Instructions: Write an expression to represent the given scenario.
You are ordering lunch for your friends. Everyone wants a cheeseburger, which costs $4, besides one friend
who is ordering a salad for $7. Write an expression to represent the total cost of your order depending on the
number of burgers (6) you order.

Answer:

$340

Step-by-step explanation:

because first i divided 3,400 by 800 because thats how many bags pf ice that was sold over the weekend and then I got 4.25 and then I did 4.25*80 and I got $340 and I hope this helps u let me know

Answer:  $340

Step-by-step explanation:

Create a proportion with the given values of 800 lbs = $3400

           \(\dfrac{dollars}{pounds}:\ \dfrac{3400}{800}=\dfrac{x}{80}\)

Cross Multiply:    800x = 3400(80)

Divide by 800:           x = 340

It took approximately 5.3 years for the amount of undeveloped land to decrease to approximately 15.39 acres, starting from 30 acres in 2002.

Let L(t) be the amount of undeveloped land in acres at time t, where t is measured in years since 2002. Then, we can write:

L(t) = 30 * (7/8)^t

We know that the amount of undeveloped land we are interested in is approximately 15.39 acres. Therefore, we can set up the following equation:

15.39 = 30 * (7/8)^t

To solve for t, we can first divide both sides by 30:

0.513 = (7/8)^t

Next, we can take the natural logarithm of both sides:

ln(0.513) = ln[(7/8)^t]

ln(0.513) = t * ln(7/8)

t = ln(0.513) / ln(7/8)

t ≈ 5.3

Therefore, it took approximately 5.3 years for the amount of undeveloped land to decrease to approximately 15.39 acres, starting from 30 acres in 2002.

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The total number of books on the shelf is 12 books

Given the following parameters

Total number of puzzle books on the shelf = 30 books

If the number of puzzle books is 25 of all the books on the shelf, the total number of books on the shelf is expressed as:

= 2/5 of 30

= 2/5 * 30

= 2 * 6

= 12

Hence the total number of books on the shelf is 12 books

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Answer:

75

Step-by-step explanation:

(a) The 95% lower confidence bound for the true average proportional limit stress of all such joints is approximately 8.07 MPa. With 95% confidence, we can say that the value of the true mean proportional limit stress of all such joints is greater than this value.

To calculate the lower confidence bound, we use the formula:

Lower bound = sample mean - (critical value * standard deviation / √n)

Given:

Sample mean (x) = 8.51 MPa

Sample standard deviation (s) = 0.75 MPa

Sample size (n) = 18

Critical value (obtained from the t-distribution for 95% confidence with 17 degrees of freedom) ≈ 1.74

Substituting these values into the formula, we have:

Lower bound = 8.51 - (1.74 * 0.75 / √18) ≈ 8.07 MPa

The interpretation is that with 95% confidence, we can say that the value of the true mean proportional limit stress of all such joints is greater than 8.07 MPa.

Assumption: We must assume that the sample observations were taken from a normally distributed population.

(b) The 95% lower prediction bound for the proportional limit stress of a single joint of this type is approximately 7.85 MPa. If this bound is calculated for sample after sample, in the long run, 95% of these bounds will provide a lower bound for the corresponding future values of the proportional limit stress of a single joint of this type.

To calculate the lower prediction bound, we use the formula:

Lower bound = sample mean - (critical value * standard deviation)

Given the same values as in part (a), we have:

Lower bound = 8.51 - (1.74 * 0.75) ≈ 7.85 MPa

The interpretation is that if this bound is calculated for sample after sample, in the long run, 95% of these bounds will provide a lower bound for the corresponding future values of the proportional limit stress of a single joint of this type.

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Answer:  \(\frac{28}{27}\) or \(1\frac{1}{27}\)

Step-by-step explanation:

\(\frac{7}{9} /\frac{6}{8} = \frac{7}{9}(\frac{8}{6})\)

\(\frac{7}{9} (\frac{8}{6} ) = \frac{28}{27}\)

\(\frac{28}{27} = 1 \frac{1}{27}\)

In this given figure, the given statement (PS≅QS) is incorrect.

Note that from the SAS congruence rule: The side angle side postulate states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then these two triangles are congruent.

