from the mean, Σx is the sum of the deviations from the mean, n is the sample size.

Alternatively, if we were given the mean number of patients arriving during this time period and the population variance, we could use the following formula to calculate the population standard deviation:

Population standard deviation = √(population variance)

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According to the above, we can infer that the value of FE is: 10 cm

To find the value of FE we must analyze the image of this triangle. Additionally, we must take into account the information we know, that is, the length of two sides (5 cm) and the height (4 cm), the area (20cm²).

So we must use the formula for the area of a triangle and isolate the values that we do know to find the value of the base.

According to the above, the value of segment FE is 10 cm.

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Answer:

  G  descends about 8 ft per second

Step-by-step explanation:

You want to know the descent rate of an airplane whose altitude is shown on a graph as being 1500 ft at 0 seconds and 0 ft at 180 seconds.

The airplane descended 1500 feet over a period of 180 seconds. That rate of change is ...

  (-1500 ft)/(180 s) ≈ -8.333 ft/s

The plane descends about 8 feet per second.

__

Additional comment

The slope of the line segment is the change in y divided by the change in x. For computing these changes, it is useful to consider points whose coordinates are obvious. Here, the y-intercept (1500 ft) and the x-intercept (180 seconds) are good choices.

The change in y from 1500 to 0 is a change of -1500. The change in x from 0 to 180 is a change of +180. The ratio of these changes is the slope, which is often designated by the letter m:

  m = -1500/+180 = -25/3 = -8 1/3 . . . . . . about -8

The units of the slope are the ratio of the y-axis units to the x-axis units: feet/second.

The slope of -8 feet/second tells you the plane is descending about 8 feet per second.

Answer:

a. 54 = 2 * 3³

b. 108 = 2² * 3³

c. 360 = 2² * 3² * 5

etc.

Step-by-step explanation:

So, you need to have a list of primes handy:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, ...

Now, take your number and try to divide it by the first prime, 2.

54 = 27 * 2

That worked. Note down the 2 and repeat with the result. You find 27 cannot be divided by 2 again, but it can be divided by 3 (the next prime in the list):

27 = 9 * 3

Note down the 3 and repeat:

9 = 3 * 3

Note down a 3 again.

So you have

54 = 2*3*3*3 = 2 * 3³

You can continue this until the result is a prime number itself. Then you are done.

The required weight of a hippo in pounds is given as 3,000 pounds.

What is a unit of measurement?

Unit of measurement is defined as every entity having its measures in dimensions, weight, and time. Such as for length we have a meter, for liquid we have liters, and so on.

Here,
One ton is equal to 2,000 pounds, so a hippo that weighs 1.5 tons would weigh,

1.5 tons × 2,000 pounds/ton = 3,000 pounds

Therefore, the hippo at the zoo weighs 3,000 pounds.

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The IQR of the data is 10 years and option B is the correct answer.

The dispersion of the middle 50% of the sample is measured by the interquartile range, or IQR, which is the difference between the top and lower quartiles.

The given data is:  2, 4, 5, 5, 5, 7, 9, 10, 12, 14, 15, 15, 18, 20, 24.

The median of the data is:

M = 15 + 1 /2 = 16/2 = 8th value.

M = 10

Ignoring the median divide the data into two parts.

The lower quartile median is 4th term:

Q1 = 5

The upper quartile median is 12th term:

Q2 = 15

IQR = Q2 - Q1

IQR = 15 - 5 = 10 years.

Hence, the IQR of the data is 10 years and option B is the correct answer.

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On solving the provided question we can say that by bodmas ((4 / 3) / (1/4)) + ((2 / 5) / (1/4)) + ((4 / 15) / (1/4)) =8

The acronym BODMAS helps children learn the hierarchy of math operations (the correct order for solving math problems). The acronym BODMAS is made up of the following terms:

B Bracket, O Degrees (Power/Exponent or Square Root), D Division, M Multiplication, A Addition, and S Subtraction. BODMAS is also known as PDMAS in some areas. It symbolizes exponents, division, multiplication, addition and subtraction. It also represents brackets. The BODMAS rule states that parentheses must be handled first, then powers or roots (that is, of), division, multiplication, addition, and finally subtraction. Known as BODMAS in India and the UK, PEMDAS is primarily used in the US. However, they are identical to each other. The parentheses, order, and order of addition, subtraction, multiplication, and division are the same for the two rules.  

by bodmas

((4 / 3) / (1/4)) + ((2 / 5) / (1/4)) + ((4 / 15) / (1/4)) =8

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The cost of a pair of pants is $17.

