Demographics Suppose the number of citizens aged 45-64 years is approximated by
P(t)= 197.9/( 1 +3.274e^{ -0.0361} 0<=t<=25 where P(t) is measured in millions and is measured in years, with to corresponding to the beginning of 1990. People belonging to this age group to sell them annulles. What is the expected population of citizens aged 45-64 years in 2010? In 2013? (Round your answers to one decimal place)

Answer:

2

Step-by-step explanation:

First distribute the first x into the first parenthesis:  x (2x - 4) = (2x + 1) (x - 2)

x times 2x is \(2x^{2}\) and x times -4 is -4x

This changes the equation to: \(2x^{2}\)-4x = (2x + 1) (x - 2)

Now multiply the other parentheses: \(2x^{2}\)-4x = (2x + 1) (x - 2)

Do this by using the Foil method (I attached a picture of the method if you don't know it)

First: (2x + 1) (x - 2)

Do 2x times x which = \(2x^{2}\)

Then 2x times -2 which = -4x

Then 1 times x which = x

Lastly, 1 times -2 which = -2

The order you do this is the order that the foil method says.

Now the equation is:

\(2x^{2}\)-4x =\(2x^{2}\)-4x+x-2 (I just added all the numbers we just got)
Next cancel out the equal terms. To combine like terms you'd usually move the right \(2x^{2}\)  over to the left one and subtract it. But since they are the same number, subtracting it would leave you with 0. So you can just get rid of both.

You can also do this with both -4x

This leaves you with:

0=x-2

Now you move the variable to the left

you also make it negative since it is going to the other side of the =

this leaves: -x=-2

You can't have a negative x so now you have to change the signs for both. Make them both positive.

Now you have x=2

so your answer is 2

well, the difference is £20 - £3 simply £17.

now, if we take £20 to be the 100%, what is £17 off of it in percentage?

\(\begin{array}{ccll} \pounds &\%\\ \cline{1-2} 20 & 100\\ 17& x \end{array} \implies \cfrac{20}{17}=\cfrac{100}{x}\implies 20x=1700 \\\\\\ x=\cfrac{1700}{20}\implies x=85\)

Answer: A cup of coffee costs $2.50 and a bagel costs $3.50.

Step-by-step explanation: Let's use the following variables to represent the price of each item:

c: price of a cup of coffee (in dollars)

b: price of a bagel (in dollars)

From the problem statement, we know that:

b = c + 1 (a bagel costs $1 more than a cup of coffee)

We also know that you bought 4 cups of coffee and 6 bagels for a total of $31. This can be expressed as:

4c + 6b = 31

Now we can substitute the first equation into the second equation to eliminate b:

4c + 6(c + 1) = 31

Simplifying this equation, we get:

10c + 6 = 31

Subtracting 6 from both sides, we get:

10c = 25

Dividing both sides by 10, we get:

c = 2.5

Now we can use the first equation to find the value of b:

b = c + 1 = 2.5 + 1 = 3.5

Therefore, a cup of coffee costs $2.50 and a bagel costs $3.50.

Answer:

25x

Step-by-step explanation:

Find the lower quartile (Q1), which is the median of the lower half of the data. The lower half is 11, 14, and 21.Start by arranging the scores in ascending order: 11, 14, 21, 23, 30, 31, 32. . In this case, the median is 23.

Then, find the lower quartile (Q1), which is the median of the lower half of the data. The lower half is 11, 14, and 21. The median of these values is 14.Similarly, find the upper quartile (Q3), which is the median of the upper half of the data. The upper half is 30, 31, and 32. The median of these values is 31.

Finally, identify any outliers, which are extreme values that are significantly higher or lower than the rest of the data.

Using these calculations, you can construct a box plot with the lower whisker starting at 11, the box extending from 14 to 31, the median line at 23, and the upper whisker ending at 32.

