Town officials want to estimate the number of households that own a dog. Answer the following.

There are 300 households in the town.

Estimate how many households that own a dog

__ households

Answer:

The cost of each salad is $12.

Step-by-step explanation:

Each time she goes she pays a $1.50 tip. And since she went four times it would be 1.5*4 which equals 6. Then you would take $6 off of $54. Which would be $48. Because she went four times then she would take $48 and divide it by 4. Which gives you $12. She spent $12 per salad.

Answer: Each salad cost $12

Step-by-step explanation:

She visited the restaurant 4 times and each time she ordered a salad and left 1.50 tip  so multiply  1.50 by 4 to find the total amount of  tip she paid during the four visits.

1.50 * 4  = 6  so in total  she paid a total of $6 in tips

Now subtract the total amount of tip from the total amount of money she spent and divide it by for to find how much each salad cost.

54 - 6 = 48  

48/ 4 = 12  

The fifth term of the arithmetic sequence is -1190.

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms remains constant. To find the fifth term, we can use the formula for the nth term of an arithmetic sequence:

aₙ = a₁ + (n - 1) * d

where aₙ represents the nth term, a₁ is the first term, n is the position of the term, and d is the common difference.

Given that the 100th term is -1240 and the common difference is -25, we can substitute these values into the formula.

Since the fifth term corresponds to n = 5, we can calculate:

a₅ = -1240 + (5 - 1) * (-25)

= -1240 + 4 * (-25)

= -1240 - 100

= -1340

Therefore, the fifth term of the arithmetic sequence is -1190.

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Answer:

It is true that the product of a complex number and its conjugate is a real number.

Step-by-step explanation:

You're welcome.

Answer:

True

Step-by-step explanation:

....this is how you 'rationalize' denominators that have complex numbers in them

A survay of 600 people related to time(in hours) which they spent on excercise each week,

a) The percentage of respondents said that they exercise less than three hours per week is 46.

b) The number of respondents who exercise between two and four hours per week are 32% i.e 32×600/100 = 192 respondents.

A histogram is a chart which display the statistical information that uses rectangles to show the frequency of data items in successive numerical intervals of equal size.

Relative frequency is defined as how often something happens divided by all the possible outcomes. The relative frequency formula is:

Relative frequency = Number of sucessful trials/total number of trials. A relative frequency histogram is a type of graph that display how often something happens, in percentages.

We have provide a relative frequency histogram (above figure)for results of this survey of polling companie' people about how much time they spend exercising each week.

Total survayed people = 600

a) We have to determine the percentage of respondents said that they exercise less than three hours per week ,

from the histogram, the required percentage = one hour + two hour = 20% + 26% = 46%.

b)Respondents said that they exercise between two and four hours per week = two hours + four hours = 19% + 13% = 32%

Hence,required percentage is 32%i.e 192.

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Complete question:

Suppose that a polling company surveyed 600 people about how much time they spend exercising each week. The results of this survey were compiled and used to create this relative frequency histogram. 30- 20 10 Weekly hours of exercise Assume that all percentages shown in the histogram are whole numbers. Each of the bars in this histogram includes only the left endpoint of the class except for the last bar, which also includes the right endpoint. What percentage of respondents said that they exercise less than three hours per week? How many respondents said that they exercise between two and four hours per week? respondents.

The condition under which |a⃗ − b⃗ | = a + b is when the vectors a⃗ and b⃗ are parallel and have the same direction.

When two vectors are parallel, it means they have the same or opposite direction. In this case, we consider the scenario where they have the same direction. When a⃗ and b⃗ are parallel and have the same direction, the difference between them, a⃗ − b⃗, results in a vector that has a magnitude equal to the difference between their magnitudes, |a| − |b|.

In order for |a⃗ − b⃗ | to be equal to a + b, the magnitudes of the vectors a⃗ and b⃗ should satisfy the condition |a| − |b| = a + b. This implies that the magnitude of vector a⃗ should be twice the magnitude of vector b⃗. By setting these magnitudes appropriately, we can achieve the equality between the magnitudes of the difference vector and the sum of the vectors.

