In a group of students , 12 read maths, 15 read statistics , 11 read physics, 4 read maths only , 7 read statistics only, 3 read statistics and physics only and 1 read maths and statistics only . What is the number of the students who were there altogether ( universal set)

The volume of the cone is (5/3)π(9²) cubic units ≈ 381.7 cubic units.

The formula for the volume of a cone is V = (1/3)πr²h, where r is the radius of the circular base and h is the height of the cone. However, we are given the base area B instead of the radius, so we need to find the radius first.

We know that the area of a circle is A = πr², so if the base area of the cone is B = 5π square units, then πr² = 5π, which means r² = 5. Solving for r, we get r = √5.

Now that we have the height h = 9 units and the radius r = √5 units,

we can use the formula for the volume of a cone:

V = (1/3)πr²h.

Substituting the values, we get

V = (1/3)π(√5)²(9) = (5/3)π(9²) cubic units, which simplifies to ≈ 381.7 cubic units.

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Answer:

I believe it's D

Step-by-step explanation:

You plug in 0 and you get 5 as your Y value

The function of the graph is y = (5 + 3x)/(1 + x), so the correct option is d.

A graph contains data of which input maps to which output.

Analysis of this leads to the relations which were used to make it.

If we know that the function crosses x axis at some point, then for some polynomial functions, we have those as roots of the polynomial.

The graph is first shifted to the right by 4 units and another one to the left by 1/2.

So, we have:

y = (5 + 3x)/(1 + x)

Hence, the function of the graph is y = (5 + 3x)/(1 + x)

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The value of the chi-square test statistic is χ2 = 9.34, and the P-value is between 0.02 and 0.025.

To calculate the expected counts under the assumption of equal distribution, we divide the total sample size (100) by 3:

Expected count = Total sample size / Number of options

= 100 / 3

= 33.33 (approximately)

Now, we can calculate the chi-square test statistic:

χ2 = Σ((O - E)^2 / E)

where O is the observed count and E is the expected count for each category.

Calculating the chi-square test statistic:

χ2 = ((38 - 33.33)^2 / 33.33) + ((45 - 33.33)^2 / 33.33) + ((17 - 33.33)^2 / 33.33)

≈ 2.44 + 3.43 + 3.47

≈ 9.34

To determine the P-value, we need to compare the chi-square test statistic to the chi-square distribution with (number of options - 1) degrees of freedom. In this case, we have (3 - 1) = 2 degrees of freedom.

Referring to the chi-square distribution table, the P-value for a chi-square test statistic of 9.34 and 2 degrees of freedom is approximately between 0.02 and 0.025.

Therefore, the value of the chi-square test statistic is χ2 = 9.34, and the P-value is between 0.02 and 0.025.

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Answer:

\(2187\)

Step-by-step explanation:

\(\frac{3^3}{3^-^4}\)

When attempting to solve this, we have to consider the exponent rule of fractional exponents:

\(\frac{x^a}{x^b} =x^a^-^b\)

Therefore, our initial problem would become:

\(3^3^-^(^-^4^)\\\)

Two negatives become positive:

\(3^3^+^4\)

Add:

\(3^7\)

\(3\) × \(3\) × \(3\) × \(3\) × \(3\) × \(3\) × \(3\)

\(= 2187\)

Answer:

16 ft

Step-by-step explanation:

Difference in a math question always signifies that we are subtracting. When finding the difference between an elevation you need to subtract the highest point first from the lowest point or starting point. Therefore in this scenario, we subtract 14 feet which is the highest point from the starting point which is -2 ft. Since the starting point is at a negative elevation, the negatives will cancel out and becomes a positive.

14 - (-2) = x ... negative cancel out and become a positive or addition

14 + 2 = x

16 ft = x

Finally, we can see that the difference between these two points is 16 ft.