And the cost of a shirt is $31.

One or many equations having the same number of unknowns that can be solved simultaneously are called simultaneous equations. And the simultaneous equation is the system of equations.

Given:

The total cost of 5 shirts and 3 pairs of pants is $206.

The total cost of a shirt and a pair of pants is $48.

Let y be the cost of a pair of pants and x be the cost of a shirt.

That means,

we have the system of equations,

x + y = 48   {equation 1}

5x + 3y = 206   {equation 2}

Multiply 5 to the equation 1 and then subtract equation 2 to equation 1,

we get,

2y = 34

y = 17

And x = 48 - 17 = 31.

Hence, $17 is the cost of a pair of pants.

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By using Python to calculate the value of sin4 is a simple process that involves understanding the concept of radians and using the sine function available in Python's math module.

A radian is a unit of measurement for angles. It is defined as the angle formed when the arc length of a circle is equal to the radius of that circle. This means that an angle of 1 radian is equal to the angle formed by an arc length of 1 radius on a circle.

The sine function, denoted as sin(x), is a mathematical function that takes an angle x as input and returns the ratio of the opposite side to the hypotenuse in a right-angled triangle with an angle x.

Now, we can proceed to calculate the value of sin4 using Python. In Python, the sine function is available in the math module, so we will need to import this module at the beginning of our code. We will then use the sin() function to calculate the sine of 4 radians as follows:

import math

sin4 = math.sin(4)

Here, we are calling the sin() function and passing it the value of 4 as an argument. Since the sine function in Python accepts radians, we do not need to convert 4 to degrees.

Finally, we store the result of this calculation in a variable called sin4. This variable will now hold the value of the sine of 4 radians, which we can use in our program as needed.

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The cost to print 50 photos is $12.50

What is proportion?

The proportion formula is used to determine whether or not two ratios or fractions are equal.

We can use a proportion to find the cost to print 50 photos based on the cost to print 20 photos. Since Ms. Morris charges $5.00 to print 20 photos, we can set up the proportion:

[tex]\frac{cost \ of \ 20\ photos}{number \ of\ photos } =\frac{cost \ of \ 50 \ photos}{number\ of \ photos}[/tex]

Plugging in the given values, we get:

$5.00 / 20 photos = x / 50 photos

Simplifying, we can cross-multiply to get:

20 photos * x = $5.00 * 50 photos

Multiplying and simplifying further, we get:

20x = $250.00

Dividing both sides by 20, we get:

x = $12.50

Therefore, the cost to print 50 photos is $12.50.

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The cost of 600 copies is  $90.10

The cost of 900 copies is $137.80.

The equation that expresses cost is y = 1.06 x ($10 + $15x)

The equation that represents the information in the question is:

Total cost = 1 + sales tax x [cost of the first 100 copies + (x x cost of every additional 100 copies)]

y = 1.06 x ($10 + $15x)

Cost of 600 copies:

x = (600 - 100) / 100 = 500 / 100 = 5

y = (1 + 6/100) x [$10 + (5 x $15)]

y = 1.06 x [$10 + $75)

y = 1.06 x $85

y = $90.10

Cost of 900 copies:

x = (900 - 100) / 100 = 800 / 100 = 8

y = (1 + 6/100) x [$10 + (8 x $15)]

y = 1.06 x [$10 + $120)

y = 1.06 x $130

y = $137.80

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Answer:

This is a math problem. To solve it, you need to use algebra. Let me show you how.

Let x be the number of badges Katya sold. Then we can write an equation using the given information:

46 × 1.40 + 32 × 1.50 + 0.90 × x = 134

Simplifying the equation, we get:

64.4 + 48 + 0.9x = 134

Subtracting 64.4 and 48 from both sides, we get:

0.9x = 21.6

Dividing both sides by 0.9, we get:

x = 24

Therefore, Katya sold 24 badges.

Step-by-step explanation:

Answer:

2[tex]\sqrt{3}[/tex]

Step-by-step explanation:

The rule for a 30:60:90 triangle is [tex]\sqrt{3}:x: 2[/tex]

That means that to get the bottom side, we can divide 4/2

That makes 2, so then we can find x by  multiplying 2 by [tex]\sqrt{3}[/tex]

That makes 2[tex]\sqrt{3}[/tex]

When Y directly varies with X, the direct variation equation is X = 2.

A direct variation is a relationship between two variables when their ratio is constant. One variable is said to vary in direct proportion to another. Y = kx, where k is the variational constant, is the formula for direct variation. If y varies in direct proportion to x and y = 6 when x = 2, the variational constant is k = = 3. Consequently, y = 3x is the equation that describes this direct variation.

If y directly correlates with x, we can apply the direct variation formula as follows:

y = kx

where k is the proportionality constant.

We may utilise the y and x values provided to find k:

y = kx

16 = k(4)

Solving for k, we get:

k = 16/4 = 4

Now we can use the value of k to find x when y = 8:

y = kx

8 = 4x

Dividing both sides by 4, we get:

x = 2

Therefore, when y = 8, x = 2.

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Question:

If y varies directly with x and y = 16 when x = 4, find x when y = 8.

Write and solve a direct variation equation to find the answer.

X =?

The percentage of the increase in the temperature of the mixture is 27.34%.

What is the percentage?

A percentage is a figure or ratio that may be stated as a fraction of 100 in mathematics. If we need to compute the percentage of a number, divide it by the entire and multiply by 100. As a result, the percentage denotes a part per hundred. Per 100 is what the term percent signifies. The sign "%" represents it.

Here are some percentage examples:

10% is 1/10 of a fraction.

20% is equal to a 1/5 portion.

25% is equal to 1/4 fractions.

Now,

As percentage increase = (final value-initial value) / initial value *100

Here initial temperature=12 1/4 F=49/4 F and

Final temperature = 15 3/5=78/5 F

then (final value-initial value) =78/5-49/4=15.6-12.25

=3.35

therefore, percentage increase=3.35/12.25*100

=0.2734*100

=27.34%

Hence,

           The percentage of the increase in the temperature of the mixture is 27.34%.

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The length of the tree remaining sides are 18 inches, 29 inches and 29 inches.

A kite is an object with four sides. It length of the two adjacent sides are of equal length. No pair of sides in a kite are parallel. The perimeter of a kite is the sum of the length of the four sides of the kite.

Perimeter of a kite = 2( a + b)

94 = 2(18 + b)

94 / 2 = 18 + b

47 = 18 + b

b = 47 - 18

b = 29 inches

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Answer:

13 buses are required.

Step-by-step explanation:

To find the number of minibuses required, take the total number of fans and divide by the number of fans each bus holds.

220 /18

12 2/9

We need to round up to make sure all the fans get on a bus.

13 buses are required.

The larger container will hold 500 ounces of soup when filled.

We know that the formula for the volume of cylinder is: V = πr²h

Let us assume that for the smaller container, d₁ represents the diameter, r₁ represents the radius, h₁ represents the height of the container and v₁ represents the volume of the container.

So, using above formula, the volume of the smaller container would be,

v₁ = π × r₁² × h₁

10 = π × r₁² × h₁

For the larger container, d₂ represents the diameter, r₂ represents the radius, h₂ represents the height of the container and v₂ represents the volume of the container.

Using above formula, the volume of the larger container would be,

v₂ = π × r₂² × h₂

The larger container’s diameter is 5​ times larger than the small container’s diameter.

so, we get an equation

⇒ d₂ = 5d₁

⇒ r₂ = 5r₁

Also, the lrger container is 2​ times taller than the small container.

⇒ h₂ = 2h₁

Consider the ratio of volume of larger cotainer to the volume of smaller container.

v₁/v₂ =  (π × r₁² × h₁) / ( π × r₂² × h₂)

10/v₂ =  (r₁² × h₁) / ( (5r₁)² × (2h₁))

10/v₂ =  (r₁² × h₁) / ( 50 × r₁² × h₁)

10/v₂ = 1/50

v₂ = 500 ounces

which is 50 times more than the smaller container.