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Therefore, the degree of the resulting polynomial is m + n when two polynomials of degree m and n are multiplied together.

What is polynomial?

A polynomial is a mathematical expression consisting of variables and coefficients, which involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents. Polynomials can have one or more variables and can be of different degrees, which is the highest power of the variable in the polynomial.

Here,

When two polynomials are multiplied, the degree of the resulting polynomial is the sum of the degrees of the original polynomials. In other words, if the degree of the first polynomial is m and the degree of the second polynomial is n, then the degree of their product is m + n.

This can be understood by looking at the product of two terms in each polynomial. Each term in the first polynomial will multiply each term in the second polynomial, so the degree of the resulting term will be the sum of the degrees of the two terms. Since each term in each polynomial has a degree equal to the degree of the polynomial itself, the degree of the resulting term will be the sum of the degrees of the two polynomials, which is m + n.

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The value of 'x' of the length of the hypotenuse is 15.4 cm.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjecen/hypotenuse and

tan = opposite/adjacent.

From the given information with respect to the reference angle of 19°,

Opposite side is 5 cm and we have to find the value of the hypotenuse 'x'.

We know, sin = opposite/hypotenuse.

Therefore, sin19° = 5/x.

x = 5/0.325.

x = 15.4 cm.

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Answer:22

Step-by-step explanation:

The type of variable that represents the names of the automobile manufacturers would be the categorical variable.

A variable is defined as the quantity that may change within the context of a mathematical problem, research work or an experiment.

There are various types of variables that include the following:

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The solutions to the equation \(2/x - 1 = 16/(x^2 + 3x - 4) are x = 2 and x = (-1 ± √17) / 2.\)

To solve the equation \(2/x - 1 = 16/(x^2 + 3x - 4),\) we'll simplify and rearrange the equation to isolate the variable x. Here's the step-by-step solution:

1. Start with the given equation: 2/x - 1 = 16/(x^2 + 3x - 4)

2. Multiply both sides of the equation by x(x^2 + 3x - 4) to eliminate the denominators:

\(2(x^2 + 3x - 4) - x(x^2 + 3x - 4) = 16x\)

3. Simplify the equation:

\(2x^2 + 6x - 8 - x^3 - 3x^2 + 4x - 16x = 16x\)

4. Combine like terms:

  -x^3 - x^2 + 14x - 8 = 16x

5. Move all terms to one side of the equation:

\(-x^3 - x^2 - 2x - 8 = 0\)

6. Rearrange the equation in descending order:

  -x^3 - x^2 - 2x + 8 = 0

7. Try to find a factor of the equation. By trial and error, we find that x = 2 is a root of the equation.

8. Divide the equation by (x - 2):

\(-(x - 2)(x^2 + x - 4) = 0\)

9. Apply the zero product property:

  x - 2 = 0 or x^2 + x - 4 = 0

10. Solve each equation separately:

   x = 2

11. Solve the quadratic equation:

   For x^2 + x - 4 = 0, you can use the quadratic formula or factoring to solve it. The quadratic formula gives:

 \(x = (-1 ± √(1^2 - 4(1)(-4))) / (2(1)) x = (-1 ± √(1 + 16)) / 2 x = (-1 ± √17) / 2\)

Therefore, the solutions to the equation\(2/x - 1 = 16/(x^2 + 3x - 4) are x = 2 and x = (-1 ± √17) / 2.\)

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Answer:

The sequences below is geometric sequences. 8,16,32

Step-by-step explanation:

It is geometric as far as it goes.

Notice that the ratio between each successive pair of terms is constant:

4/2=2

8/4=2

16/8=2

That these ratios are all the same is sufficient for the given terms to form a geometric sequence with general term:

an=\(2^{n}\)

The sequence then continues:

2

,

4

,

8

,

16

,

32

,

64

,

128

,

256

,

512

,

1024

,

2048

,

...

The question is in the "...". Any finite number of terms does not determine an infinite sequence.

