The data set shown below represents the number of times some families went out for dinner the previous week. 4, 2, 2, 0, 1, 6, 3, 2, 5, 1, 2, 4, 0, 1 an unnumbered number line labeled numbers of dinners out. create a dot plot to represent the data. what can you conclude about the dot plot of the data set? check all that apply. the range of the number line should be 0 to 7 to represent the frequency. four families said they ate out twice the previous week. one family said they ate out 5 times the previous week. the data set is symmetrical. the median best represents the data set.

Answer:

- 8n -4 +n+7

like terms (-8n, n) and (-4, 7)

so; -8n+n-4+7

    = -7n+3

Answer:

-7n + 3

Step-by-step explanation:

   Like terms are terms that have same variable with same power.

-8n and n are like terms.  subtract or add the coefficient of the like terms.

(-8) and 1. So, subtract and it is -7n

(-4) and 7 are like terms(constants).

-8n - 4 + n + 7 = -8n + n - 4 + 7

                        = -7n + 3

Using Euler's method with a step size of h = 0.1, the approximate values of the solution at t = 0.1, 0.2, 0.3, 0.4, and 0.5 can be calculated as follows:

t = 0.1:

Y1 = Y0 + h * F(X0, Y0) = 1 + 0.1 * (2 - e^1) ≈ 0.66049

t = 0.2:

Y2 = Y1 + h * F(X1, Y1) = 0.66049 + 0.1 * (2 - e^0.66049) ≈ 0.46603

t = 0.3:

Y3 = Y2 + h * F(X2, Y2) = 0.46603 + 0.1 * (2 - e^0.46603) ≈ 0.32138

t = 0.4:

Y4 = Y3 + h * F(X3, Y3) = 0.32138 + 0.1 * (2 - e^0.32138) ≈ 0.21568

t = 0.5:

Y5 = Y4 + h * F(X4, Y4) = 0.21568 + 0.1 * (2 - e^0.21568) ≈ 0.14007

In Euler's method, we approximate the solution to a differential equation by taking small steps (h) and using the formula Yn = Yn-1 + h * F(Xn-1, Yn-1), where F(X, Y) represents the derivative of the function.

Given the differential equation 2y = 2 - e^y and the initial condition y(0) = 1, we can rewrite it as dy/dx = 2 - e^y.

Using Euler's method with a step size of h = 0.1, we start with the initial condition:

At t = 0, Y0 = 1.

Now, we can calculate the approximate values at each desired time point using the formula mentioned above. We substitute the values of Xn-1, Yn-1, and h into F(Xn-1, Yn-1) to evaluate the derivative at each step.

For example, at t = 0.1:

Y1 = Y0 + h * F(X0, Y0) = 1 + 0.1 * (2 - e^1) ≈ 0.66049.

Similarly, we repeat the process for t = 0.2, 0.3, 0.4, and 0.5, updating Yn using the previous Yn-1 value and evaluating the derivative at each step.

Using Euler's method with a step size of h = 0.1, we have approximated the values of the solution at t = 0.1, 0.2, 0.3, 0.4, and 0.5 for the given differential equation. These approximate values provide an estimation of the solution at those time points based on the iterative calculations using Euler's method.

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Answer:

Area:  24

Step-by-step explanation:

Answer: If I did it corcorrectlyect the answer is  41.57²

Hope it helped :D

Answer:

1/3

Step-by-step explanation:

First find the LCD or least common denominator. The least common denominator is the number that both of the denominators are divisible by.

In this case, 2 and 3 are both divisible by 6.

Convert both fractions into a fraction with a denominator of 6.

1/2 = 3/6 (multiply numerator and denominator by 3)

2/3 = 4/6 (multiply numerator and denominator by 2)

Now you can multiply as they have the same denominator.

3/6 × 4/6 = 12/36

Simplify.

12/36 = 1/3 (numerator and denominator are divisible by 12)

Hope that helps.

Answer:

Always

Step-by-step explanation:

A whole number will always be an interger.

False. let a be a real square matrix. if a is diagonalizable then a is symmetric

Explanation: Diagonalizability and symmetry are two different properties of a square matrix. A real square matrix A is diagonalizable if it can be transformed into a diagonal matrix D through a similarity transformation with an invertible matrix P, i.e., A = PDP^(-1). A matrix is symmetric if A = A^T, where A^T is the transpose of A.

While it is true that every symmetric matrix is diagonalizable, the converse is not necessarily true. In other words, not every diagonalizable matrix has to be symmetric.

Conclusion: The statement "if A is diagonalizable then A is symmetric" is false because diagonalizability does not guarantee symmetry.