This figure is incorrect, because in the theorem,

PS≅QS

But in the figure

=>QP≠RS

Therefore this figure statement is incorrect.

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Answer:

Hey there!

The domain is the range of all the x values.

So for this graph, the domain would be \(-10<x\leq 8\).

Note that the open circle means < or > and the closed circle means ≤ or ≥.

Let me know if this helps :)

The surface area obtained by rotating the curve y = x² from x = 0 to x = 8 about the y-axis is 2048π square units.

We are given that the curve y = x² is rotated from x = 0 to x = 8. So our range of integration is from x = 0 to x = 8.

To use the disk method, we need to express the curve in terms of y instead of x. For the equation y = x², we can rewrite it as x = √y.

The radius of each disk is the distance between the y-axis and the curve. Since we are rotating the curve around the y-axis, the radius will be the value of x for a given y. Therefore, the radius is x = √y.

The area of each disk can be found using the formula for the area of a circle, which is A = πr². In this case, the area is A = π(x²) = π(√y)² = πy.

To find the total surface area, we need to sum up the areas of all the disks. We integrate the area function πy with respect to y from y = 0 to y = 64 (since x = 8 corresponds to y = 64).

Surface Area = ∫(πy)dy from 0 to 64

= π∫y dy from 0 to 64

= π[y²/2] from 0 to 64

= π[(64²/2) - (0²/2)]

= π[2048]

= 2048π square units.

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Answer:

Option (3)

Step-by-step explanation:

Given : 3x + 12 = 8x - 18

To prove : x = 6

        Statements                  Reasons

1). 3x + 12 = 8x - 18                 1). Given

2). 12 = 5x - 18                       2). Subtraction property of equality

3). 30 = 5x                             3). Addition property of equality

4). 6 = x                                  4). Division property of equality

5). x = 6                                  5). Symmetric property

For step 1 in the given proof Option (3) will be the answer.

Answer:

0

Step-by-step explanation:

m=y2-y1

____

x2-x1

m=-3-(-3) =(-3+3)/(-36) =0/-36=0

_____

-16-20

C. 0 + 4y = 2

x + y =7 .. (1)

x - 3y = 5 ..(2)

Subtracting equation (2) from (1) , we get,

•°•4y = 2

Answer: 10h+ 4

Step-by-

Answer:

L = 15 and W = 15. Hence, the dimensions of the rectangle with the smallest perimeter and area of 225 sq.ft. are 15 ft x 15 ft (i.e. a square).

Step-by-step explanation:

Let's assume the length of the rectangle is L and the width is W. The area of the rectangle is given as 225 sq.ft. Therefore, we have:

L x W = 225

The perimeter of the rectangle is given by:

2L + 2W

We need to find the dimensions of the rectangle that will give the smallest possible perimeter. To do this, we need to minimize the expression for the perimeter subject to the constraint that the area is 225 sq.ft. We can use the method of Lagrange multipliers to solve this problem.

Let f(L, W) = 2L + 2W be the expression for the perimeter and g(L, W) = L x W - 225 be the expression for the area. We want to minimize f(L, W) subject to the constraint g(L, W) = 0.

The Lagrange function is given by:

L(L, W, λ) = f(L, W) - λg(L, W)

= 2L + 2W - λ(LW - 225)

Taking partial derivatives and setting them equal to zero, we get:

∂L/∂λ = W = 0

∂W/∂λ = L = 0

∂L/∂λ = -λW = 0

∂W/∂λ = -λL = 0

∂L/∂λ = 2 - Wλ = 0

∂W/∂λ = 2 - Lλ = 0

Solving these equations, we get:

λ = 2/L = 2/W

Substituting λ in the expression for the area, we get:

L^2 = 225

Therefore, L = 15 and W = 15. Hence, the dimensions of the rectangle with the smallest perimeter and area of 225 sq.ft. are 15 ft x 15 ft (i.e. a square).