For example we can match the sequence  

2

,

4

,

8

,

16

 with a cubic polynomial:

\(a_{n}\)=1/3(\(n^{3}\) -3\(n^{2}\) +8n)

Then we would find that the next terms would be  

30

,

52

,

84

,

.

the second 4 11 ,17 is wrong

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The total surface area of the triangular prism is  225  in²

Remember that the area of a rectangle of length L and width W is:

A = L*W

And the area of a triangle of base B and height H is:

A = B*H/2

The areas of the 2 triangular faces is:

A = (4.5 in)*6in/2 = 13.5 in²

And the areas of the 3 rectangular faces are:

Then the total surface area is:

2*(13.5 in²) + 66 in² + 49.5 in² + 82.5 in² = 225  in²

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Binding constraints directly influence the optimal solution in a linear Programming problem, whereas constraints with positive slack are non-binding and do not directly impact the solution.

binding constraints and positive slack in the context of linear programming. In a linear programming problem, we aim to find the optimal solution for an objective function, given a set of constraints. The terms "binding constraints" and "positive slack" are related to these constraints.

1. Binding constraints: These are constraints that directly impact the optimal solution of the problem. In other words, they "bind" the feasible region (the area where all the constraints are satisfied) and affect the maximum or minimum value of the objective function. Binding constraints are active constraints, as they influence the final solution.

2. Positive slack: Slack is the difference between the left-hand side and right-hand side of a constraint when the constraint is satisfied. If this difference is positive, it means that there is some "extra" or "unused" resource in that constraint. Positive slack indicates that the constraint is non-binding, meaning it does not directly impact the optimal solution. It shows that there is some room for the constraint to be further tightened without affecting the final outcome.

In summary, binding constraints directly influence the optimal solution in a linear programming problem, whereas constraints with positive slack are non-binding and do not directly impact the solution. Knowing the difference between these terms can help you better understand and analyze linear programming problems.

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The point estimate for the proportion of registered voters who wish to see Mayor Waffleskate defeated is 0.4773.

A point estimate is a single value that is used to estimate an unknown population parameter. In this case, we are trying to estimate the proportion of registered voters who wish to see Mayor Waffleskate defeated.

The point estimate is calculated by taking the number of voters who wish to see her defeated (158) and dividing it by the total number of voters surveyed (331). This gives us a proportion of 0.4773, which is the point estimate for the population proportion. However, it's important to note that this is only a point estimate, and the true proportion could be higher or lower.

To calculate a margin of error and confidence interval, we would need to use statistical methods.

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The amount that a $90,000 loan cost Lauren than Demarcus will be $8280.

Simple interest is a quick and easy method of calculating the interest charge on a loan. Simple interest is determined by multiplying the daily interest rate by the principal by the number of days that elapse between payments.

From the information, Demarcus and Lauren each take out a $90,000 loan for a new condo and each has to repay the loan in 10 years. It should be noted that 10 years in months will be:

= 10 × 12 = 120 months

The difference in the amount paid as a result of the credit score will be:

= ($840 × 120) - ($771 × 120)

= $100800 - $92520

= $8280

Therefore, the amount is $8280.

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The values of the first six terms of the sequence are

1) a₀ = -1

2) a₁ = 2

3) a₂ = -4

4) a₃ = 8

5) a₄ = -16

6) a₅ = 32

The given sequence is defined recursively as follows

aₙ = -2aₙ-1

where a₀ = -1.

This means that each term in the sequence is equal to twice the negative of the previous term. To find the first few terms of the sequence, we can start with the given value of a0 and apply the recursive formula repeatedly to generate the next terms.