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The artist should divide the region with vertical lines at x1 = 0.5000, x2 = 0.7500 and x3 = 1.0000 to get 3 pieces with equal areas.

Let the length of the region be l. Then, the area of the region = l x l = l^2

To divide the region into 3 equal areas, let the 3 divisions be at x1, x2, and x3 such that x1 < x2 < x3.

Then, the area of each division = (x2-x1) x l = l x (x2-x1) = l^2/3

Therefore,

l x (x2-x1) = l^2/3

or, x2 - x1 = l/3

Using this equation, we can find the values of x1, x2, and x3 that divide the region into 3 equal areas:

x1 = 0, x2 = l/3 and x3 = 2l/3

Therefore, for the given region, the artist should divide it with vertical lines at x1 = 0.5000, x2 = 0.7500 and x3 = 1.0000 to get 3 pieces with equal areas.

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The image of the car park showing the 2 angles is attached.

Answer:

Their lines are parallel.

Step-by-step explanation:

From the attached image, we can see that ∠1 and ∠2 form a pair of alternate exterior angles. Thus; ∠1 = ∠2.

Now since they are congruent, it means that their lines will be parallel.

Thus, we can conclude that their lines are parallel.

The number that gives the exact value of 3 7/15 is 52/15

The number is given as:

Number = 3 7/15

The above number is a mixed fraction, and it can be converted to an improper fraction as follows:

Number = 3 7/15

Multiply 15 by 3 and add the result to 7; this becomes the numerator

Number = 52/15

Hence, the number that gives the exact value of 3 7/15 is 52/15

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Answer:

a. True

Step-by-step explanation:

a. True

A cost that changes in total as output changes is indeed a variable cost. Variable costs are expenses that vary in direct proportion to the level of production or business activity. As output increases, variable costs increase, and as output decreases, variable costs decrease. Examples of variable costs include direct labor, raw materials, and sales commissions.

Mary's speed, given the kilometers she rode in 7 hours, can be found to be 12. 8 km / hr

To find the speed that Mary was going in order to have been able to travel 89.6 kilometers in 7 hours, you can use the speed formula which is:

= Distance / Time

Distance =  89. 6 kilometers

Time = 7 hours

The speed that Mary was going at is therefore :

= 89. 6 km / 7 hours

= 12. 8 km / hr

In conclusion, the speed that Mary was going at was 12. 8 km / h.

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Answer:

\(first \: answer \: is \: true\)

Answer:

the middle of the shape

Step-by-step explanation:

Answer:

X = {O,B,A,N,D}

Y = {B,U,L,A,C,N}

Step-by-step explanation:

Given

Words: OBANDO and BULACAN,

Such that X and represent either of those words respectively.

Next, is to remove all repetition and assign X and Y to the words as thus:

X = {O,B,A,N,D}

Y = {B,U,L,A,C,N}

Answer:

False

Step-by-step explanation:

Because it is convex, that is, it has bulges

Answer: 25

Step-by-step explanation: take the square inches and put it to the side... then multiply how many sides to the number of square inches and you got 25

As per the question, All four students A, B, C, and D are loss-averse over money and have the same value function as below:v(x dollars)={√x     x ≥ 0   {-2√-x  x < 0They are also loss averse over mugs and have the same value function.