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The weight of the baby marked "10" is 10 pounds. The weight of the baby marked "89/10" is 8 pounds plus 9/10 of a pound, which can be written as an improper fraction: 8 + 9/10 = 80/10 + 9/10 = 89/10. Weights Difference : 10 - 89/10 = 100/10 - 89/10 = 11/10.Weights Difference between the two heaviest babies is 11/10 of a pound, or 1 and 1/10 pounds.

To interpret the line plot and find the difference in weight between the two heaviest babies, follow these steps:

1. Identify the heaviest baby's weight: In the line plot, the heaviest baby's weight is represented by the highest value on the right side, which is 10.
2. Identify the second heaviest baby's weight: The second heaviest baby's weight is the second highest value, which is 9.
3. Subtract the second heaviest baby's weight from the heaviest baby's weight: 10 - 9 = 1

The difference in weight between the two heaviest babies is 1 pound. Your answer is a proper fraction: 1/1.

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Por lo tanto, hace 50 años que el Abuelo era 10 veces mayor que el Nieto.

Primero, definimos las edades en una ecuación.

Padre = 25

Hijo = 20

Abuelo = 4 × Nieto = 1

Para encontrar cuántos años han pasado desde que el Abuelo era 10 veces mayor que el Nieto, restamos 25-20=5 años desde que el Padre era 5 años mayor que el Hijo. Luego, multiplicamos esto por 10 para encontrar los años transcurridos desde que el Abuelo era 10 veces mayor que el Nieto. Entonces, 5 x 10 = 50 años. Por lo tanto, hace 50 años que el Abuelo era 10 veces mayor que el Nieto.

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Answer: C.

Step-by-step explanation:
The probability of spinning a blue on the first spinner is 1/2 and the probability of spinning a 1 on the second spinner is 1/6. To find the probability of both events happening, we multiply the probabilities:

P(blue and 1) = P(blue) x P(1) = (1/2) x (1/6) = 1/12

Therefore, the probability of spinning a blue and spinning a 1 is 1/12, which is closest to answer choice C.

The required solution is g = h(s- p) for the given equation.

A solution to an equation is a variable value that, when replaced into the equation, produces a true assertion. Solving an equation refers to the process of determining the solution to an equation.

The equation is given as follows:

s = p + g/h

We have to determine the solution for g.

As per the question, we have

s = p + g/h

Now, solving for g:

s = p + g/h

Multiply both sides of h and we get,

sh = ph + g

Isolate the variable g,

g = sh - ph

g = h(s- p)

Therefore, the required solution is g = h(s- p) for the given equation.

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Answer:

yes

Step-by-step explanation:

half of 6 is 3 so

The simplified form of the expression is -1/√5 + 2√3 + (2+√2)/2

Surds are the values in square root that cannot be further simplified into whole numbers or integers.

Given the expression

2/√5+√3+1/√2+√3-3/√5+√2

Collect the like terms

2/√5-3/√5+√2+√3+1/√2+√3

-1/√5 + 2√3 + √2 + 1/√2

-1/√5 + 2√3 + (2+√2)/2

Hence the simplified form of the expression is -1/√5 + 2√3 + (2+√2)/2

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To answer the questions, let's first evaluate the given sets.

A = {a, b, c}

B = {c, d, e, f}

C = {1, 2, 3, 4}

D = {2, 3, 4, 5, 6}

Now, let's proceed with the calculations:

1. A - Bx(D - C)

  First, let's find (D - C):

  D - C = {2, 3, 4, 5, 6} - {1, 2, 3, 4} = {5, 6}

 Next, let's find Bx(D - C) (the Cartesian product of B and (D - C)):

  Bx(D - C) = {c, d, e, f} x {5, 6} = {(c, 5), (c, 6), (d, 5), (d, 6), (e, 5), (e, 6), (f, 5), (f, 6)}

 Finally, let's find A - Bx(D - C):

  A - Bx(D - C) = {a, b, c} - {(c, 5), (c, 6), (d, 5), (d, 6), (e, 5), (e, 6), (f, 5), (f, 6)} = {a, b, c}

 Therefore, A - Bx(D - C) = {a, b, c}.