The equation in slope-intercept form of the line passing through the given points is \(y = -5x + 37\)

Given the following points:

To write an equation in slope-intercept form of the line passing through the given points, we would use the following formula;

\(Slope. \;m = \frac{Change \; in \; y \;axis}{Change \; in \; x \;axis} \\\\Slope. \;m = \frac{y_2 - y_1}{x_2 - x_1}\)

Substituting the points into the formula, we have;

\(Slope. \;m = \frac{12\; - \;2}{2\; - \;7}\\\\Slope. \;m = \frac{10}{-5}\)

Slope, m = -5

Next, we would find the intercept:

The standard form of an equation of line is given by the formula;

\(y = mx + b\)

Where:

Substituting the values, we have:

\(2 = -5(7) + b\\\\2 = -35 + b\\\\b = 35 + 2\)

b = 37

Now, we would write the equation in slope-intercept form:

\(y = -5x + 37\)

Therefore, the equation in slope-intercept form of the line passing through the given points is \(y = -5x + 37\)

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Answer:

Step-by-step explanation:

(12 - 2)/(2 - 7)= 10/-5= -2

y - 2 = -2(x - 7)

y - 2 = -2x + 14

y = -2x + 16

The 98% confidence interval for the population mean (μ) is approximately (2.711, 3.009).

1: Identify the given data

Sample size (n) = 150 students

Sample mean (x) = 2.86

Population standard deviation (σ) = 0.78

Confidence level = 98%

2: Find the critical z-value (z*) for a 98% confidence level

Using a z-table or calculator, you'll find that the critical z-value for a 98% confidence level is 2.33 (approximately).

3: Calculate the standard error (SE)

SE = σ / √n

SE = 0.78 / √150 ≈ 0.064

4: Calculate the margin of error (ME)

ME = z* × SE

ME = 2.33 × 0.064 ≈ 0.149

5: Construct the confidence interval

Lower limit = x - ME = 2.86 - 0.149 ≈ 2.711

Upper limit = x + ME = 2.86 + 0.149 ≈ 3.009

The 98% confidence interval is approximately (2.711, 3.009).

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Answer:

10

Step-by-step explanation:

I mean if you need help then like you shouldn't be on here :/

i wasted 10 hours but i solved it is 10 because 1+1+1+1+1=5 and 1+1+1+1+1=5 add them you get 10 (づ｡ ◕‿‿◕｡) づ

Answer:

Step-by-step explanation:

U still in school

Answer:

42 square units

Step-by-step explanation:

We can divide the figure in two triangles and one rectangle

the two triangles are congruent

base  = |-5-2| = 7

height = 2

Total area of the two triangles = (7 *2)/2 * 2 = 14 square units

the rectangle have the length that is equal to the base of the triangles

height = |-2-2| = 4

Area = 7 *4 = 28 square units

Final area = 14+ 28 = 42 square units

Answer:

6x – 150 = 2400

Step-by-step explanation:

Each plate of food was sold for $8, but cost the school $2 to prepare:

-2x + 8x = 6x

A school spent $150 on advertising for a breakfast fundraiser:

-150

After all expenses were paid, the school raised $2400 at the fundraiser:

6x – 150 = 2400

In case you want to solve it:

6x – 150 = 2400

+ 150 + 150

_________________

6x = 2550

___ _____

6 6

x = 425

So, four hundred twenty-five plates were sold.

Answer:

Answer:

-8

Step-by-step explanation:

28 + 10x = 6x - 4

10x = 6x - 32

4x = -32

x = -8

Best of Luck!

Answer:

2y - 5 (read below)

Step-by-step explanation:

-8y + 10y = 2y

2 + (-7) = -5

Your expression could/would be:

2y - 5.

Hope this helps!

Answer:

you can combine -8y and 10y since 8 is negative it would be =2y

an you can do 2+-7=-5

The constant of proportionality is 1/18 teaspoons per muffin.

To find the constant of proportionality that relates the number of muffins made, y, to the number of teaspoons of vanilla used, x, we need to determine the ratio of these two quantities.

According to the given recipe, 2 teaspoons of vanilla are used to make 36 muffins. This can be expressed as:

x₁ = 2 teaspoons (vanilla)

y₁ = 36 muffins

To find the constant of proportionality, we can set up a ratio:

x₁ / y₁ = 2 teaspoons / 36 muffins

Now, we can simplify this ratio:

x₁ / y₁ = 1/18 teaspoons per muffin

Therefore, the constant of proportionality is 1/18 teaspoons per muffin.

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Answer:

-7x²-13x+2

Step-by-step explanation:

-7x²-14x+1x+2

-27-36i .................................................................... not sure

The result of (3 - 6i)² will be -27 -36i .

Given,

(3 - 6i)²

Now,

The multiplication is of complex number .

So,

(3-6i)(3 - 6i)

So,

Multiply the terms ,

9 - 18i - 18i -36

Simplifying further,

-27 - 36i

Thus the resultant will be  -27 -36i  .