v(y mugs)={3y y ≥ 0
        {4y y < 0
Now, we have to find the values of a, b, c and d as below:
- Student A owns a mug and is willing to sell it for a price of a dollars or more. i.e v(a) = v(0) + v(a-A), where A is the initial endowment of A. According to the given function, v(0) = 0, v(a-A) = 3, and v(A) = 4.
So, a ≥ A+3/2
- Student B does not own a mug and is willing to pay up to b dollars for buying it. i.e v(B-b) = v(B) - v(0), where B is the initial endowment of B. According to the given function, v(0) = 0, v(B-b) = -4, and v(B) = -3.
So, b ≤ B+1/2
- Student C does not own a mug and is indifferent between getting a mug and getting c dollars. i.e v(c) = v(0) + v(c), where C is the initial endowment of C. According to the given function, v(0) = 0, v(c) = 3.
So, c = C/2
- Student D is indifferent between losing a mug and losing d dollars. i.e v(D-d) = v(D) - v(0), where D is the initial endowment of D. According to the given function, v(0) = 0, v(D-d) = -3.
So, d = D/2
2) In this case, value function for money changes to:v(x dollars)={√x     x ≥ 0
            {-√-x   x < 0
However, the value function for mugs remains the same:v(y mugs)={3y y ≥ 0
         {4y y < 0
Therefore, values for a, b, c, and d will remain the same as calculated in part (1).
3) In this case, students are not loss-averse. Value function for money:v(x dollars)={√x     x ≥ 0
            {-√-x   x < 0
Value function for mugs:v(y mugs)={3y y ≥ 0
The reference point is the status quo, i.e initial endowment. So,
- Student A owns a mug and is willing to sell it for a price of a dollars or more. The value of mug for A is 3 initially and he would sell it for 3 or more.
So, a ≥ A+3/2
- Student B does not own a mug and is willing to pay up to b dollars for buying it. The value of mug for B is 3 initially and he would buy it for 3 or less.
So, b ≤ B+3/2
- Student C does not own a mug and is indifferent between getting a mug and getting c dollars. The value of the mug for C is 3 initially.
So, c = 3
- Student D is indifferent between losing a mug and losing d dollars. The value of the mug for D is 3 initially.
So, d = 3
4) In this case, value function for money:v(x dollars)={√x     x ≥ 0
            {-√-x   x < 0
Value function for mugs: Mug will have a value of 4 for someone who owns it and 3 for someone who does not own it.
The reference point is the status quo, i.e initial endowment. So,
- Student A owns a mug and is willing to sell it for a price of a dollars or more. The value of mug for A is 4 initially and he would sell it for 4 or more.
So, a ≥ A+2
- Student B does not own a mug and is willing to pay up to b dollars for buying it. The value of mug for B is 3 initially and he would buy it for 3 or less.
So, b ≤ B+3/2
- Student C does not own a mug and is indifferent between getting a mug and getting c dollars. The value of the mug for C is 3 initially and he would like to buy it for 3.
So, c = 3
- Student D is indifferent between losing a mug and losing d dollars. The value of the mug for D is 3 initially.
So, d = 3.

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By defining how exponents work, we conclude that 4^3 = 64, so the correct option is A.

Let's remember how exponents work.

If we have a number a to the exponent n:

a^n

It means that we need to multiply the number a by itself n times.

Then, in this case:

4^3

Can be rewritten to.

4*4*4

Now we can solve that product:

4*4*4 = (4*4)*4 = 16*4 = 64

Then we conclude that the correct option is A

4^3 = 64

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You would travel 200 kilometers in 2.5 hours along the Old Geelong Road if you drove at the speed limit of 80 km/h.

If the speed limit along the Old Geelong Road is 80 km/h, it means that you are not allowed to drive faster than 80 km per hour on this road. To find the distance you would travel in 2.5 hours, you need to know how far you can travel in one hour at this speed.

Since the speed limit is 80 km/h, you can travel 80 kilometers in one hour. Therefore, in 2.5 hours, you would travel:

Distance = Speed × Time

Distance = 80 km/h × 2.5 h

Distance = 200 km

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True, there exists a function f such that f(x) > 0, f'(x) < 0, and f"(x) > 0 for all x.

An example of such a function is\(f(x) = e^(-x)\), where e is the base of the natural logarithm (approximately 2.718).

Let's verify the given conditions:

f(x) > 0:

Since e^(ax) is always positive for any real value of x and any constant a, \(e^(-x)\)is also always positive for any real value of x.

f'(x) < 0:

To find the first derivative, apply the chain rule: \(f'(x) = -e^(-x). As e^(-x)\) is always positive, the derivative

\(f'(x) = -e^(-x)\) is  always negative for all x.

f"(x) > 0:

To find the second derivative, apply the chain rule again:

\(f"(x) = e^(-x). As e^(-x)\)is always positive, the second derivative\(f"(x) = e^(-x)\) is always positive for all x.

Thus, it is true that there exists a function f with the given conditions.

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The function \(f(x) = e^(-x)\) meets all the given conditions.

True. There exists a function f such that \(f(x) > 0, f'(x) < 0, and f"(x) > 0\) for all x. One example of such a function is \(f(x) = e^(-x)\).
True. There exists a function f(x) that satisfies the given conditions: f(x) > 0, f'(x) < 0, and f''(x) > 0 for all x.

Consider the function \(f(x) = e^(-x)\). This function has the following properties:

1. f(x) > 0 for all x because the exponential function is always positive.
2. \(f'(x) = -e^(-x)\)which is always negative because e^(-x) is always positive, and the negative sign in front makes the derivative negative.
3. \(f''(x) = e^(-x)\)which is always positive.

Thus, the function \(f(x) = e^(-x)\)meets all the given conditions.

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The given statement "A and B are n x n matrices. The determinant of A is the product of the diagonal entries in A" is False because the product of the diagonal entries in A for n x n matrix will not be equal to determinant of A.

The determinant of a matrix is a scalar value that can be calculated using a specific formula. The formula for finding the determinant of an n x n matrix involves finding the sum of products of the elements in certain combinations of rows and columns.

