Need help asap! Tysmmm

Explanation:

The expression r/6 is the quotient of r and 6. The quotient is the result of a division problem. For example, the quotient of 100 and 25 is 4 because 100/25 = 4.

We'll then raise r/6 to the 3rd power to get the final answer (r/6)^3

We could rewrite it in its equivalent form (r/6)^3 = (r^3)/(6^3) = (r^3)/216, but the answer in bold is sufficient in my opinion.

Given :

A company currently has an advertisement that covers a bill board that is 30 ft wide by 70 ft high. The company wants to reduce the same advertisement to fit on a new billboard that is 25 ft wide by 40 ft high.

To Find :

The dimensions of the largest advertisement that will fix on the billboard without cropping the advertisement.

Solution :

Area of original bill board :

\(A_i=30\times 70 = 2100\ ft^2\)

Area of new bill board :

\(A_f=25\times 40 = 1000\ ft^2\)

Since, new bill board can be completely fitted in original bill board as its length and breadth both are smaller than that.

So, the dimensions of the largest advertisement that will fix on the billboard without cropping the advertisement is equal to 1000 ft².

Hence, this is the required solution.

Answer:

Option D

Hope this helps!

a) The pumpkin thrown downward from a five-story building (15 meters high) results in the messiest impact (highest velocity impact).

b) The second pumpkin will hit the ground at the same velocity as the first pumpkin, regardless of the direction of throw.

c) Throwing the pumpkin downwards results in a higher velocity impact because the gravitational force of the Earth adds to the initial velocity.

The velocity of the pumpkin is directly proportional to the height of the building from where it is thrown. Thus, the pumpkin thrown from a five-story building has a higher velocity than that thrown from a shorter building. To get the messiest impact, the pumpkin must be thrown downward, and not upward. This is because the gravitational force of the Earth adds to the initial velocity, making the pumpkin hit the ground with a higher velocity. The velocity at which the second pumpkin hits the ground will be the same, regardless of the direction of throw. This is because the initial velocity of the pumpkin is the same in both cases, and the force of gravity acting on it is also the same.

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Answer:

163.73

Step-by-step explanation:

Triangle area:

16x12 = 192cm²

Circle area:

pi(3²) = 28.27cm²

Difference in the area:

192-28.27 = 163.73cm²

Answer:

The 5 in the thousands place is 100 times larger than the 5 in the tens place.

Answer: 5 in thousands and 5 in the tens

Answer:

Step-by-step explanation:

We are here given that,

length= 2√24 in.

breadth= 4√3 in .

As we know that,

Area = length*breadth

Area = 2√24 * 4√3 in.²

Area = 8 * √{2*3*2*2*3} in.²

Area = 8 * 6√2 in.²

Area= 48√2 in.²

And ,

Perimeter= 2( l + b )

Perimeter= 2( 2√24 + 4√3) in.

Perimeter= 2( 4√6 + 4√3) in.

Perimeter= 2 * 4 ( √3 + √6) in.

Perimeter= 8√3 + 8√6 in.

and we are done!

-5a – 2 >8 equals a<−2

2a +4>14 equals a>5

Using the hypergeometric distribution, there is a 0.4894 = 48.94% probability of selecting none of the correct six integers in a lottery.

The formula is:

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are:

For this problem, we want to take 6 numbers from a set of 56, hence the values of the parameters are:

N = 56, k = 6, n = 6.

The probability of selecting none of the correct six integers in a lottery is of P(X = 0), hence:

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}\)

\(P(X = 0) = h(0,56,6,6) = \frac{C_{6,0}C_{50,6}}{C_{56,6}} = 0.4894\)

0.4894 = 48.94% probability of selecting none of the correct six integers in a lottery.

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a. The matrices whose entries are all greater than or equal to 0: Yes, it is a subspace.

b. The matrices with trace (the sum of diagonal entries): No, it is not a subspace.

c. The matrices with all zeros in the third row: Yes, it is a subspace.

d. The matrices of rank 3: No, it is not a subspace.

e. The non-invertible matrices: No, it is not a subspace.

f. The matrices such that the vector [1, 2, 3] is in the kernel: Yes, it is a subspace.

What is matrix?

A matrix is a rectangular array of numbers or elements arranged in rows and columns. It is a fundamental concept in linear algebra and has various applications in mathematics, science, engineering, and computer science.