Using this approach, we get

a₁ = -2a₀ = -2(-1) = 2

a₂ = -2a₁ = -2(2) = -4

a₃ = -2a₂ = -2(-4) = 8

a₄ = -2a₃ = -2(8) = -16

a₅ = -2a₄ = -2(-16) = 32

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Answer:

10.00 & 0.05

Step-by-step explanation:

\(10.00 - 0.05 = 9.95\)

The amount of money as change is $ 0.05 and the amount of money given is $ 10.00

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

Let the cost of the item = $ 9.95

The amount of money given = $ 10.00

So , the amount of money received as change = amount of money given - cost of the item

On simplifying the equation , we get

The amount of money received as change = 10.00 - 9.95

The amount of money received as change = $ 0.05

Hence , the amount of change is $ 0.05

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The height of the 10th bounce of the ball will be 0.6 feet.

A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value.

The nth term of the geometric sequence is given by

\(\sf T_n=ar^{n-1}\)

Where,

According to the given question.

During the first bounce, height of the ball from the ground, a = 4.5 feet

And, the each successive bounce is 73% of the previous bounce's height.

So,

During the second bounce, the height of ball from the ground

\(\sf = 73\% \ of \ 10\)

\(=\dfrac{73}{100}(10)\)

\(\sf = 0.73 \times 10\)

\(\sf = 7.3 \ feet\)

During the third bounce, the height of ball from the ground

\(\sf = 73\% \ of \ 7.3\)

\(=\dfrac{73}{100}(7.3)\)

\(\sf = 5.33 \ feet\)

Like this we will obtain a geometric sequence 7.3, 5.33, 3.11, 2.23,...

And the common ratio of the geometric sequence is 0.73

Therefore,

The sixth term of the geometric sequence is given by

\(\sf T_{10}=10(0.73)^{10-1\)

\(\sf T_{10}=10(0.73)^{9\)

\(\sf T_{10}=10(0.059)\)

\(\sf T_{10}=0.59\thickapprox0.6 \ feet\)

Hence, the height of the 10th bounce of the ball will be 0.6 feet.

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Answer:

Both of your answers are correct

Step-by-step explanation:

Answer:

d

e

Step-by-step explanation:

2x ≤ 5x - 15

step 1 subtract 5x from each side

2x - 5x = -3x

5x - 5x cancels out

we now have -3x ≤ -15

step 2 divide each side by -3

-3x / -3 = x

-15 / -3 = 5

IMPORTANT NOTE ( when you divide by a negative number you must flip the sign )

We would be left with x ≥ 5

now let's Plug in 10

2(10) ≤ 5(10) - 15

2(10) = 20

20 ≤ 5(10) - 15

5(10) = 50

20 ≤ 50 - 15

50 - 15 = 35

20 ≤ 35 ✓

I think it would be a right scalene triangle because it seems that none of the sides add up.

a) The 95% confidence interval estimate for the mean ticket sales revenue per theater is $21613 to $24857.

b) The estimated of the mean number of customers per theater is 2536 customers.

c) The total number of customers who saw black panther are 10194720 and the total box office ticket sales for the weekend is 92862000.

A number derived from a random sample that provides an estimation of the probable magnitude of the sampling error in a population parameter estimate.

a) The goal of this section is to calculate and understand the 95% confidence interval estimate for the mean ticket sales revenue per theater.

The following is a definition of the confidence interval formula:

\(\bar{x}\)±margin of error

The margin of error is the value obtained as a 95% confidence interval.

The sample mean is so calculated to be $23100.

Additionally, a margin of error of 1486.864 is determined.

When these values are used in the formula above, we get

\(\bar{x}\)±margin of error

=23100±1486.864

=23100-1486.864 to 23100+1486.864

=21613.136 to 24586.864

=21613 to 24857

The 95% confidence interval estimate for the mean ticket sales revenue per theater is $21613 to $24857.

b) Mean number of customers per theater=23100/9.11

=2573.675

=2536 customers per theater.

The estimated of the mean number of customers per theater is 2536 customers.

c) Total number of customers=2536(4020)

=10194720

The total number of customers who saw black panther are 10194720

Total box office sales in weekend=4020(23100)

=92862000

The total box office ticket sales for the weekend is 92862000

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Answer: 4823243.75 square miles

Step-by-step explanation:

We know that each unit represents 175 miles. This means that one square unit is equal to \(175^2 =30625\) square miles.

Thus, the area is \((30625)(15.75)=4823243.75\) square miles.

Answer:

1.45%+4.2%= 5.65%

100%->650

5.65%-> 36.725

650- 36.725 - 10 = 603.275

~ 603. 27

hence answer is b

Correct Answer: $603.27

a. U'(ct) = β(1 + r)U'(ct+1). This equation is known as the Euler equation, which represents the intertemporal marginal rate of substitution between consumption at time t and consumption at time t+1.

b. U'(c1) = β(1 + r)^2U'(c3). This relationship shows that the marginal utility of consumption at time 1 is equal to the discounted marginal utility of consumption at time 3.

c. C0 = ∑t=0[infinity]​(β(1 + r))^tct. This equation represents the sum of the discounted values of consumption at each period, where the discount factor β(1 + r) accounts for the diminishing value of future consumption.

d.  U0 = ∑t=0[infinity]​(β(1 + r))^tln(ct). This equation represents the sum of the discounted values of utility at each period, where the discount factor β(1 + r) reflects the time preference and the logarithmic utility function captures the agent's preference for consumption.

Y0 = y0 + (1 + γ)y1 + (1 + γ)^2y2 + ..., where γ represents the growth rate of income.

a. The optimization problem of the representative agent involves maximizing the present discounted value of utility subject to the period-by-period budget constraint. The Euler equation is derived as follows:

At each period t, the agent maximizes the utility function U(ct) = ln(ct) subject to the budget constraint ct = (1 + r)wt + yt, where wt is the agent's wealth at time t. Taking the derivative of U(ct) with respect to ct and applying the chain rule, we obtain: U'(ct) = β(1 + r)U'(ct+1). This equation is known as the Euler equation, which represents the intertemporal marginal rate of substitution between consumption at time t and consumption at time t+1.

b. The Euler equation between time 1 and time 3 can be written as U'(c1) = β(1 + r)U'(c2), where c1 and c2 represent consumption at time 1 and time 2, respectively.

Similarly, we can write the Euler equation between time 2 and time 3 as U'(c2) = β(1 + r)U'(c3). Combining these two equations, we fin

d U'(c1) = β(1 + r)^2U'(c3). This relationship shows that the marginal utility of consumption at time 1 is equal to the discounted marginal utility of consumption at time 3.

c. The present discounted value of optimal lifetime consumption can be written as C0 = ∑t=0[infinity]​(β(1 + r))^tct. This equation represents the sum of the discounted values of consumption at each period, where the discount factor β(1 + r) accounts for the diminishing value of future consumption.

d. The present discounted value of optimal lifetime utility can be written as U0 = ∑t=0[infinity]​(β(1 + r))^tln(ct).

This equation represents the sum of the discounted values of utility at each period, where the discount factor β(1 + r) reflects the time preference and the logarithmic utility function captures the agent's preference for consumption.

e. The present discounted value of lifetime income, denoted as Y0, can be expressed as Y0 = y0 + (1 + γ)y1 + (1 + γ)^2y2 + ..., where γ represents the growth rate of income. The income in each period is multiplied by (1 + γ) to account for the increasing income over time.

This assumption of income growth allows for a more realistic representation of the agent's economic environment, where income tends to increase over time due to factors such as productivity growth or wage increases.

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Answer:

Step-by-step explanation:

Good morning,

You just do it in the pathway, and there is the answer for you :D.

Answer:

c

Step-by-step explanation:

–2.24, 2, 2.24

The solution to the equation of the polynomial function \(x^3 - 5x + 5 = 2x^2 - 5\) is (c) –2.24, 2, 2.24

The function is given as:

\(x^3 - 5x + 5 = 2x^2 - 5\)

Split the function.

So, we have:

\(y = x^3 - 5x + 5\)

\(y = 2x^2 - 5\)

Using a graphing calculator, we have the x coordinate at the point o intersection of both equations to be

x = –2.24, 2, 2.24

Hence, the solution to the equation is (c) –2.24, 2, 2.24

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