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Answer:

nice thats my last name but I do not understand the question

Step-by-step explanation:

Answer: what is the main question?

Step-by-step explanation:

Answer:

Step-by-step explanation:

If Carlos is 6ft tall and looks up at the tree that is 275 ft tall, subtract those two.

275 - 6 = 269

Use tangent with the given angle and the new height. The distance is x.

tan15 = 269/x

x = 269/tan15

x = 1004ft

The distance from Carlos to the tree, given he is 6 feet tall and looks up at a 15° angle of elevation to see the top of a 275-foot tall tree located in Sequoia National Park, is 1026.

Hence option C is correct.

According to the information given,

We can set up a right triangle with Carlos's eye level, the top of the tree, And the base of the tree as the three points of the triangle.

Carlos's height of 6 feet can be used as one side of the triangle,

And we can use the tangent function to find the length of the adjacent side.

A tangent of 15 degrees is equal to the opposite side (height of the tree) divided by the adjacent side (distance from Carlos to the tree).

So, we can solve for the adjacent side by multiplying the height of the tree by the tangent of 15 degrees:

tan(15) = height of the tree / distance from Carlos to the tree

Distance from Carlos to the tree = height of the tree / tan(15)

Plugging in the values given:

Distance from Carlos to the tree = 275 / tan(15)

                                                      ≈ 1026

Therefore,

The nearest foot to the distance from Carlos to the tree is option C. 1026.

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I) f is continuous at x=2

II) f is differentiable at x=2

These both f (function ) are true

The given limit can be recognized as the definition of the derivative of f at x=2. Specifically, it states that the derivative of f at x=2 is equal to 5.

Using this information, we can make the following conclusions:

I) We cannot say for sure whether f is continuous at x=2 based on the given limit alone. While a function being differentiable at a point implies that it is also continuous at that point, the converse is not necessarily true. Therefore, we would need additional information to determine whether f is continuous at x=2.

II) The given limit implies that f is differentiable at x=2, since the limit exists and is finite. Specifically, we can say that the derivative of f at x=2 exists and is equal to 5.

III) The given limit also implies that the derivative of f is continuous at x=2. This is because the limit defines a continuous function at x=2, and it is well-known that if a function is differentiable at a point, then it is also continuous at that point.

Therefore, the correct answers are II and III.

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Answer:

First answer is 80, second answer is 24

Step-by-step explanation:

area= length × width

Answers:

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

Explanation:

The entire store is 8 m by 10 m, so its area is 8*10 = 80 m^2

The clothing area is 6 m by 4 m, so its area is 6*4 = 24 m^2

The equipment area is 80 - 24 = 56 m^2, so that may be what you were thinking of when you typed that into the first box; however, that's not correct for the entire store (as it only applies to the equipment area).

Answer:

(3,7)

Step-by-step explanation: My favorite song rn is like I want you by giveon

Answer:x=-0.5

Step-by-step explanation:

You would add the 2.5 on both sides of the equal sign

It will take 11 years for the canyon floor to have an elevation of −31 feet.

A mathematical statement known as an equation makes two expressions' values equal. It is a mathematical statement that says "this is equivalent to that," in other words. The left side appears to be a mathematical expression, the centre appears to be an equal sign, and the right side is another mathematical expression. The right side of the equation frequently has a value of zero.

Given,

The first step in this situation is to define the variables.

So, we have:

x: the age in years

y: height in feet

The equation used to model the issue is then written.

So, we have:

y = 1.5x - 14.5

Then, at a -31 foot elevation, we have:

-31 = 1.5x - 14.5

For years,

x = -16.5/1.5

x = 11

In 11 years it will take for the canyon floor to have an elevation of −31 feet.

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(make them equal to each other)

10x-1 = 14x-37

(combine like terms)

-4x = -36

(divide by -4)

x=9

Hope this helps! Have a good day/night!

The probability of getting heads in one toss of the unfair coin can be expressed as 1/3. Adding the numerator and denominator, we get 1 + 3 = 4. So, m + n = 4.