Let's analyze each subset and determine whether they are subspaces of the set of matrices.

a. The matrices whose entries are all greater than or equal to 0:

This subset is a subspace of the set of matrices since it satisfies the three conditions for being a subspace: closure under addition, closure under scalar multiplication, and containing the zero vector.

b. The matrices with trace (the sum of diagonal entries):

This subset is not a subspace of the set of matrices because it does not satisfy closure under scalar multiplication. Multiplying a matrix by a scalar will change the diagonal entries and, thus, the trace.

c. The matrices with all zeros in the third row:

This subset is a subspace of the set of matrices since it satisfies the three conditions for being a subspace: closure under addition, closure under scalar multiplication, and containing the zero vector.

d. The matrices of rank 3:

This subset is not a subspace of the set of matrices because it does not satisfy closure under addition. Adding two matrices of rank 3 may result in a matrix with a rank less than 3.

e. The non-invertible matrices:

This subset is not a subspace of the set of matrices because it does not satisfy closure under scalar multiplication. Multiplying a non-invertible matrix by a non-zero scalar will result in a matrix that may be invertible.

f. The matrices such that the vector [1, 2, 3] is in the kernel:

This subset is a subspace of the set of matrices since it satisfies the three conditions for being a subspace: closure under addition, closure under scalar multiplication, and containing the zero vector (which makes the vector [1, 2, 3] in the kernel).

In summary:

a. Yes, it is a subspace.

b. No, it is not a subspace.

c. Yes, it is a subspace.

d. No, it is not a subspace.

e. No, it is not a subspace.

f. Yes, it is a subspace.

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The indefinite integral of (x+3)² + (3-x)⁶ with respect to x is  (1/3)x³ + 3x² + 9x + (1/7)(x-3)⁷ + C.

The indefinite integral of the expression is calculated as follows;

The given expression;

∫(x+3)² + (3-x)⁶ dx

The expression can be expanding as follows;

∫(x² + 6x + 9 + (3 - x)⁶) dx

We can simplify the expression as follows;

∫(x² + 6x + 9 + (x-3)⁶) dx

Now we can integrate each term separately;

∫x² dx + ∫6x dx + ∫9 dx + ∫(x-3)⁶ dx

(1/3)x³ + 3x² + 9x + (1/7)(x-3)⁷ + C

where;

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We know that the given strain in the strain gauge isϵ = GF × R1/δR. The uncertainty in the strain is given by:Δϵ/ϵ = √(ΔGF/GF)² + (√(ΔR₁/R₁)² + √(ΔδR/δR)²).

We know that strain gauge's strain ϵ is expressed as the ratio of its change in resistance δR, which is given by the formula:ϵ = GF × R1/δRWhere ϵ is the strain, δR is the change in resistance, GF is the gauge factor, and R1 is the unstrained resistance of the gauge. Now, if we are asked to calculate the uncertainty in ϵ, we have to first determine the uncertainty in all the parameters given.

The uncertainty in gauge factor (GF), unstrained resistance (R1), and change in resistance (δR) is given by ΔGF, ΔR1, and ΔδR respectively.

To determine the uncertainty in the strain (ϵ), we can use the formula:Δϵ/ϵ = √(ΔGF/GF)² + (√(ΔR₁/R₁)² + √(ΔδR/δR)²).

This formula expresses the uncertainty in the strain in terms of the uncertainties in gauge factor, unstrained resistance, and change in resistance. This is the required expression for the uncertainty in ϵ.

The uncertainty in the strain in the strain gauge is expressed asΔϵ/ϵ = √(ΔGF/GF)² + (√(ΔR₁/R₁)² + √(ΔδR/δR)²).

This expression expresses the uncertainty in ϵ in terms of the uncertainties in gauge factor (GF), unstrained resistance (R1), and change in resistance (δR).

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Answer:

[-4,0]

Step-by-step explanation:

we use closed bracket to show " it includes" and -4 and 0 are included in the solution set

Given that tanθ = 3 and cosθ < 0, we are asked to find the values of (a) sin2θ and (b) cos2θ using trigonometric identities.

(a) To find sin2θ, we can use the identity sin2θ = 2sinθcosθ. We know that tanθ = 3, which means sinθ/cosθ = 3. Rearranging this equation, we have sinθ = 3cosθ. Substituting this into the identity sin2θ = 2sinθcosθ, we get sin2θ = 2(3cosθ)(cosθ) = 6cos^2θ.

(b) To find cos2θ, we can use the identity cos2θ = cos^2θ - sin^2θ. From the given information, we know that cosθ < 0. Since tanθ = sinθ/cosθ = 3, sinθ must be positive. Therefore, sin^2θ = (3cosθ)^2 = 9cos^2θ. Substituting these values into the identity cos2θ = cos^2θ - sin^2θ, we have cos2θ = cos^2θ - 9cos^2θ = -8cos^2θ.

Hence, the values we obtained are (a) sin2θ = 6cos^2θ and (b) cos2θ = -8cos^2θ.

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The first- and second order partial derivatives of the function f(x,y) = 3xy - 2xy² - x²y are:

∂f/∂x = 3y - 4xy - x², ∂f/∂y = 3x - 4xy - x²∂²f/∂x² = -4y, ∂²f/∂y² = -4x and ∂²f/∂y∂x = -4y.

Given function:

f (x,y) = 3xy - 2xy² - x²y

Let's find the first order partial derivatives.