2. AxC ∩ (AxD)

  First, let's find AxC (the Cartesian product of A and C):

  AxC = {a, b, c} x {1, 2, 3, 4} = {(a, 1), (a, 2), (a, 3), (a, 4), (b, 1), (b, 2), (b, 3), (b, 4), (c, 1), (c, 2), (c, 3), (c, 4)}

Next, let's find AxD (the Cartesian product of A and D):

  AxD = {a, b, c} x {2, 3, 4, 5, 6} = {(a, 2), (a, 3), (a, 4), (a, 5), (a, 6), (b, 2), (b, 3), (b, 4), (b, 5), (b, 6), (c, 2), (c, 3), (c, 4), (c, 5), (c, 6)}

 Finally, let's find AxC ∩ (AxD):

AxC ∩ (AxD) = {(a, 1), (a, 2), (a, 3), (a, 4), (b, 1), (b, 2), (b, 3), (b, 4), (c, 1), (c, 2), (c, 3), (c, 4)} ∩ {(a, 2), (a, 3), (a, 4), (a, 5), (a, 6), (b, 2), (b, 3), (b, 4), (b, 5), (b, 6), (c, 2), (c, 3

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Answer:

A

Step-by-step explanation:

It is a 90-degree rotation counterclockwise 2 units left and 3 units down.

The expression that represents the value of z is \(\sqrt[3]{3 + i\sqrt 3 }\)

Complex numbers are numbers that have real and imaginary parts

A complex number (n) is represented as:

\(n = a + bi\)

From the above expression, we have:

Given that:

\(z^3 = 3 + \sqrt 3 i\)

Rewrite the above expression as:

\(z^3 = 3 + i\sqrt 3\)

Take the cube roots of both sides

\(z = \sqrt[3]{3 + i\sqrt 3 }\)

The letters are not given.

Hence, the expression that represents the value of z is \(\sqrt[3]{3 + i\sqrt 3 }\)

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Answer:

112m

Step-by-step explanation:

The area of the given  Parallelogram is 112 m².

given that the parallelogram in fig.. We splits this parallelogram in three parts, that is, first is triangle ,second is square and third is again a triangle.

Since, the area of triangle:

\(\mathrm{Area\ of\ triangle}=\frac{1}{2}\) × base × height

and the \(\mathrm {Area\ of\ Square}=\) width × height.

Here in triangle, base=6 and height=8

\(\mathrm {Area\ of\ Square}=\)

therefor the \(\mathrm{Area\ of\ triangle}=\frac{1}{2}\)×6×8

                                               =24m².

Here in square,  width=8 and height=8

therefore the \(\mathrm {Area\ of\ Square}=\) 8×8

                                               =64m².

Area of first split, that is, triangle is 24 m².

Area of second split, that is, square is 64 m².

Area of third split, that is, again a triangle is 24 m².

Total area= 24+64+24

                 =112 m².

Therefor the total area of parallelogram is 112 m².

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Answer:

17

Step-by-step explanation:

\( 28 - 12 + \sqrt{n} \div 2 = \)

n = 4

\( = 28 - 12 + \sqrt{4} \div 2 \)

\( = 16 + 2 \div 2 \)

\( = 16 + 1 \)

\( = 17 \)

Answer:

Step-by-step explanation:

The attached figure shows several kinds of quadrilaterals. The sum of angles of a quadrilateral is 360°. A pair of sides will be parallel if the sum of consecutive angles between them is 180°.

Trapezium/Trapezoid

By definition, a trapezium/trapezoid has exactly one pair of parallel sides.

Concave quadrilateral

This is a quadrilateral with a reflex angle (one that measures more than 180°). Such an angle demands that no consecutive pair of internal angles have a total of 180°. Hence no two sides can be parallel.

Convex quadrilateral

If a simple quadrilateral is not concave, it is convex. Since the sum of angles is 360°, there exists the possibility for at least one adjacent pair of angles to total 180°. That would make at least one pair of sides be parallel.