To find the probability of getting at least one tails in three tosses, we can use the complement rule.
The complement rule states that the probability of an event occurring is equal to 1 minus the probability of the event not occurring.
So, the probability of getting at least one tails in three tosses is equal to 1 minus the probability of getting all heads in three tosses.
Let's assume the probability of getting heads in one toss is p.
The probability of getting all heads in three tosses is (p)^3.
Therefore, the probability of getting at least one tails in three tosses is 1 - (p)^3.
We are given that this probability is equal to 26/27.
So, 1 - (p)^3 = 26/27.
Simplifying the equation, we have (p)^3 = 1 - 26/27 = 1/27.
Taking the cube root of both sides, we get p = 1/3.
Therefore, m = 1 and n = 3.
Adding m and n, we have 1 + 3 = 4.
So, m + n = 4.
Therefore, the answer is 4.
m + n = 4.
To find the probability of getting at least one tails in three tosses of an unfair coin, we can use the complement rule. The complement rule states that the probability of an event occurring is equal to 1 minus the probability of the event not occurring. Let's assume the probability of getting heads in one toss of the unfair coin is p.

Therefore, the probability of getting all heads in three tosses is (p)³. The probability of getting at least one tails in three tosses is equal to 1 minus the probability of getting all heads, which is 1 - (p)³.

We are given that this probability is equal to 26/27. Setting up the equation, we have 1 - (p)³ = 26/27.

Simplifying, we get (p)³ = 1 - 26/27

= 1/27.

Taking the cube root of both sides, we find that p = 1/3. Therefore, the probability of getting heads in one toss is 1/3. To compute m + n, we simply add the numerator and denominator of the probability of getting heads in one toss, which gives us 1 + 3 = 4.

Therefore, the answer is 4.

The probability of getting heads in one toss of the unfair coin can be expressed as 1/3. Adding the numerator and denominator, we get 1 + 3 = 4. So, m + n = 4.

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Zone(area) = L x W = 2.5 x 2.5 = 6.25 square meters. 

Of all rectangles with an edge of 10 meters, the one that has the greatest zone(area) could be a square.

To see why, let's assume that a rectangle with a border of 10 meters has measurements of length L and width W.

At that point, we know that:

2L + 2W = 10

Rearranging this condition, we get:

L + W = 5

Presently, we need to discover the most extreme range encased by the rectangle, which is given by:

Area = L x W

Able to illuminate for one variable in terms of the other utilizing the condition L + W = 5:

L = 5 - W

Substituting this expression for L into the condition for the zone, we get:

Zone = (5 - W) x W

Extending and disentangling this expression, we get:

Area = 5W - W²

To discover the most extreme esteem of this quadratic expression, we will take its subsidiary with regard to W and set it to break even with zero:

dArea/dW = 5 - 2W =

Tackling for W, we get:

W = 2.5

Substituting this esteem back into the condition for the edge, we get:

L = 2.5

Hence, the measurements of the rectangle that has the greatest region are L = 2.5 meters and W = 2.5 meters, which implies it could be a square. The most extreme zone enclosed by the rectangle is:

Zone(area) = L x W = 2.5 x 2.5 = 6.25 square meters. 

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the answer is in the picture

Answer:

2/29 or 0.06896551724

Step-by-step explanation:

Answer: if you mean what it is simplified to it is 2/29

Step-by-step explanation:

Step-by-step explanation:

7+8+9=24

second integer is 8 so 8*3=24

a) X'Y' + X'Y + XY simplifies to X' + Y.

b) A'BC' + ABC' + BC'D simplifies to BC'.

Complement of the functions:

a) Complement is W' + X' + YZ.

b) Complement is (A' + B + C)(A'B' + C' + A'B).

a) To prove X'Y' + X'Y + XY = X' + Y, we can use Boolean algebra identities:

X'Y' + X'Y + XY

= Y'(X' + X) + XY(Distributive Law)

= Y' + XY(X + X' = 1)

= X' + Y(Commutative Law)

Therefore, X'Y' + X'Y + XY simplifies to X' + Y.

b) To prove A'BC' + ABC' + BC'D = BC', we can simplify the expression using Boolean algebra:

A'BC' + ABC' + BC'D

= BC'(A' + A) + BC'D   (Distributive Law)

= BC' + BC'D(A + A' = 1)

= BC'(BC' + BC'D = BC' + BC'(1) = BC')

Hence, A'BC' + ABC' + BC'D simplifies to BC'.

Complement of the given functions:

a) The complement of WX(Y'Z + YZ') + W'X'(Y' + Z)(Y + Z') is W' + X' + YZ.

b) The complement of (A + B' + C')(A'B' + C)(A + B'C') is (A' + B + C)(A'B' + C' + A'B).

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