The product of the diagonal entries is only one element in the calculation of the determinant of a matrix, and it is not equal to the determinant unless the matrix has all zeros except on the diagonal.

For example, consider the following 2x2 matrices:

A = [2 3; 4 5]

B = [1 0; 0 1]

The determinant of A is (25) - (34) = -2

The product of the diagonal entries in A is 2*5 = 10, which is not equal to the determinant.

The determinant of B is (11) - (00) = 1

The product of the diagonal entries in B is 1*1 = 1, which is equal to the determinant.

Therefore, the statement "The determinant of A is the product of the diagonal entries in A" is false in general, and the determinant of a matrix is typically calculated using a more involved formula that takes into account all the elements in the matrix.

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Answer:

165 inches, or 13 feet and 9 inches

Step-by-step explanation:

Because the ratio of the model to the actual car is 1:10, you know that the actual car is ten times bigger than the model. You can multiply the length of the model by ten to get the length of the actual car with this information.

16.5 x 10 = 165 inches

If you're being asked to convert to feet, do so by dividing by twelve and taking the remainder as your remaining inches.

165 / 12 = 13 r 9, meaning 13 feet and 9 inches

Let me know if you need more of an explanation for anything!

Answer:

Answer 4

width = 4

Length = 13

Step-by-step explanation:

Givens

Length = x + 9

width = x

Area = 52

Equation

Area = L * W

Area = x (x + 9 )  = 52

Solution

x (x + 9) = 52            remove the brackets

x^2 + 9x = 52           Subtract 52 from both sides

x^2 + 9x - 52 = 0     Factor

(x + 13)(x - 4) = 0

x + 13 is an extraneous solution. You cannot have a length or width of - 13 or minus anything for that matter.

x - 4 = 0                    Add 4 to both sides

x = 4                         This is the only possible solution.

Answer:

y = |x+6|

Step-by-step explanation:

To represent horizontal shift of a graph, we use the equation y = |x - h|, where h is the amount of units the graph is shifted.  

If we are shifting 6 units to the left, h = -6.  Therefore, the new equation will be: y = |x - (-6)| or y = |x + 6|

Answer:

Step-by-step explanation:

\(\pmb {sin(22)^o=\cfrac{x}{35} }\)

\(\pmb {35sin(22)=w}\)

\(\pmb {w=13.11}\)

_________________

Hope this helps!

Have a great day! :)

Answer:

4

Step-by-step explanation:

Simplify the following:

2^5/2^3

Hint: | For all exponents, a^n/a^m = a^(n - m). Apply this to 2^5/2^3.

Combine powers. 2^5/2^3 = 2^(5 - 3):

2^(5 - 3)

Hint: | Subtract 3 from 5.

5 - 3 = 2:

2^2

Hint: | Evaluate 2^2.

2^2 = 4:

Answer: 4

Answer:

y=4x+2

Step-by-step explanation:

y=mx+b

replace m for 4 and b for 2

Answer:

360 in

Step-by-step explanation:

To figure out how many inches the dressmaker has in 10, 3 ft rolls, we can multiply by the conversion ratio:

\(\dfrac{12 \text{ in}}{1\text{ ft}} \\ \\ \text{} \ \ \implies (10 \cdot 3 \text{ ft}) \cdot \dfrac{12 \text{ in}}{1\text{ ft}} \\ \\ \text{} \ \ \implies 30 \text{ ft} \cdot \dfrac{12 \text{ in}}{1\text{ ft}} \\ \\ \text{} \ \ \implies 30\cdot 12 \text{ in} \\ \\ \text{} \ \ \implies \boxed{360 \text{ in}}\)

So, the dressmaker has 360 in of ribbon.

For a \(725\)-mile journey, the needed driver must refuel the gas tank twice.

For flammable and dangerous fuels like fuel, gasoline, petroleum, and others, a fuel tank provides a secure storage option. Some are built to carry and dispense gasoline to job locations as needed since they are very portable or transportable.

Cylinder-contained gases may be poisonous, combustible, caustic, inert, or a mix of these dangers. A leak from the cylinders, regulator, or any other component of the system used to transport the gas can quickly pollute a sizable area since the pressurized chemicals is expelled in gaseous form.

If a car can go \(25\) miles on \(1\) gallon of gas, then it can go:

\(20 gallons * 25 miles/gallon = 500 miles\)

Therefore, on a \(725\)-mile trip, the driver will need to refill the gas tank:

\(725\) miles ÷ \(500\) miles/tank \(= 1.45\) tanks

Since the driver cannot refill the gas tank \(0.45\)  times, they will need to refill the tank twice during the trip.

So the driver has to refill the gas tank \(2\) times on a \(725\) -mile trip.

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Answer:

x > -10

Step-by-step explanation: