A box of clearance clothes at a shop contains 3 red shirts and 12 black shirts. What is the probability that Ned will choose 2 red shirts randomly from the box?
1/35
2/75
3/70
12/35

Answer:(4,-3); 2x-7y=14

Step-by-step explanation:

In testing the hypotheses H0: p = 0.5 vs Ha: p > 0.5, the test statistic is found to be 1.83. We need to determine the correct p-value. From the options provided, the correct p-value is d) 0.0336

The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed test statistic, assuming that the null hypothesis is true. Since this is a right-tailed test (Ha: p > 0.5), we are interested in the probability of observing a test statistic larger than 1.83. Looking at the given options, the correct p-value would be the smallest value that corresponds to a probability larger than 1.83. From the options provided, the correct p-value is d) 0.0336, as it represents a probability smaller than 1.83. Therefore, 0.0336 is the correct p-value for this hypothesis test.

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The series ∑[n=1 to ∞] \(8e^n\) / (3n(n+1)) is convergent.

To determine whether the series ∑[n=1 to ∞] \(8e^n\) / (3n(n+1)) is convergent or divergent, we can apply the ratio test.

Using the ratio test, we calculate the limit as n approaches infinity of the absolute value of the ratio of the (n+1)-th term to the n-th term:

lim(n→∞) |\((8e^(^n^+^1^) / (3(n+1)(n+2))) / (8e^n / (3n(n+1)))\)|

Simplifying the expression:

lim(n→∞) |\((8e^(^n^+^1^) * 3n(n+1)) / (8e^n * 3(n+1)(n+2))\)|

The common factors cancel out:

lim(n→∞) |e * n / (n+2)|

As n approaches infinity, the ratio tends to e, which is a finite non-zero value.

Since the ratio is a constant (e), which is less than 1, the series is convergent by the ratio test.

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Answer:

x=3

Step-by-step explanation:

19x−3(x−6)=66

19x+(−3)(x)+(−3)(−6)=66(Distribute)

19x+−3x+18=66

(19x+−3x)+(18)=66(Combine Like Terms)

16x+18=66

16x+18=66

Step 2: Subtract 18 from both sides.

16x+18−18=66−18

16x=48

Step 3: Divide both sides by 16.

16x/16=48/16

x=3

Answer:

solution: x = 3

Step-by-step explanation:

this looks totally like

f(x) = 1/3 x - 3

to me.

because

f(0) = -3

f(3) = -2

f(6) = -1

so, f(9) = 1/3 × 9 - 3 = 3 - 3 = 0

f(9) = 0

you did not list that as answer option, but that is the correct answer.

Answer: x=2

Step-by-step explanation:

Given AC = 2x+9 and BD = 7x-1

AC=BD,

2x+9 = 7x-1

10=5x

x=10/5 = 2

Answer:

5/9

Step-by-step explanation:

brainliest when possible.

For maximum volume: Coat the sphere with a radius of approximately 0.5641 meters.

For minimum volume: Coat the cube with an edge length of approximately 0.8165 meters.

To determine the dimensions of the sphere and the cube that maximize and minimize the total volume of the silvered solids, we need to establish some equations and constraints based on the given information.

Let's denote the radius of the sphere as 'r' and the edge length of the cube as 'a'.

Maximizing the Total Volume:

For the maximum volume, we need to consider the possibility that all of the silver can be coated on either the sphere or the cube. We can set up two scenarios:

1) If all of the silver is coated on the sphere:

The surface area of a sphere is given by the formula:

A(sphere) = 4πr²

Since we have enough silver to cover 4 square meters, we can set up the equation:

4 = 4πr²

r² = 1/π

r ≈ 0.5641

So, if all of the silver is coated on the sphere, the radius should be approximately 0.5641 meters.

2) If all of the silver is coated on the cube:

The surface area of a cube is given by the formula:

A(cube) = 6a²

Again, considering that we have enough silver to cover 4 square meters, we can set up the equation:

4 = 6a²

a² = 2/3

a ≈ 0.8165

If all of the silver is coated on the cube, the edge length should be approximately 0.8165 meters.

Minimizing the Total Volume:

For the minimum volume, we need to consider the case where one solid is entirely coated with the silver, while the other solid remains uncoated.

1) If all of the silver is coated on the sphere:

In this case, the volume of the sphere will be maximum, and the cube will remain uncoated.

We can calculate the volume of the sphere using the formula:

V(sphere) = (4/3)πr³

Substituting the value of r we obtained earlier (r ≈ 0.5641), we can find the volume of the sphere:

V(sphere) ≈ (4/3)π(0.5641)³ ≈ 0.7556 cubic meters

2) If all of the silver is coated on the cube:

In this case, the volume of the cube will be maximum, and the sphere will remain uncoated.

We can calculate the volume of the cube using the formula:

V(cube) = a³

Substituting the value of a we obtained earlier (a ≈ 0.8165), we can find the volume of the cube:

V(cube) ≈ (0.8165)³ ≈ 0.5352 cubic meters

Therefore, if we want to minimize the total volume, we should coat the cube, resulting in a volume of approximately 0.5352 cubic meters, while leaving the sphere uncoated.