1. First order partial derivative with respect to x.

Keep y constant and differentiate with respect to x.∂f/∂x = 3y - 4xy - x²2.

First order partial derivative with respect to y

Keep x constant and differentiate with respect to y.

∂f/∂y = 3x - 4xy - x²

Let's find the second order partial derivatives.

1. Second order partial derivative with respect to x.

Keep y constant and differentiate ∂f/∂x with respect to x.∂²f/∂x² = -4y2. Second order partial derivative with respect to y.Keep x constant and differentiate ∂f/∂y with respect to y.∂²f/∂y² = -4x3. Second order partial derivative with respect to x and y.

Keep x and y constant and differentiate ∂f/∂y with respect to x.∂²f/∂y∂x = -4y

From the above steps, we can say that the first order partial derivatives are:∂f/∂x = 3y - 4xy - x²and ∂f/∂y = 3x - 4xy - x²The second order partial derivatives are:

∂²f/∂x² = -4y∂²f/∂y² = -4x

and ∂²f/∂y∂x = -4y

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Answer:

P = a + b + c

P = (8x + 2) + (5x - 4) + (9x + 3)

P = 8x + 5x + 9x + 2 - 4 + 3

P = 22x + 1

I hope this helps.

The expected value with a sample size of 20 and a probability of 0.25 will be 5.

The anticipated value is an extension of the weighting factor in statistical inference. Informally, the anticipated value is the simple average of a significant number of outcomes of a randomly selected variable that was separately chosen.

The expected value is given below.

E(x) = np

Where n is the number of samples and p is the probability.

If x is a binomial random variable with n = 20 and p = 0.25. Then the expected value is given below.

E(x) = 20 x 0.25

E(x) = 5

The expected value with n = 20 and p = 0.25 will be 5.

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Answer:

X=84.6

Step-by-step explanation:

732=9x-30

You subtract 30 from both sides which leaves us with

762=9x

Then you divide both sides by 9

So x=84.66

Answer:

84.66

Step-by-step explanation:

732=9x-30

732+30=9x

(732+30)/9= x

x = 762/9 = 84.667

Answer:

No, because a triangle will have to add up to 180 degrees. And if the two angles are already set for both triangles, there is only one answer that will make these triangles equal 180 degrees. So no there is no way possible.

Step-by-step explanation:

The calories in a cup of low fat milk is 102 calories and the  calories in a cup of milk in skim 86 calories .

2/3l + 1/2s = 111

4l + 3s = 666 equation 1

l + s = 188 equation 2

Where:

l = calories in the low fat milk

s = calories in the skim milk

Multiply equation 2 by 4

4l + 4s = 752 equation 3

Subtract equation 1 from 3

s = 86

Substitute for s in equation 2

l + 86 = 188

l = 188 - 86

l = 102

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a. The server worked for about 2.5 hours to earn $35

b. the server earn $77 for 5 hours of work

c. the earnings will increase as the number of hours worked increases

This solved by tracing the information from the graph

Tracing the graph the information that coincides with earning $35 is about 2.5 hours

Tracing the graph the information that coincides with earning $77 is about 5 hours

The graph shows that increase in earning will lead to increase n hours of work

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The probability of choosing a 5 and then a 6 is 1/49

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

The tiles

Where we have

Total = 7

The probability of choosing a 5 and then a 6 is

P = P(5) * P(6)

So, we have

P = 1/7 * 1/7

Evaluate

P = 1/49

Hence, the probability of choosing a 5 and then a 6 is 1/49

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Question

You randomly choose one of the tiles. Without replacing the first tile, you choose a second tile. Find the probability of the compound event. Write your answer as a fraction or percent rounded to the nearest tenth. The probability of choosing a 5 and then a 6

Answer:

No

Step-by-step explanation:

Answer:

Because there are fewer than 30 (not no more than 30) one of the answer i x+y < 30

Because he needs both small and large another answer is x>0 and not x  0

Finally because he need at least dozen large cones the last answer is y

Step-by-step explanation:

Answer: The answer is x=0

Step-by-step explanation:

Rewrite the equation as a trinomial.

x 2 + 12 x + 0

Move 0 to the right-hand side.

x 2 + 12 x = 0

Divide the coefficient of the  x

-term by 2, then square the result. Add the result to both sides.

12 /2 = 6 ;6^2   = 36

x 2 + 12 x + 36 = 36

Factor the perfect square trinomial  

x 2 + 12 x + 36

on the left-hand side.

( x + 6 ) 2 = 36

Take the square root of both sides and solve for  x .

√ ( x + 6 )^ 2 = ± √ 36 =

x+ 6 =  ± 6

x =  − 6 + 6 = 0

x =  − 6  − 6 = − 12

Check

If  x = 0 :

( 0 ) ^2 + 12 ( 0 ) = 0

0 = 0

If  x = − 12 :

( − 12 ) ^2 + 12 ( − 12 ) = 0

144 − 144 = 0

0 = 0