In the attached figure, all of the quadrilaterals shown, except the "dart" at upper left, are convex quadrilaterals. Most of them, except the "kite" at lower left, have at least one pair of parallel sides.

There is no assurance that a convex quadrilateral will have no parallel sides.

Kite

A kite has two pairs of congruent adjacent sides. It cannot have any parallel sides.

Rhombus

A rhombus has all four sides of equal length. It is a parallelogram with two pairs of parallel sides.

The two figures on the list that have no pairs of parallel sides are ...

These are shown in the left column of the attached figure.

Any graph that has a horizontal line at a period stays constant for a while.

In all cases, the function is moving right. If the function is moving right but the vertical axis remains constant, forming an horizontal line, the function is constant for that period.

Hence the graph in this problem shows that the height stays constant for a while because it has a horizontal line.

(the problem is incomplete as the graph is not given, but the explanation for a constant function is always this).

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Therefore, the (positive) margin of error for the 90% confidence interval is approximately 7.82 when the sample mean is 100, the sample standard deviation is 19, and the sample size is 16.

To find the margin of error for a 90% confidence interval, we need to use the formula:

Margin of Error = Critical Value * Standard Error

The critical value is obtained from the z-table for a 90% confidence level. For a 90% confidence level, the critical value is approximately 1.645.

The standard error can be calculated as the sample standard deviation divided by the square root of the sample size. In this case, the sample standard deviation is 19 and the sample size is 16.

Standard Error = 19 / sqrt(16) = 19 / 4 = 4.75

Now we can calculate the margin of error:

Margin of Error = 1.645 * 4.75 ≈ 7.82

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Answer:

0.1

Step-by-step explanation:

Just take 24/24 which is 1 and move the decimal one place to the left because there is an extra 0 on the denominator

The 15th term of the given geometric sequence is 9565938

From the question, we are to determine the 15th term of the given geometric sequence.

The given sequence is

2, 6, 18, ...

From the formula for the nth term of a geometric sequence, we have that

aₙ = ar⁽ⁿ⁻¹⁾

Where aₙ is the nth term

a is the first term

and r is the common ratio

In the given sequence,

a = 2

r = a₂/a₁ = 6/2 = 3

Thus,

The 15th term of the sequence is

a₁₅ = 2(3)¹⁵ ⁻ ¹

a₁₅ = 2(3)¹⁴

a₁₅ = 9565938

The 15th term is 9565938

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Answer:

4 days

Step-by-step explanation:

There are 8 pints in a gallon, so it would take 4 days to finish 1 gallon.

Natalie take 4 days to drink 1 gallon of milk.

What is Unitary method?

It is a method where we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.

First, let us make a note of the information we have. There are 5 ice-creams. 5 ice-creams cost $125.

Step 1: Let’s find the cost of 1 ice cream. In order to do that, divide the total cost of ice-creams by the total number of ice-creams. The cost of 1 ice-cream = Total cost of ice-creams/Total number of ice-creams = 125/5 = 25. Therefore, the cost of 1 ice cream is $25.

Step 2: To find the cost of 3 ice-creams, multiply the cost of 1 ice cream by the number of ice-creams. The cost of 3 ice-creams is cost of 1 ice-cream × number of ice-creams = 25 × 3 = $75. Finally, we have the cost of 3 ice-creams i.e. $75.

Given:

Natalie drinks = 2 pints milk each day.

We know

1 gallon = 8 pints

So, 1 gallon drinks take= 8/2 = 4 days

Hence, Natalie take 4 days to drink 1 gallon of milk.

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In the first month's payment for a $180,000 mortgage with a 5.5 percent, 30-year loan, a portion will go towards the principal. The exact amount can be determined using an amortization schedule.

To calculate how much of the first month's payment goes towards the principal, we can follow these steps:

Step 1: Determine the monthly interest rate: Divide the annual interest rate by 12 to obtain the monthly interest rate. In this case, 5.5 percent divided by 12 equals 0.004583 (approx).