To summarize:

For maximum volume: Coat the sphere with a radius of approximately 0.5641 meters.

For minimum volume: Coat the cube with an edge length of approximately 0.8165 meters.

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The farmer knows that the 5 camp division is an easier practical solution than the 9 camp division because it does not require dealing with fractions or decimals.

Both fractions and decimals are just two ways to represent numbers. Fractions are written in the form of p/q, where q≠0, while in decimals, the whole number part and fractional part are connected through a decimal point.

To understand why the 5 camp division is an easier practical solution than the 9 camp division, we need to consider the common factors of 8,085 and the numbers 9 and 15.

The prime factorization of 8,085 is:

8,085 = 3 x 3 x 3 x 5 x 5 x 6

The prime factorization of 9 is:

9 = 3 x 3

The prime factorization of 15 is:

15 = 3 x 5

From the prime factorizations, we can see that 9 has a common factor of 3 with 8,085, while 15 has two common factors of 3 and 5 with 8,085. This means that dividing 8,085 into 9 or 15 camps of equal size would require dealing with fractions or decimals, which can be impractical in a farming context.

On the other hand, the prime factorization of 5 is:

5 = 5

Since 5 is a prime number, it does not have any common factors with 8,085. This means that dividing 8,085 into 5 camps of equal size would not require dealing with fractions or decimals. The farmer can simply divide the grazing land into 5 equal parts, each with an area of 1,617 hectares, without needing to perform any division calculations or deal with any fractions or decimals.

Therefore, the farmer knows that the 5 camp division is an easier practical solution than the 9 camp division because it does not require dealing with fractions or decimals.

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Answer:

14/14

Step-by-step explanation:

multiply 7/7 by 2/2

=14/14

Answer:

1000 cubic metre

Step-by-step explanation:

hopes it help

Answer:

solution,

length=10 cm

volume=?

now,

volume of cube=l×l×l

=10×10×10

therefore,the answer is 1000 cubic centimeter

Answer:

i think its 3 if im not mistaken

Step-by-step explanation:

Points M and N will be located on the number line as:

M is at -15

N is at 3.

Here, we have,

to Find the Coordinate of a Point on a Number Line:

The number line gives us an idea of how real numbers are ordered, where we have the negative numbers to the left, and the positive numbers to the right.

The distance between two points on a number line is the number of units between both points.

Given that point L is at -6 on a number line, thus:

Point M is 9 units away from point L = -6 - 9 = -15

Point N is 9 units away from point L = -6 + 9 = 3

Therefore, points M and N will be located on the number line as:

M is at -15

N is at 3.

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Answer:

no

Step-by-step explanation:

you cannot divide zero into two equal parts because there is nothing there to start.  Since Pablo has no candy, he cannot divide it into two piles because there isn't anything to divide.

Answer: No because 0 means nothing  and you can't divide nothing among something so  that is like undefined.

Step-by-step explanation:

Answer:

= -4(2.3x + 0.7)

Step-by-step explanation:

=(3x + 5.1) + (-12.2x - 7.9)

= 3x + 5.1 - 12.2x - 7.9

= -9.2x - 2.8

= -4(2.3x + 0.7)

Answer:

Hello! The answer is 2000

Answer:

1. congruent? No

Similar? Yes

2. congruent? No

similar? yes

3. congruent? no

similar? yes

4. congruent? yes

similar? yes

I tried my best I hope it's right

Answer: THe person who rented a apartment had been in debt for 50 dollars, but she didnt have a lot of money so the land lord would divide the rent by 5

Step-by-step explanation:

Answer:

4sqrt(3)

Step-by-step explanation:

If the triangle is equilateral, the hypotenuse is 2x

We can use the Pythagorean theorem

a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse

x^2 + 12^2 = (2x)^2

x^2 + 144 = 4x^2

144 = 4x^2 -x^2

144 = 3x^2

48 = x^2

Taking the square root of each side

sqrt(48) = sqrt(x^2)

sqrt(16*3) = x

4 sqrt(3) =x

Answer:

28 students

Step-by-step explanation:

7 times 4 = 28

there are are seven students in 4 teams, so that means there are 4 groups of seven, and you multiply them together to get how many students in the class

Answer:

28

Keyword(s):

divided, four, 7, per team, how many

Step-by-step explanation:

7 × 4 = 28

The determinant of an elementary matrix of this form is always equal to 1. Therefore, the determinant of this matrix is 1.

A single elementary row operation on the identity matrix yields a square matrix known as an elementary matrix. Simple row operations include adding a multiple of one row to another row and multiplying a row by a non-zero scalar. The resulting matrix is still invertible, and the opposite elementary row operation can be used to create the inverse of the identity matrix. In linear algebra, elementary matrices are used to describe and work with systems of linear equations. They also offer a practical method for computing determinants and resolving matrix equations. Additionally, they are used in encryption and computer graphics.

