You take your friend out to dinner for their birthday. The bill was $65.00. You left $75.00 which includes the tip. What was the percentage of the tip? (hint divide the tip amount by the amount of the dinner) (use a % sign in your answer and round to one decimal place)

The table shows the multiplication of two linear expressions and the subsequent simplification and standard form conversion. The reasons given are the input expressions,  Distributive property, Associative Property, simplification to standard form conversion. So, the correct option answer for reason 1, 2, 3 and 3 are B, C, A and D respectively.

The table shows the multiplication of two linear expressions is

Step Step

1      (1/4)x(5x-1)

2      (1/4)x(5x)+(1/4)x(-1)

3      (1/4)(5x^2)+(-1/4)x

4      (5/4)x^2+(-1/4)x

Reason 1: The multiplication of two linear expressions is given in the first column for each step.

Reason 2: The given linear expressions are rearranged in the second column for each step. It is Distributive Property.

Reason 3: The rearranged expressions in the second column are simplified using algebraic operations. It is  Associative Property.

Reason 4: The simplified expressions in the second column are written in the standard form of a quadratic polynomial.

So, the correct order of options for reason 1, 2, 3 and 3 are B, C, A and D respectively.

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_____The given question is incomplete, the complete question is given below:

A 2-column table with 5 rows. First column is labeled Step with entries one-fourth x (5 x minus 1), (one-fourth x) (5 x) + (one-fourth x)(negative 1), one-fourth times 5 times x times x + (negative 1) times one-fourth times x, (one-fourth times 5) (x times x) + (negative 1 times one-fourth) x, 5 over 4 x squared minus one-fourth x. Second column is labeled Reason with entries given, 1, 2, 3, 4. The table shows the multiplication of two linear expressions. Select the correct reason for each step. Reason 1:

Reason 2:

Reason 3:

Reason 4:

(A)associative property of multiplication

(B)multiplication

(C)Distributive property

(D) simplify

Answer:

I think it 648.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The strength of a linear relationship between two variables is typically measured by the correlation coefficient (r) or the coefficient of determination (r^2). A value of r or r^2 closer to 1 indicates a stronger positive linear relationship, whereas a value closer to -1 indicates a stronger negative linear relationship. A value of r or r^2 closer to 0 indicates a weaker or no linear relationship.

Looking at the given regression equations and their correlation coefficients, the regression with the weakest linear relationship between x and y is Regression 3:

Regression 1: y = -5.8x - 6.5, r = -0.7621

Regression 2: y = 2.4x - 14.7, r = 0.809

Regression 3: y = -7.4x - 17.4, r = -0.233

Regression 4: y = -3.4x - 8.5, r = -0.6121

Regression 3 has the lowest absolute value of r (0.233), indicating the weakest or no linear relationship between x and y. Therefore, Regression 3 represents the weakest linear relationship between x and y among the given options.

Out of 8 members of the committee, it is possible to create two subcommittees only.

We know that in order to create subcommittees. we need to divide the total number of people on the committee into equal parts so that they form subcommittees.

Here, it is given that there are 8 members on the committee.

A subcommittee needs to have 3 people in it.

On dividing 8 people into groups of three, we get

⇒ \(\frac{8}{3}\)

⇒ 2.66..

Here, it is obvious that the 0.66... can not be considered because it is not a whole number and hence, does not mean any number of people.

So, we can create only two different subcommittees from 8 members on the main committee.

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Answer:

-7

Step-by-step explanation:

Answer:

hello guys ^_^ its -7 and if it is wrong don't be afraid to tell me

~your friendly austrailian~

Answer:

x + 5 = 5×

7x - 5 = 2x

5x + 2x + x = 180

8× = 180

8 8

x = 22.5

Answer:

Similar to the question: They figure that they will drive 792 miles round trip. If their car gets 25 miles per gallon and the current cost of gasoline is $2.35, what will the gas for their trip cost? $74.45 George is taking the same trip to San Antonio (792 miles)

Step-by-step explanation:

Hope it helps :)

9514 1404 393

Answer:

  15

Step-by-step explanation:

The proportion can be written as fractions:

  \(\dfrac{20}{40}=\dfrac{d}{30}\\\\\dfrac{600}{40}=d\qquad\text{multiply by 30}\\\\\boxed{d=15}\qquad\text{finish the computation}\)

Answer:

Step-by-step explanation:

Given

proportions. 20 : 40 :: d : 30

20/40=d/30

d=20×30/40

d=30/2

d=15.