Answer:

width = 15 ft

length = 15 ft

Step-by-step explanation:

Let x = length and y = width.

area = length × width

A = xy

perimeter = 2(length + width)

P = 2(x + y)

P = 2x + 2y

A = 225

xy = 225

y = 225/x

P = 2x + 2(225/y)

P = 2x + 450/x

P = 2x + 450x^-1

dP/dx = 2 + 450(-1)(x^-2)

dP/dx = 2 - 450/x²

2 - 450/x² = 0

2x² - 450 = 0

x² - 225 = 0

x = ±√225

x = ±15

Discard x = -15.

width = 15 ft

length = 15 ft

Subtracting 3 hours 3 seconds and 1 hour 15 minutes 55 seconds is 1 hour 44 minutes 8 seconds.

The following are important to solve the questions:

1 minute = 60 seconds

1 hour = 3600 minutes

Therefore 3 hours 3 seconds will be:

= (3 × 3600) + 3

= 10800 + 3

= 10803 seconds.

1 hour 15 minutes 55 seconds will be:

= 3600 + (15 × 60) + 55

= 3600 + 900 + 55

= 4555 seconds.

The difference will be:

= 10803 - 4555

= 6248 seconds

= 1 hour 44 minutes 8 seconds.

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The matrix I - A(A^T) is the projection matrix that projects vectors onto the orthogonal complement of the range of matrix A, effectively removing any components lying within the range of A.

To prove this, let's consider a vector x in the column space (range) of matrix A. Then there exists a vector y such that Ax = Ay. The projection matrix onto the orthogonal complement of the range of A, denoted Pᵤ, is defined as Pᵤ = I - A(A^T).

Now, let's apply the projection matrix Pᵤ to vector x. We have Pᵤx = (I - A(A^T))x. Using matrix multiplication, this simplifies to Pᵤx = x - A(A^T)x.

Since Ax = Ay, we can substitute Ay for Ax in the equation above, resulting in Pᵤx = x - Ay. Rearranging, we have Pᵤx = x - Ax, which is the definition of the orthogonal complement.

Therefore, Pᵤx is equal to the projection of vector x onto the orthogonal complement of the range of A, proving that I - A(A^T) is the projection matrix onto the orthogonal complement of range A.

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Given: Mary, Gracie, and Nancy all have little collections of seashells, but Gracie has 5 more than 14 times as many as Mary does. So Mary has 16 shells

To find: Recognize the equation that captures this circumstance and recognize its resolution.

olution:

Let x be mary's shells, so according to question, we get:

gracie = 14x + 5   nancy  = 1 x+ 1

Now we have given that:

          gracie = nancy

So: 14x + 5 = 1 x + 1

  5/4x + 5 = 3/2x + 1

Fractions will be eliminated by multiplying by the common denominator of 4, but this step is optional; you can still work with fractions if you choose.

Now solving further, we get:

        5x + 20 = 6x + 4  5x - 6x = 4 - 20    -x = - 16    x = 16.

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Answer: $2.45

Step-by-step explanation:

Answer:

the first step is wrong

it should be 4(x-4)/(x+1)(x-4) - (x+2)/(x-4)(x+1)

Answer:

my answer is letter c thats may answer

The number 96 into simplest radical form is 4√6.

In the given question we have to simplify the number into simplest radical form.

The given number is 96.

To simplify and obtain the radical form of square roots, we will first identify every element below the square root.

The square factor for 96 is 16.

Now we can factor 96 as 16 * 6.

The radicals are not in their least complicated form, as should be evident.

When we pay close attention now and subtract the square root of 16 * 6.

As √16 = 4 is the starting point, which leads to 4√6.

Currently, all radicals have been upgraded.

Never again will the extreme have any square factors.

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The complete question is:

Simplify the number into simplest radical form. Use the factor tree to help determine the factors 96.

Use the factor tree, the simplest radical form of 64 is 8.

Lets Simplify the number 64 into the simplest radical form.

To solve this, we can use a factor tree.

First, we will start with the number 64. We can break this down into two groups of two numbers, one being 4 and the other being 16.

Next, we can break down the 4 into two groups of two numbers, one being 2 and the other being 2.

Finally, we can break down the 16 into two groups of two numbers, one being 4 and the other being 4.

Now we have our factors, 2, 2, 4, and 4. We can use these factors to simplify the number 64 into its simplest radical form.

The formula for the radical form of a number is √(a × b × c × d).

In this case, our a, b, c, and d values are 2, 2, 4, and 4 respectively.