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The Distance between P and Q is PQ² = 2 - 2 ( cos β. cos α + sin β. sin α).

The two points on the cartesian plane having coordinates P(a, b) and Q( c, d) then the distance between P and Q is

PQ²= ( c- a )² + (d -b)²

Given:

we have the coordinates P( cos α, sin α) and Q( cos β, sin β).

Using Distance formula

PQ²= ( cos β- cos α)² + (sin β - sin α)²

PQ²= cos² β  + cos² α - 2 cos β. cos α  +  sin² β  + sin² α - 2 sin β. sin α

PQ²= (cos² β +  sin² β) + (cos² α + sin² α ) -  2 cos β. cos α- 2 sin β. sin α

As, we know that sin² x + cos² x = 1

PQ² = 1 + 1 - 2 ( cos β. cos α + sin β. sin α)

PQ² = 2 - 2 ( cos β. cos α + sin β. sin α)

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The dilation of the triangle is illustrated below.

Resizing an object uses a transformation called dilation. Dilation is used to enlarge or contract the objects. The result of this transformation is an image that retains the original shape.

The image's size will depend on the scale factor, which is used to dilate a mathematical object. See the diagram below. We end up with a triangle where the sides are 3/2 = 1.5 times longer compared to the original diagram.

Because segment AC is going through P (center of dilation), this means that segment A'C' will also go through P. Furthermore, it means AC and A'C' overlap. However, as mentioned earlier, A'C' is 1.5 times longer than AC.

Another thing to note is that line BC is parallel to line B'C', and line AB is parallel to A'B'.

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The minimum and maximum values of f(x,y) subject to the constraint 8 - 2x - 5y^2 = 0 are both equal to 1.


We can use the method of Lagrange multipliers to solve this problem. Let's define the Lagrangian as L(x,y,λ) = x^2 y^2 + λ(8 - 2x - 5y^2). We need to find the values of x, y, and λ that minimize or maximize L subject to the constraint 8 - 2x - 5y^2 = 0.

Taking partial derivatives of L with respect to x, y, and λ, we get:

∂L/∂x = 2xy^2 - 2λ

∂L/∂y = 2x^2y - 10λy

∂L/∂λ = 8 - 2x - 5y^2

Setting these equal to zero and solving for x, y, and λ, we get:

x = ±√(2λ/y^2)

y = ±√(2λ/5)

λ = xy^2/2

Substituting these back into the constraint equation, we get:

8 - 2x - 5y^2 = 0

8 - 2(±√(2λ/y^2)) - 5(±√(2λ/5))^2 = 0

Simplifying this equation, we get:

√(5λ) = √2

λ = 2/5

Substituting this back into the equations for x and y, we get:

x = ±1

y = ±1

Now we can evaluate the function f(x,y) = x^2 y^2 at the four possible points (1,1), (-1,1), (1,-1), and (-1,-1):

f(1,1) = 1

f(-1,1) = 1

f(1,-1) = 1

f(-1,-1) = 1

Therefore, the minimum and maximum values of f(x,y) subject to the constraint 8 - 2x - 5y^2 = 0 are both equal to 1.

the minimum and maximum values of f(x,y) subject to the constraint 8 - 2x - 5y^2 = 0 are both equal to 1.

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The minimum and maximum values of f(x,y) subject to the constraint 8 - 2x - 5y^2 = 0 are both equal to 1.

We can use the method of Lagrange multipliers to solve this problem. Let's define the Lagrangian as L(x,y,λ) = x^2 y^2 + λ(8 - 2x - 5y^2). We need to find the values of x, y, and λ that minimize or maximize L subject to the constraint 8 - 2x - 5y^2 = 0.

Taking partial derivatives of L with respect to x, y, and λ, we get:

∂L/∂x = 2xy^2 - 2λ

∂L/∂y = 2x^2y - 10λy

∂L/∂λ = 8 - 2x - 5y^2

Setting these equal to zero and solving for x, y, and λ, we get:

x = ±√(2λ/y^2)

y = ±√(2λ/5)

λ = xy^2/2

Substituting these back into the constraint equation, we get:

8 - 2x - 5y^2 = 0

8 - 2(±√(2λ/y^2)) - 5(±√(2λ/5))^2 = 0

Simplifying this equation, we get:

√(5λ) = √2

λ = 2/5

Substituting this back into the equations for x and y, we get:

x = ±1

y = ±1

Now we can evaluate the function f(x,y) = x^2 y^2 at the four possible points (1,1), (-1,1), (1,-1), and (-1,-1):

f(1,1) = 1

f(-1,1) = 1

f(1,-1) = 1

f(-1,-1) = 1

Therefore, the minimum and maximum values of f(x,y) subject to the constraint 8 - 2x - 5y^2 = 0 are both equal to 1.

the minimum and maximum values of f(x,y) subject to the constraint 8 - 2x - 5y^2 = 0 are both equal to 1.

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Answer:

15

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

6+9 is equal to fifteen. I don't really know how to explain it, its just adding 6 to 9.