To find the average value of the function f(x, y) = 8x + 5y over the given triangle, we need to calculate the double integral of f(x, y) over the region and then divide it by the area of the triangle.

The vertices of the triangle are (0, 0), (2, 0), and (0, 7). We can set up the integral as follows:

∬R f(x, y) dA = ∫₀² ∫₀ᵧ (8x + 5y) dy dx

Integrating with respect to y first, the inner integral becomes:

∫₀ᵧ (8x + 5y) dy = 8xy + (5y²/2) |₀ᵧ = 8xᵧ + (5ᵧ²/2)

Now integrating with respect to x, the outer integral becomes:

∫₀² (8xᵧ + (5ᵧ²/2)) dx = (4x²ᵧ + (5ᵧ²x)/2) |₀² = (8ᵧ + 10ᵧ² + 20ᵧ)

To find the area of the triangle, we can use the formula for the area of a triangle: A = (1/2) * base * height.

The base of the triangle is 2 and the height is 7.

A = (1/2) * 2 * 7 = 7

Finally, to find the average value, we divide the double integral by the area of the triangle:

Average value = (8ᵧ + 10ᵧ² + 20ᵧ) / 7

Simplifying this expression gives:

Average value = (8 + 10ᵧ + 20ᵧ) / 7 = (8 + 10(7) + 20(7)) / 7 = 142/7 = 20 2/7

Therefore, the correct answer is not listed among the options provided.

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Answer:

You don't have a picture

Step-by-step explanation:

Answer:

Hmmm the picture....? Please send it

To find the Total Cost Function C(x) for a product, we need to integrate the given marginal cost function MC(x). Given that MC(x) = 4x + 20 and the cost of producing 2 units is $78, we can determine the Total Cost Function.

The Total Cost Function C(x) represents the cumulative cost of producing x units. To find C(x), we need to integrate the marginal cost function MC(x) with respect to x.

Integrating MC(x), we get:

C(x) = ∫(MC(x))dx = ∫(4x + 20)dx.

Integrating each term separately, we obtain:

C(x) = 2x² + 20x + C,

where C is the constant of integration.

To find the value of C, we use the given information that the cost of producing 2 units is $78. Substituting x = 2 and C(x) = 78 into the equation, we have:

78 = 2(2)² + 20(2) + C,

78 = 8 + 40 + C,

78 = 48 + C,

C = 78 - 48,

C = 30.

Therefore, the Total Cost Function for the product is:

C(x) = 2x² + 20x + 30.

Hence, the correct answer is option a. C(x) = 2x² + 20x + 30.

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Answer:

<abc is 30*

<fde is 60*

Step-by-step explanation:

Hope this helps!

The graph of the given functions is (see in attachments).

From the question, we have

g(x) = 0.44√3.2x−4.1

Graph:

A graph is an organized visual representation of any data in mathematics. The relationship between the variable quantities is depicted on the graph. In a graph theory, the set of items that are somehow connected to one another is represented by a graph. The vertices or nodes of the objects are essentially mathematical notions, and the edges between the nodes represent the relationships between the nodes. In mathematics and statistics, there are various types of graphs that are used to visually display data. The study of points and lines is known as graph theory. It is a branch of mathematics that focuses on the investigation of graphs. The mathematical truth is shown visually in this picture. Relationships are studied using graph theory.

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The probability of choosing a uni-color pair of socks from the bag is 199/799.

The probability of choosing a uni-color pair of socks from a large bag with 100 pairs of each of red, blue, black, and white socks is calculated as follows:

Step 1: Calculate the total number of socks in the bag.
There are 100 pairs of each color, and each pair consists of 2 socks, so there are 100 x 2 = 200 socks of each color.
The total number of socks in the bag is 200 x 4 = 800 socks.

Step 2: Calculate the probability of choosing a uni-color pair of socks.
The probability of choosing a red sock on the first draw is 200/800 = 1/4.
The probability of choosing another red sock on the second draw is 199/799.
The probability of choosing a red pair is (1/4) x (199/799) = 199/3196.

Similarly, the probability of choosing a blue pair, a black pair, or a white pair is also 199/3196.

The probability of choosing a uni-color pair is the sum of the probabilities of choosing a red pair, a blue pair, a black pair, and a white pair.

So the probability of choosing a uni-color pair is (199/3196) x 4 = 796/3196 = 199/799.

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Answers:

x = angle MLN = 35 degrees

angle FLJ = 55 degrees

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

Explanation:

This problem is fairly tricky if you're not sure what to look for. A slight clue is that they've marked a red point that strangely doesn't have a label on it. It's a fairly small point but it's definitely there if you look closely. While this point's location isn't exactly what we want, we're fairly close. Start at point L and draw a ray through the center point P. Ray LP will intersect the circle at point A, as shown in the diagram below.

From here, draw segments FA and MA. Now notice that inscribed angle LMF = 55 and inscribed angle FAL both subtend the same arc. The term "subtend" basically means "cut off". This arc that the inscribed angles subtend is minor arc FL. A minor arc is where you travel the shorter path around the circle, which indicates its measure is less than 180 degrees.

Since inscribed angles LMF and FAL subtend the same minor arc, this makes the inscribed angles to be congruent.

In short: angle FAL is 55 degrees

----------------------

Segment LA goes through the center P. Through Thales theorem, we know that inscribed angle LFA is 90 degrees. Consequently, we can determine that inscribed angle FLA is 90-55 = 35 degrees.

Segment JL is tangent to the circle, meaning that angle ALJ is 90 degrees. So angle FLJ is 90-35 = 55 degrees.

It's not a coincidence that angle FLJ, angle FAL, and angle LMF are the same measure.

----------------------

We found that angle FAL was 55 degrees. Applying Thales theorem again shows that angle MAF is 90 degrees. Therefore, angle LAM is 90-55 = 35 degrees.

Focus now on triangle LMA. This is also a right triangle (Thales Theorem). The upper acute angle we found was angle LAM = 35, so the lower acute angle is ALM = 55.

Then we can find angle MLN = (angle ALN) - (angle ALM) = 90 - 55 = 35

In short, angle MLN = 35 degrees

Similar to the previous section, it is not a coincidence that angles LFM, LAM and MLN are the same measure.

------------------------

As an alternative, since we know angle FLJ = 55, and angle FLM is 90 degrees, this means...

(angle FLJ)+(angle FLM) + (angle MLN) = 180

55 + 90 + angle MLN = 180

145 + angle MLN = 180

angle MLN = 180 - 145

angle MLN = 35 degrees

A prism is a three-dimensional object.

There are triangular prism and rectangular prism.

The volume of a triangular prism is given as,

V = 1/2 x base x height x length

The height of the rectangular prism is 2.5 cm

A prism is a three-dimensional object.

There are triangular prism and rectangular prism.

We have,

The volume of a triangular prism is given as,

V = 1/2 x base x height x length

Now,

From the given figure we see that,

base = 4 cm

Length = 7 cm

Volume = 35 cm³

Now,

35 = 1/2 x 4 x height x 7

35 = 2 x height x 7

height = 35 / 14

height = 5/2

height = 2.5 cm

Thus,

The height of the rectangular prism is 2.5 cm

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After approximately 12.13 years, the revenue of this firm is going to drop to $1 million.

The value of shares t years after their floatation on the stock market, is modelled by V = 10e0.09t

The initial value of shares = V when t = 0. So, putting t = 0 in V = 10e0.09t,

we get

V = 10e0.09 × 0= 10e0 = 10 × 1 = 10 million dollars.

The values after 5 years, 10 years and 12 years, respectively are:

For t = 5, V = 10e0.09 × 5 ≈ 19.65 million dollarsFor t = 10, V = 10e0.09 × 10 ≈ 38.43 million dollarsFor t = 12, V = 10e0.09 × 12 ≈ 47.43 million dollars

The total revenue (TR) in t years' time is modelled as TR = 10e−0.19t (in million dollars)

The current revenue is the total revenue when t = 0.