Step 2: Calculate the monthly payment: Use a loan payment formula or a mortgage calculator to determine the monthly payment amount. For a $180,000 mortgage with a 30-year loan term and a 5.5 percent interest rate, the monthly payment would be approximately $1,019.32 (approx).

Step 3: Create an amortization schedule: An amortization schedule shows the breakdown of each monthly payment, indicating the amount allocated to interest and principal. Using the loan details, create an amortization schedule or use an online tool to generate one.

Step 4: Locate the first month on the schedule: Find the first month's entry on the amortization schedule to determine the amount allocated to principal. This amount will vary depending on the specific terms of the loan. Locate the principal portion of the payment, which represents the reduction of the loan balance.

By following these steps and referencing the amortization schedule, you can determine the exact amount of the first month's payment that goes towards the principal of the $180,000 mortgage.

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Answer:

£36

Step-by-step explanation:

1400-320=1080/45=24

so it is more than 10

10bag=10% discount

10% of 1080=108*2=216-45*4=36

Answer:

$27

Step-by-step explanation:

We know that the employees have a total of $1400

We also know that they spent $320 on a coffee machine

So, we start by subtracting 320 from 1400

1400 - 320 = 1080

So they have $1080 to spend on as many bean bags as possible

We also know they will have a 10% discount because they are able to buy more than 10

We know they can buy more than 10 because 10 would only cost $450 + discount, and they have over $1000

So, we subtract 10% from 45

45 x 0.10 = 4.5

45 - 4.5 = 40.5

So, with the discount, each bean bag costs $40.50

So, we just divide 40.5 by 1080

1080 ÷ 40.5 = 26.6667

Since you can't buy a fraction of a bean bag, they are able to buy a total of 26 bean bags

26 x 40.5 = 1053

1080 - 1053 = 27

They have $27 left over

Answer:

No, you would graph the y-intercept, you do not graph the m-value (slope). The slope value is the rate that the y-value increases per unit of x. This is how you graph your line from the y-intercept

Answer:

No you are incorrect. The correct answer is (y - intercept) b = -4

Step-by-step explanation:

You need to plot the y - intercept first so that you can create the line using the slope starting from the y - intercept. You can't plot the line unless you first plot a point on the line which would be the y - intercept or -4 THEN from there you use the slope to create the line.

The ∆ABC is an isosceles triangle and have the base angles m∠A and m∠C equal to 51° and the angle m∠B is equal to 78°.

An isosceles triangle have the measure of its base angles to be equal, and the sum of the interior angles sum up to 180°.

Given that sides AB ≅ BC, then the triangle ∆ABC has two sides with similar length and base angles so;

angles m∠A and m∠C are the base angles are both equal to 51°

m∠B = 180° - (51 + 51)° {sum of interior angles of a triangle}

m∠B = 180° - 102°

m∠B = 78°

Therefore, the isosceles triangle ∆ABC have the base angles m∠A and m∠C equal to 51° and the angle m∠B is equal to 78°.

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( - 5 / 7 ) / ( 2 / 4 )

= ( - 5 / 7 ) * ( 4 / 2 ) = - 10 / 7

Answer:

-2.5

Step-by-step explanation:

I am good at math

The relation between mode, mean and median is:

mode=3median-2mean

Now, to find mean:

2mean=3median-mode

mean=7/2 = 3.5

Let we wish to evaluate the mean  μ of a population. In real practice we would typically take just one sample. Imagine still that we take sample after sample, all of the same size n, and compute the sample mean x¯ every time.

The sample mean x is a random variable: it differs from sample to sample in a way that cannot be predicted with sureness. We will write X¯ when the sample mean is idea of as a random variable and write x for the values that it takes.

The random variable X¯ has a mean, denoted  μX¯, and a standard deviation, denoted  σX¯. Here is an example with such a small population and small sample size that we can indeed write down every single sample.

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