(1+5 to the power of 2)-16(1/2 to the power of 3)

Given that John climbs a height of \($(x + 5)$\) miles in \($(x - 1)$\) hours and Jane climbs a height of \($(x + 11)$\) miles in \($(x + 1)$\) hours. We know that the distance covered by both John and Jane are equal.

Distance covered by John = Distance covered by Jane

Therefore, \($(x + 5) = (x + 11)$\)

Thus, x = 6

Now, we need to find the speed of both, which is given by the formulae:

Speed = Distance / Time

So, speed of John = \($(x + 5) / (x - 1)$\) Speed of John =\($11 / 5$\) mph

Similarly, speed of Jane = \($(x + 11) / (x + 1)$\)

Speed of Jane = \($17 / 7$\) mph

Since both have to be equal, Speed of John = Speed of Jane Therefore,

\($(x + 5) / (x - 1) = (x + 11) / (x + 1)$\)

Solving this equation we get ,x = 2Speed of John = \($7 / 3$\) mph

Speed of Jane = \($7 / 3$\) mph

Thus, their speed was \($7 / 3$\) mph.

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Answer:

b is 10.5 c is 11

Step-by-step explanation:

9+1.5

10.5

3(5)-4

15-4

11

Answer:

x = 6.5

Step-by-step explanation:

The image below shows that the equation y = 2x - 2 (which has a slope of 2) passes the the points (3, 4) and (6.5, 11); when x = 6.5

Hope this helps! :)

Answer:

\(y = 2x - 2 \\ y = mx + c\)

When the point is (3,4) and slope=2

\(4 = 2 \times 3 + c \\ 4 = 6 + c \\ \boxed{c = - 2}\)

Now, when the point is (x,11) and slope=2

\(11 = 2x - 2 \\ 2x = 13 \\ x =\frac{13}{2} \\ \boxed{x = 6.5 }\)

A. Rachel have the amount of money left in her account after 9 trips, $112

B. Rachel can take a number of trips until her account is empty, 16 trips

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

For example, 3x+2y=0.

Types of equation

1. Linear Equation

2. Quadratic Equation

3. Cubic Equation

Given that,

Rachel spends amount of money in each trip = $16

Rachel has total money in beginning of a month = $256

Equation for a relation between number of trips and amount of money in account,

A(t)=256-16t

A.   Amount of money left in account after 9 trips

    A(9) = 256-16×9

    A(9) =  256 - 144

    A(9) =    112

B.   Number of trips she can do till her account becomes empty

      0 = 256 - 16t

      16t = 256

       t =  256/16

       t = 16

Hence, the results are respectively,   $112 and 16    

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The correct answer is 28 units.To find the perimeter of the rectangle, we need to calculate the sum of the lengths of all four sides.

From the given coordinates, we can determine the lengths of the sides:

Side 1: Distance between (-4, 2) and (5, 2)

The length of this side is 5 - (-4) = 9 units.

Side 2: Distance between (5, 2) and (5, -3)

The length of this side is 2 - (-3) = 5 units.

Side 3: Distance between (5, -3) and (-4, -3)

The length of this side is 5 - (-4) = 9 units.

Side 4: Distance between (-4, -3) and (-4, 2)

The length of this side is 2 - (-3) = 5 units.

Now, we add the lengths of all four sides:

9 + 5 + 9 + 5 = 28 units.

Therefore, the perimeter of the rectangle is 28 units.

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Answer:

2396

Step-by-step explanation:

Let the diameter = d

Let the height = h

Formula

Metric Tons = k * d^4 / h^2

Solution

Metric Tons = 64

d = 2

h = 9

k = ?

(You can't do the second part by not using a ratio unless you  put k in and solve for it)

64 = 2^4 k / 9^2

64 = 8 *k / 81

64 * 81 / 8 = k

5184 / 8 = k

k = 648

Solve for the second example

Metric Tons = d^4 * k / h^2

Metric Tons = ?

d = 5

h = 13

k = 648

Metric Tons = 5^4 * 648 / 13^2

Metric Tons = 625 * 648 / 169

Metric Tons = 2396 rounded.

To identify the correct scatter plot for variables y1 and x1, you need to analyze the data and look for a clear pattern in the relationship between the two variables.

What is scatter plots?

A scatter plot is a type of data visualization that displays the relationship between two variables.

In a scatter plot, each point represents a pair of values, one for each of two variables. The horizontal axis represents the values of one variable (in this case, x1), and the vertical axis represents the values of the other variable (y1).

The scatter plot can show the relationship between the two variables. If there is a positive correlation, the points will tend to cluster in a line that slopes up and to the right. If there is a negative correlation, the points will cluster in a line that slopes down and to the right. If there is no correlation, the points will be scattered randomly.

To determine which scatter plot is correct, you need to examine the data and see which plot matches the pattern of the data. If there is a clear positive or negative correlation, the correct plot will show a line sloping up or down. If there is no correlation, the correct plot will show a scatter of points with no clear pattern.

In summary, to identify the correct scatter plot for variables y1 and x1, you need to analyze the data and look for a clear pattern in the relationship between the two variables.

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Answer:

(5,354 + x)

or

536.4*x

Step-by-step explanation:

We know that x = 10.

Now we want to write an expression (in terms of x) for the number 5,364.

This could be really trivial, remember that x = 10.

Then:  (x - 10) = 0

And if we add zero to a number, the result is the same number, then if we add this to 5,364 the number does not change.

5,364 = 5,364 + (x - 10) = 5,364 + x - 10

5,364 = 5,354 + x

So (5,354 + x) is a expression for the number 5,364 in terms of x.

Of course, this is a really simple example, we could do a more complex case if we know that:

x/10 = 1

And the product between any real number and 1 is the same number.

Then:

(5,364)*(x/10) = 5,364

(5,364/10)*x = 5,364

536.4*x = 5,364

So we just found another expression for the number 5,364 in terms of x.

Hey there!☺

\(Answer:\boxed{8n-9}\)

\(Explanation:\)

\(-2n-1(9-10n)\)

Step 1: Distribute.

\(-2n+(-1)(9)+(-1)(-10n)\\-2n+-9+10n\)

Step 2: Combine like terms.

\((-2n+10n)+(-9)\)

Answer:

\(8n-9\)

Hope this helps!☺

The number of children who like both pistachio and chocolate ice cream is 73.

Here we have to find at least one kind of ice cream liked by the children.

It is given that the total number of children is 395. The number of children who don't like any ice cream is 170.

So we get the number of students who like one or both the ice cream is 395 - 170 = 225.

Here it is provided that 123 children like pistachio ice cream and 175 children like chocolate ice cream.

So the total number of children who like pistachio and chocolate ice cream is 175+ 123 = 298. Which cannot be greater than 225.

So the number of children who like both ice creams is 298 - 225 = 73.

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Answer:

Step-by-step explanation:

Each term is 3 times the previous term:  

                                                                r = 3

The sum of the first nine terms in a sequence is 49,205:

                                                      \(S_n=a_1\cdot\dfrac{1-q^n}{1-q}\\\\\\49205=a_1\cdot\dfrac{1-3^9}{1-3}\\\\49205=a_1\cdot\dfrac{1-19683}{-2}\\\\49205=a_1\cdot9841\\\\a_1=5\)

What is the third term?

                                     \(a_n=a_1\cdot q^{n-1}\\\\a_3=5\cdot3^8=32805\)

The proportion of students with a z-score between -1.20 and -0.30 is about 0.304. So for every 100 students.

What is the z-score?

Z-score indicates how much a given value differs from the standard deviation. The Z-score, or standard score, is the number of standard deviations a given data point lies above or below the mean. Standard deviation is essentially a reflection of the amount of variability within a given data set.

Assuming that the grading follows a standard normal distribution (i.e., with a mean of 0 and a standard deviation of 1), we can use the z-score formula to find the proportions of students that fall within each grade range:

For an A grade: z-score > 1.65

For a B grade: 0.67 < z-score ≤ 1.65

For a C grade: -0.40 < z-score ≤ 0.67

For a D grade: -1.60 < z-score ≤ -0.40

To convert from the standard normal distribution to the distribution with the course mean and standard deviation, we can use the formula:

z-score = (x - mean) / standard deviation

We don't know the actual mean and standard deviation for the course, so we'll use the given range for the D grade (-1.60 < x < -0.4σ) to estimate the standard deviation. Since the D grade range is 1.2 standard deviations wide (from -1.60 to -0.4σ), we can solve for the standard deviation:

1.2σ = -1.60

σ = -1.60 / 1.2

σ = 1.33

(Note that we have a negative value for σ, which is not possible for a standard deviation. This is because we are using the estimated value of σ to convert from the standard normal distribution to the course distribution, which may not perfectly match the actual distribution of grades.)

Now we can use the z-score formula with the estimated mean and standard deviation to find the proportions of students in each grade range:

For an A grade: z-score > 1.65

z-score = (x - mean) / standard deviation

z-score = (1.65 - 0) / 1.33

z-score = 1.24

From standard normal distribution tables or a calculator, we can find that the proportion of students with a z-score greater than 1.24 is about 0.107. So for every 100 students, we can expect about:

A grades: 100 * 0.107 = 10.7 or approximately 11

For a B grade: 0.67 < z-score ≤ 1.65

z-score = (0.67 - 0) / 1.33

z-score = 0.50

From standard normal distribution tables or a calculator, we can find that the proportion of students with a z-score between 0.50 and 1.24 is about 0.205. So for every 100 students, we can expect about:

B grades: 100 * 0.205 = 20.5 or approximately 21

For a C grade: -0.40 < z-score ≤ 0.67

z-score = (-0.40 - 0) / 1.33

z-score = -0.30

From standard normal distribution tables or a calculator, we can find that the proportion of students with a z-score between -0.30 and 0.50 is about 0.307. So for every 100 students, we can expect about:

C grades: 100 * 0.307 = 30.7 or approximately 31

For a D grade: -1.60 < z-score ≤ -0.40

z-score = (-1.60 - 0) / 1.33

z-score = -1.20

Hence, From standard normal distribution tables or a calculator, we can find that the proportion of students with a z-score between -1.20 and -0.30 is about 0.304. So for every 100 students,

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Answer:

Consistent independent

Consistent dependent

Inconsistent

Step-by-step explanation:

Consistent and Inconsistent Linear Systems

A system of equations is consistent if it has at least one solution. If the solution is unique, then the system is consistent independent, otherwise is consistent dependent, i.e., it has an infinite number of solutions.

When there is no solution for the system, the lines of each equation are parallel but not coincident. A consistent dependent has two non-parallel lines, and a consistent independent system has only one line, i.e. the same line represents both equations.

Two lines are parallel if they have the same slope. To find the slopes, we represent the equations in slope-intercept form:

y = mx + b

Where m is the slope and b is the y-intercept.

Consider the system:

4x + y   = 8

x  + 3y = 8

Rearranging both equations:

y = -4x + 8

y = -1/3 x + 8

The slopes of the lines are -4 and -1/3 respectively, since they are different, the system is consistent independent.

Consider the system:

-4x + 6y = -2

2x - 3y = 1

Rearranging both equations:

y = 4/6 x - 2/6 = 2/3 x - 1/3

y = 2/3 x - 1/3

Both equations are exactly the same, thus the system is consistent dependent.

Consider the system:

5x - 2y = 4

5x - 2y = 6

Rearranging both equations:

y = 5/2 x - 2

y = 5/2 x - 3

These lines are parallel but not coincident. Thus this system is inconsistent.

Answer: 1306.5 m^3

Step-by-step explanation:

1. The formula for the volume of a cylinder is: V=\(\pi\)r^2h

2. If you substitute the values into the equation, you get

V = pi * 5.7^2 * 12.8 = 1306.5

3. 1306.5 is already to the nearest tenth, so that is the answer.

In the given case, people staying away from the city centre are not being irrational but, their opportunity cost of commuting must be lower

Opportunity cost is the price of forgone options or the worth of the next best option that must be given up in order to pursue a certain choice. The opportunity cost of commuting might encompass not just the time and money spent on transportation, but also the advantages and disadvantages of living in various places. In the given case, living close to the city centre, could make it simpler to access social events, entertainment, and cultural activities, while relocating further away might provide you access to more space, privacy, and natural surroundings.

As a result, depending on their personal and professional ambitions, financial limitations and other considerations, different people may have various preferences and trade-offs when deciding where to live and how much to commute. Some people might put their commute time and cost reduction first, while others might put other aspects of their lifestyle and surroundings first.

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Answer:

The 5th term in the sequence is 19

Step-by-step explanation:

Step-by-step explanation:

-5x+2y= 4         <==== Multiply entire equation by -3 to get:

15x-6y = -12  

2x+3y= 6          <====  Multiply entire equation by 2 to get :

4x+6y = 12    Add the two underlined equations to eliminate 'y'

19x = 0     so x = 0

sub in x = 0 into any of the equations to find:  y = 2

(0,2)

To order a calzone with 6 distinct topping from available list of 8 vegetarian toppings, number of choices of calzone available is 28.

Therefore, the answer is 28.

Total number of available toppings equals 8 and the number of toppings selecting is 6.

The number of ways calzone can be chosen with 6 distinct topping from 8 vegetarian toppings can be obtained by combination formula.

nCm = n!/ (m! × (n - m)!)

Therefore, the number of ways = nCm

= 8C6

= 8!/ (6! × (8 - 6)!)

= 8!/ (6! × 2!)

= (8 × 7)/ 2

= 28

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Answer:

48

Step-by-step explanation:

3*12=36

4*12=48

Can I have brainliest?

The function φ : F[x] → F[x] defined by φ(f(x)) = f(x + 1) is an automorphism of F[x] and fixes every element of F.

To show that φ is an automorphism, we need to prove two things: (1) φ is a bijection, and (2) φ preserves the operations of F[x], i.e., φ(f + g) = φ(f) + φ(g) and φ(fg) = φ(f)φ(g) for all f, g ∈ F[x].

First, we show that φ is a bijection. Let f, g ∈ F[x] such that φ(f) = φ(g). This means that f(x + 1) = g(x + 1) for all x ∈ F. Substituting x - 1 for x, we get f(x) = g(x) for all x ∈ F. Therefore, f = g, and φ is injective. To show that φ is surjective, let h ∈ F[x]. Define f(x) = h(x - 1). Then, φ(f) = f(x + 1) = h(x) for all x ∈ F. Hence, φ is surjective.

Next, we show that φ preserves the operations of F[x]. Let f, g ∈ F[x]. Then, φ(f + g) = (f + g)(x + 1) = f(x + 1) + g(x + 1) = φ(f) + φ(g), and φ(fg) = (fg)(x + 1) = f(x + 1)g(x + 1) = φ(f)φ(g). Therefore, φ is an automorphism of F[x].

Finally, we need to show that φ fixes every element of F. Let a ∈ F. Then, φ(a) = a(x + 1) = a for all x ∈ F. Therefore, φ fixes every element of F.

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The total revenue that will be maximized is 20 - 2a

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

Qd = 20 - P

The revenue equation is calculated using

Revenue = Quantity * Price

So, we have

R = Qd * P

This gives

R = (20 - P) * P

Expand

R = 20P - P²

Differentiate

R' = 20 - 2P

Next, we have

Q = a

So, we have

R = 20 - 2a

Hence, the total revenue that will be maximized is 20 - 2a

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Answer:

d=24

Step-by-step explanation:

If you were to invest in an account that compounds interest annually or even monthly, the total amount of money you'll have at the end of 30 years would be significantly higher.

If you invest $3000 in an account that pays simple interest of 4% for 30 years, the amount of money you'll have at the end of 30 years can be calculated using the simple interest formula:
Interest = Principal x Rate x Time
In this case, Principal = $3000, Rate = 4%, and Time = 30 years
Interest = 3000 x 0.04 x 30 = $3600
Therefore, the total amount of money you'll have at the end of 30 years will be the sum of the principal and interest:
Total Amount = Principal + Interest = $3000 + $3600 = $6600
It's important to note that the interest earned in a simple interest account does not compound over time, meaning you earn the same fixed interest rate each year. If you were to invest in an account that compounds interest annually or even monthly, the total amount of money you'll have at the end of 30 years would be significantly higher.

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The probability of Nevaeh landing on blue and a multiple of 4 is 1 out of 16, or 1/16.

To determine the probability of Nevaeh landing on blue and a multiple of 4, we need to gather information about the spinner and the numbers on the table. Since you haven't provided specific details about the spinner or table, let's assume that the spinner has four equally sized sectors labeled 1, 2, 3, and 4, and the table contains numbers from 1 to 12.

To find the probability, we need to determine the favorable outcomes (landing on blue and a multiple of 4) and the total number of possible outcomes.

Favorable outcomes:

Blue: Let's assume that the spinner has one blue sector. So, the probability of landing on blue is 1 out of 4.

Multiple of 4: From the given table, we need to identify the numbers that are multiples of 4. In this case, the numbers are 4, 8, and 12. Therefore, the probability of landing on a multiple of 4 is 3 out of 12 (since there are 3 multiples of 4 out of a total of 12 numbers on the table).

Total number of possible outcomes:

Assuming the spinner has four sectors, the total number of possible outcomes is 4 (since each sector represents a different outcome).

Now, we can calculate the probability of Nevaeh landing on blue and a multiple of 4 by multiplying the probabilities of the favorable outcomes:

Probability of landing on blue and a multiple of 4 = Probability of landing on blue × Probability of landing on a multiple of 4

Probability of landing on blue = 1/4

Probability of landing on a multiple of 4 = 3/12

Probability of landing on blue and a multiple of 4 = (1/4) * (3/12) = 3/48 = 1/16

Therefore, the probability of Nevaeh landing on blue and a multiple of 4 is 1 out of 16, or 1/16.

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Answer:

Mark me as brainliest please!

Step-by-step explanation:

Answer:

e.

Step-by-step explanation:

e.