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The complete question is:

At a farmer’s market, a vendor sells soup that comes in two different-sized containers, both shaped like cylinders. When the small container is filled, it holds10​ ounces of soup. The larger container’s diameter is 5​ times larger than the small container’s diameter, and it is 2​ times taller than the small container. How many ounces of soup will the larger container hold when filled?

Volume of the composite shape is =  114 ft³

Volume is a measure of three-dimensional space.

A composite shape can be defines as a shape created with two or more basic shapes. We often refer to composite shapes as compound and complex shapes as well.

Now, According to the question:

The shape above shows two cuboid joined together.

Volume of the base cuboid = lbh

= 6×3×1 = 18ft³

Volume of the second cuboid = lbh

= 4×3×8 = 96 ft³

Volume of the composite shape = 18ft³ + 96ft³

= 114 ft³

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The probability that a randomly chosen physical therapist does not use the gym membership given that they bring their lunch to work is 2/3, in simplest form.

The table shows the information about the gym membership and lunch habits of 100 physical therapists.

Given that a physical therapist brings their lunch to work, we can use the information in the table to calculate the probability that they do not use the gym membership. To do this, we'll use the formula:

P(not using gym membership | brings lunch) = P(not using gym membership and brings lunch) / P(brings lunch)

We can use the information in the table to find the values of P(not using gym membership and brings lunch) and P(brings lunch).

P(not using gym membership and brings lunch) = 40/100 = 2/5

P(brings lunch) = 60/100 = 3/5

So, the probability that a randomly chosen physical therapist does not use the gym membership given that they bring their lunch to work is:

P(not using gym membership | brings lunch) = P(not using gym membership and brings lunch) / P(brings lunch) = (2/5) / (3/5) = 2/3

Therefore, the probability that a randomly chosen physical therapist does not use the gym membership given that they bring their lunch to work is 2/3, in simplest form.

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The measure of BC from the triangle ABC is 40.82 units.

The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.

Given that, in triangle ABC, AB=21 units and AC=35 units.

By using Pythagoras theorem,

BC²=AB²+AC²

BC²=21²+35²

BC²=441+1225

BC²=1666

BC=√1666

BC=40.82

Therefore, the measure of BC is 40.82 units.

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Answer:

12

Step-by-step explanation:

6 with 9 figers

Answer:

Let x be 6 and y be 9.

x + y = 6 + 9 = 15.

However, x + y does not equal 15. Hence, we can deduce that:

x + y = 15 [tex]\neq[/tex] 15.

15 does not equal 15, so if 15 is 15 and not equal to 15, we can prove that since 6 does not equal 9, 6 is 9. We can therefore conclude that we need to solve for x + x. Since we proved that something is something by not being something, 2x ix 2x but not 2x.

2x isn't 2x but is 2x, so the answer isn't the answer but is still the answer. Therefore, this question isn't a question when it is a question.

:) I am teaching you Maths in Ohio.

The proportion EF/DF = BC/AC is true. Hence, option A is the accurate answer to this question.

We are given that the two triangles ΔABC and ΔDEF are similar.

According to the definition of a similar triangle, we know that the ratio of the corresponding sides is proportional and the corresponding angles are always congruent.

Since ΔABC and ΔDEF are similar, this implies that -

∠A corresponds to ∠D,

∠B corresponds to ∠E, and

∠C corresponds to ∠F.

Thus we can say -

EF/DF = BC/AC

AB/DF = DE/AC

AB/EF = DE/BC

Only option A satisfies the condition. Hence, the proportion EF/DF = BC/AC is true.

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The complete question is -

The triangle abc and triangle def are similar. Which proportion must be true?

By Using the table to work out the values of a , b , c , and d. X y = 2 x + 1 − 3 a − 2 − 3 − 1 b 0 1 1 c 2 d a = b = c = d =

Therefore, The solutions are : a = -3, b = 0, c = 6, d = 9

Equation:

In mathematics, an equation is an expression that indicates equality of two expressions by connecting them with the equal sign = . The word "equation" and related words in other languages ​​can have slightly different meanings. For example, in French an equation is defined as containing one or more variables, whereas in English a well-formed formula consisting of two expressions connected by an equal sign is an equation.