Therefore, our simplified radical form of 64 is √(2 × 2 × 4 × 4) = √64 = 8.

This means that the simplest radical form of 64 is 8.

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Answer:

0, 5%, 1/5, 5

5% is equal to 5÷100=0,05

1/5 is equal to 1÷5=0,2

The value of x is 14 and the measure of angle DGF is 90°   .

In the question ,

we can see that the triangle DGF is a right angled triangle , right angled at G .

So, the measure of angle DGF is 90°  ,

but it is given that angle DGF = (7x - 8)°

So , equating both the sides , w

we get ,

7x - 8 = 90

on adding 8 to both sides in the equation,

we get ,

7x = 90 + 8

7x = 98

on dividing both side of the equation by "7" ,

we get

x = 98/7

x = 14

Therefore , The value of x is 14 and the measure of angle DGF is 90°   .

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However, we need to substitute a with s since that is the value we have calculated. Therefore, we get \(A(s) = (1/4)(5 + sqrt(5))s^2.\) This is the function notation that represents the area of a regular pentagon whose perimeter is 140 cm.

Let's consider that s be the length of a side of the regular pentagon.

The perimeter of the regular pentagon will be 5s. Therefore, we have the equation:5s = 140s = 28 cm

Also,

we have the formula for the area of a regular pentagon as:

\($A=\frac{1}{4}(5 +\sqrt{5})a^{2}$,\)

where a is the length of a side of the pentagon.

In order to represent the area of a regular pentagon whose perimeter is 140 cm, we need to substitute a with s, which we have already calculated.

Therefore, we have:\(A(s) = $\frac{1}{{4}(5 +\sqrt{5})s^{2}}$\)

Now, we have successfully used function notation (with the appropriate functions above) to represent the area of a regular pentagon whose perimeter is 140 cm.

The area of a regular pentagon can be represented using function notation (with the appropriate functions above). The first step is to calculate the length of a side of the regular pentagon by dividing the perimeter by 5, since there are 5 sides in a pentagon.

In this case, we are given that the perimeter is 140 cm, so we get 5s = 140, which simplifies to s = 28 cm. We can now use the formula for the area of a regular pentagon, which is\(A = (1/4)(5 + sqrt(5))a^2\), where a is the length of a side of the pentagon.

However, we need to substitute a with s since that is the value we have calculated. Therefore, we get\(A(s) = (1/4)(5 + sqrt(5))s^2.\) This is the function notation that represents the area of a regular pentagon whose perimeter is 140 cm.

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Answer:

True

Step-by-step explanation:

Assuming this is a true or false question, the given formula is used to convert temperatures that are in degrees Celsius to degrees Fahrenheit.

\(F(C)=\frac{9}{5} C+32\)

Answer:

y = 1/2x+11

Step-by-step explanation:

There will be 221 highway signs on the road trip.

What is Total Length?

Whole Length (TL) is the measurement taken in a straight line, with the fish lying on its side, from the tip of the snout to the end of the tail (caudal fin).

The total length of the road trip is 13.2 hours.

Highway signs are posted every 0.06 hours. To find out how many highway signs are on the road trip, we can divide the total length of the road trip by the interval between each sign and then add one more sign for the end of the road trip:

(number of signs) = (total length of road trip) / (interval between signs) + 1

Substituting the values, we get:

(number of signs) = 13.2 / 0.06 + 1

(number of signs) = 220 + 1

(number of signs) = 221

Therefore, there will be 221 highway signs on the road trip.

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For this combination can be used , the answer would be  639450 ways

What is combination?

In arithmetic, a combination may be a choice of things from a group that has distinct members, such the order of choice doesn't matter.

Main body:

Given, the total number of members in the chorus are 30.

Also, it is given that 6 members from the chorus have to be

chosen for a special performance.

The number of ways of choosing r people out of given n people

is given by the expression

nCr

= n!/r!(n-r)!

So the number of ways of choosing 6 members out of 30 are

³⁰C₆

=  30!/24!6!

= 639450 ways

But since only the expression to represent the number of ways

was asked not the exact number of ways we can leave the

answer as ³⁰C₆ .

Hence total number of ways is 639450 ways.

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