So, putting t = 0 in TR = 10e−0.19t, we get

TR = 10e−0.19 × 0= 10e0= 10 million dollars

Revenue in 5 years' time is TR when t = 5.

So, putting t = 5 in TR = 10e−0.19t, we get

TR = 10e−0.19 × 5≈ 4.35 million dollars

To find when the revenue of this firm is going to drop to $1 million, we need to solve the equation TR = 1.

Substituting TR = 1 in TR = 10e−0.19t, we get1 = 10e−0.19t⟹ e−0.19t= 0.1

Taking natural logarithm on both sides, we get−0.19t = ln 0.1 = −2.303

Therefore, t = 2.303 ÷ 0.19 ≈ 12.13 years.

So, after approximately 12.13 years, the revenue of this firm is going to drop to $1 million.

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Answer:

I believe the simplified form of this ratio is 1:3

*The common factor to both numbers is 27.

27÷27=1 and 81÷27=3

So, that's where the 1:3 came from

Answer:

64

Step-by-step explanation:

The exponent of a number says how many times to use the number in a multiplication.

8 to the Power 2

In 82 the "2" says to use 8 twice in a multiplication,

so 82 = 8 × 8 = 64

In words: 82 could be called "8 to the power 2" or "8 to the second power", or simply "8 squared"

To find the possible values of k, we need to calculate the determinant of matrix D and set it equal to 1024.

Given matrix D:

D = | k 0 0 |

| 3 k² k³ |

| 0 kª k³ kº |

| k k k |

| 0 0 0 |

| k¹⁰ |

The determinant of D can be calculated by expanding along the first row or the first column. Let's expand along the first row:

det(D) = k(det | k³ k k |

| 0 k³ kº |

| 0 0 k¹⁰ |)

- 0(det | 3 k² k³ |

| 0 kª k³ |

| k k k |)

+ 0(det | 3 k² k³ |

| k k k |

| k k k |)

Simplifying further, we have:

det(D) = k(det | k³ k k |

| 0 k³ kº |

| 0 0 k¹⁰ |)

Now, we can calculate the determinant of the 3x3 submatrix:

det | k³ k k |

| 0 k³ kº |

| 0 0 k¹⁰ |

This determinant can be found by expanding along the first row or the first column. Expanding along the first row gives us:

det = k(k³(kº) - 0(k)) - 0(0(k¹⁰)) = k⁴kº = k⁴+kº

Now, we can set det(D) equal to 1024 and solve for k:

k⁴+kº = 1024

Since we are looking for all possible values of k, we need to solve this equation for k. However, solving this equation may require numerical methods or approximations, as it is a quartic equation.

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The height of 277.1 ft. would be considered an outlier based on the given 5-Number Summary for the heights of White Pine trees.

An outlier is a data point that is significantly different from other observations in a dataset. In order to identify outliers, we can use the 5-Number Summary, which includes the minimum value, first quartile (Q1), median, third quartile (Q3), and maximum value. Outliers can be identified as values that are more than 1.5 times the interquartile range (IQR) below Q1 or above Q3. The IQR is the distance between Q3 and Q1.

In this case, the IQR is 196.4 - 148.6 = 47.8 ft. The lower bound for identifying outliers is Q1 - 1.5IQR = 75.9 ft. and the upper bound is Q3 + 1.5IQR = 269.1 ft. Therefore, any value below 75.9 ft. or above 269.1 ft. would be considered an outlier.

Out of the given heights, only 277.1 ft. is greater than the upper bound of 269.1 ft., making it an outlier. The other values, including 71.8 ft. and 288.5 ft., are within the range defined by the 5-Number Summary and are not outliers.

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Move all terms that don't contain x to the right side and solve.

x = 43

Answer:

x=43

Step-by-step explanation:

2x+96=182    

2x=86      (Subtract 96 from 182)

x=43         (Divide 86 by 2)

Answer:

Solve the equation for x.

The simplified system is the arbitrary solution of the original system of equations.

Y=x+14

y=18−x2

Reorder 18

and −x2.

y=−x2+18

Y=x+14

Solve the equation for Y.