Given:

This table;

x             y = 3x+3

-3                -6

-2                 a

-1                  b

0                 3

1                  c

2                 d

To Find:

Values of a, b, c and d

Consider the 2nd row,

x = -2, y = a

Putting the values in the equation,

we get,

   a = 3(-2) + 3

⇒ a = -3

Consider the 3rd row,

x = -1, y = b

Putting the values in the equation,

we get,

   b = 3(-1) + 3

⇒ b = 0

Consider the 5th row,

x = 1, y = c

Putting the values in the equation,

   c = 3(1) + 3

⇒ c = 6

Consider the 6th row,

x = 2, y = d

   d = 3(2) + 3

⇒ d = 9

The final answer is,

a = -3, b = 0, c = 6, d = 9.

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We will prove that if we remove the root of a k-th order binomial tree, it results in k binomial trees of smaller orders.

Base case: If k = 1, the binomial tree consists of a single node. Removing the root node leaves an empty tree, which can be considered as a collection of 0 binomial trees of smaller orders.

Induction hypothesis: Assume that the statement is true for a k-th order binomial tree.

Induction step: We need to prove that the statement is true for a (k+1)-th order binomial tree, which is formed by joining two k-th order binomial trees.

Remove the root node of the (k+1)-th order binomial tree. This results in two trees, each of which is a k-th order binomial tree.

By the induction hypothesis, removing the root node of each of the two k-th order binomial trees results in k binomial trees of smaller orders.

Thus, removing the root node of the (k+1)-th order binomial tree results in a total of 2k binomial trees of smaller orders, which completes the proof.

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The equation for this circle is as stated in the above statement: (x-h)² + 2(y-k)² = r²

Today, circles are still significant symbolically; they frequently stand for peace and unity. Check out at the Olympic logo, for instance. It contains five overlapping rings of various colors that collectively symbolize the world's five major continents, which are joined in a great spirit of healthy rivalry.

A circle is a round shape that may be created by following a moving point on a plane while maintaining a constant distance from another point. This Greek word kirkos, which means hoop or ring, is whence the word circle gets its from.

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Answer:

hey there here's your answer !!!!

Step-by-step explanation:

For two-digit numbers, there is the TENS place and the ONES place. Let's take a closer look at the place value for the number 12. The 1 is in the TENS place, and the 2 is in the ONES place. That's because the number 12 is made up of 1 ten and 2 ones.

The values of x for the given equations are:

1. The value of x = 0

2. The values of x are ±1

3. The values of x are 0 and -7/16

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

To find the values of x in each of the equations, we need to simplify them using algebraic operations:

1. 8x² = 6x² + 5x²

Combining like terms on the right-hand side:

8x² = 11x²

Subtracting 6x² from both sides:

2x² = 0

Dividing both sides by 2:

x² = 0

Taking the square root of both sides:

x = 0

Therefore, the only solution to this equation is x = 0.

2.Similarly, we can calculate values of x for this equation:

-7x² + 6 = x² - 7x²

x² = 1

Taking the square root of both sides:

x = ±1

Therefore, the solutions to this equation are x = 1 and x = -1.

3. 7x² + 9x² = -6x² - 7x

x(16x + 7) = 0

Using the zero product property:

x = 0 or 16x + 7 = 0

Solving for x in the second equation:

16x = -7

Dividing both sides by 16:

x = -7/16

Therefore, the solutions to this equation are x = 0 and x = -7/16.

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The measure of angle ABC from the given circle D is 34°.

The angles at the circumference subtended by the same arc are equal. More simply, angles in the same segment are equal.

Given that, circle with the center D and measure of arc AC is 34°.

The measure of arc = m∠ABC

m∠ABC =34°

Therefore, the measure of m∠ABC is 34°.

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Answer:

The probability of tossing a fair coin and it landing on heads 8 times in a row is (1/2)^8 = 1/256. This means that there is a 1 in 256 chance that a fair coin will land on heads 8 times in a row. The probability of an event can be calculated by taking the number of favorable outcomes and dividing it by the number of possible outcomes. In this case, there is only one favorable outcome (tossing a heads 8 times in a row) and two possible outcomes for each toss (heads or tails), so the probability is 1/2^8 = 1/256.

Step-by-step explanation:

Answer:

it should be 0.04percent.