Y=−2y+50

x=36−2y

Reorder 36

and −2y.

x=−2y+36

Y=−2y+50

Step-by-step explanation:

Step-by-step explanation:

given

\(y = x + 14 \\ y - x = 14 \\ - x + y = 14\)

as equation 1

and

\(x + 2y = 36\)

as equation 2.

We will now use elimination method to solve simultaneous equations.

We will use equation 1 + equation 2 to eliminate x and solve for y.

\( - x + x + y + 2y = 14 + 36 \\ 0 + 3y = 50 \\ 3y = 50 \\ y = 50 \div 3 \\ = \frac{50}{3} \: or \: 16 \frac{2}{3} \)

Now substitute y into equation 1.

\(y = x + 14 \\ x + 14 = y \\ x = y - 14 \\ x = 16\frac{2}{3} - 14 \\ = 2 \frac{2}{3} \)

The approximate value of f(1) using Euler's method with two steps of equal size is 6.636. The range of f for t > 0 is 0 < f(t) < 6.

a. The limiting factor in this logistic differential equation is the carrying capacity, which is 6 in this case. As y approaches 6, the growth rate of y slows down, until it eventually levels off at the carrying capacity.

b. To use Euler's method, we first need to calculate the slope of the solution at t=0. Using the given differential equation, we can find that the slope at t=0 is y(0)/8(6-y(0)) = 8/8(6-8) = -1/6.

Using Euler's method with two steps of equal size, we can approximate f(1) as follows:

f(0.5) = f(0) + (1/2)dy/dx|t=0

= 8 - (1/2)(1/6)*8

= 7.333...

f(1) = f(0.5) + (1/2)dy/dx|t=0.5

= 7.333... - (1/2)(7.333.../8)*(6-7.333...)

= 6.636...

Therefore, the approximate value of f(1) using Euler's method with two steps of equal size is 6.636.

c. The range of f for t > 0 is 0 < f(t) < 6, since the carrying capacity of the logistic equation is 6. As t approaches infinity, f(t) will approach 6, but never exceed it. Additionally, f(t) will never be negative, since it represents a population size. Therefore, the range of f for t > 0 is 0 < f(t) < 6.

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Answer:

The number of cartons of concentrated orange juice she needs in 4.5 gallons of orange juice is 12 cartons of orange juice

Step-by-step explanation:

The given parameters are;

The volume of the concentrated orange juice = 12 fluid ounce cartons

The ratio of orange juice concentrate to water = 12 fluid ounces to 36 fluid ounces

The amount of orange juice James need = 4.5 gallons = 576 fluid ounces

Therefore;

The  ratio of orange juice concentrate to water is 12:36

Therefore;

Let 'x' represent the amount of concentrated orange juice in 4.5 gallons of orange juice, and let 'y' represent the amount of water in the 4.5 gallons of orange juice, we have;

x + y = 4.5 (gallons)...(1)

x:y = 12:36 = 1:3

∴ x/y = 1/3

3·x = y...(2)

From equation (1) and equation (2), we have;

x + y = 4.5

x + 3·x = 4.5

x = 4.5/4 = 1.125

x = 1.125

The amount of concentrated orange juice in 4.5 gallons of orange juice, x = 1.125 gallons

∴ y = 3 × x = 3 × 1.125 = 3.375

y = 3.375

The amount of water in the 4.5 gallons of orange juice, y = 3.375

Therefore, we have;

4.5 gallons = 576 fluid ounces

∴ 1.125 gallons = (576/4.5) × 1.125 = 144 fluid ounces

The amount of fluid ounces per carton = 12 fluidounces/carton

∴ The number of cartons in 144 fluid ounces = 144 fluidounces ÷ 12 fluidounces/carton = 12 cartons

The amount of concentrated orange juice she needs in 4.5 gallons of orange juice, x = 1.125 gallons = 144 fluidounces = 12 cartons

The amount of concentrated orange juice she needs in 4.5 gallons of orange juice, x = 12 cartons of orange juice

The amount (number of cartons) of concentrated orange juice she needs in 4.5 gallons of orange juice, x = 12 cartons of orange juice.