A car rental company charge $50 a day and 20 cents per mile for renting a car. Let y be the total rental charge (in dollar) for a car for one day and x be the miles driven. The equation for the relationship between x and y is y = 50 + 20x How much will a person pay who rents a car for one day and drives it 100miles​

The simplified form of (5m² - 3)² is 25m⁴ - 30m² + 9.

Given is an expression (5m² - 3)², we need to simplify the expression,

To multiply the expression (5m² - 3)², we can use the formula for squaring a binomial:

(a - b)² = a² - 2ab + b²

In this case, a = 5m² and b = 3.

Substituting these values into the formula, we get:

(5m² - 3)² = (5m²)² - 2(5m²)(3) + (3)²

= 25m⁴ - 30m² + 9

Therefore, the simplified form of (5m² - 3)² is 25m⁴ - 30m² + 9.

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The percentage improvement in reliability when test length is doubled is 15%

R(n) = 0.25n / (0.75 + 0.25n)

substitute n = 1 into the equation :

R(n) = 0.25n / (0.75 + 0.25n)

R(1) = 0.25(1) / (0.75 + 0.25(1))

R(1) = 0.25 / 1

R(1) = 0.25

when test length is doubled , n = 2

substitute n = 1 into the equation :

R(n) = 0.25n / (0.75 + 0.25n)

R(2) = 0.25(2) / (0.75 + 0.25(2))

R(2) = 0.5 / 1.25

R(2) = 0.4

Percentage improvement can be calculated thus ;

R(2)-R(1)/R(1) × 100%

(0.4-0.25)/0.25 × 100%

0.15 × 100%

=15%

Therefore, percentage improvement in reliability is 15%

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1. Create a horizontal axis labeled "Time Spent on Homework Problem (Minutes)."

2. Choose an appropriate scale for the axis, such as labeling every other unit of time from 0 to 18.

3. Plot a dot for each student's data point along the horizontal axis.

4. Arrange the dots in order from smallest to largest time spent on the problem.

5. Title the dot plot to reflect the data set being represented, such as "Math Homework Problem Time Spent: Mean 9 Minutes, MAD 7 Minutes."

6. Include a legend or key if needed to clarify the meaning of the dot plot.(The dot plot is attached below)

To draw a dot plot representing a data set where the mean amount of time spent on one math homework problem is 9 minutes and the MAD is 7 minutes for a group of ten students, we can follow these steps:

The resulting dot plot may show a spread of data between 2 and 16 minutes, with more dots around the center or mean of 9 minutes and fewer dots at the tails. The MAD of 7 minutes suggests a relatively high degree of variability in the data, with some students spending significantly less or significantly more time on the math homework problem. The dot plot can help to visualize these differences and identify any potential outliers in the data.

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The surface area of the sphere is 98 yd².

To find the surface area of a sphere, we can use the formula:

Surface Area = 4πr²

Given that the radius, r, of the sphere is 7/3.14 yd, we can substitute this value into the formula:

Surface Area = 4 x 3.14 x (7/3.14)²

= 4 x 3.14 x 49/9.86

= 4 x 49/2

= 98 yd²

Therefore, the surface area of the sphere is 98 yd².

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Answer:

The complex number represented by the polar coordinates (4, -π/4) is 4(cos(-π/4) + i*sin(-π/4)).

Answer:f(x) = (x-10)^2-49

f(x) = (x-10+7)(x-10-7)

f(x) = (x-3)(x-17)

The zeros of the function are 3 and 17.

Step-by-step explanation:

The difference between the two polynomials is 5m^(2)n^(5) - 3m^(2)n^(3) + 5mn + m + n.

To subtract the second polynomial from the first polynomial, we need to perform term-wise subtraction. Let's break down the process step by step:

The first polynomial is: 11m^(2)n^(5) - 3m^(2)n^(3) + 5mn - n.

The second polynomial is: -6m^(2)n^(5) + 3m^(2)n^(5) + m + 2n.

To subtract the second polynomial from the first, we need to change the signs of all terms in the second polynomial and then combine like terms.

First, let's change the signs of the terms in the second polynomial:

-(-6m^(2)n^(5) + 3m^(2)n^(5) + m + 2n) = 6m^(2)n^(5) - 3m^(2)n^(5) - m - 2n.

Now, we can combine like terms by adding or subtracting coefficients of similar monomials:

(11m^(2)n^(5) - 3m^(2)n^(3) + 5mn - n) - (6m^(2)n^(5) - 3m^(2)n^(5) - m - 2n)

= 11m^(2)n^(5) - 3m^(2)n^(3) + 5mn - n - 6m^(2)n^(5) + 3m^(2)n^(5) + m + 2n

= (11m^(2)n^(5) - 6m^(2)n^(5)) + (-3m^(2)n^(3) + 3m^(2)n^(5)) + (5mn + m) + (-n + 2n)

= 5m^(2)n^(5) - 3m^(2)n^(3) + 5mn + m + n.

Therefore, the difference between the two polynomials is 5m^(2)n^(5) - 3m^(2)n^(3) + 5mn + m + n.

In summary, to find the difference, we changed the signs of all terms in the second polynomial and then combined like terms with the first polynomial. The resulting polynomial is the difference between the two original polynomials.

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Answer:

17.5

Step-by-step explanation:

You can find the mean of a data set by adding all numbers in the data set together and dividing by the amount of numbers in the given data set.

In this case, your data set is:

15 , 16 , 17 , 23 , 11 , 19 , 20 , 15 , 18 , 22 , 15 , 19   (12 numbers).

Firstly, add all the numbers together: [tex]15 + 16 + 17 + 23 + 11 + 19 + 20 + 15 + 18 + 22 + 15 + 19 = 210[/tex]

Next, divide 210 (total sum) with the amount of terms in total (12):

[tex]\frac{(210)}{(12)} = 17.5[/tex]

17.5 is already in the tenth digit place value, and so you do not need to round.

17.5 is your answer.

~

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Answer:

Step-by-step explanation:

To solve the expression 4(-2)² + 8(-2) + 3(-2) + 6, we need to follow the order of operations, which is also known as PEMDAS (Parentheses, Exponents, Multiplication and Division - from left to right, Addition and Subtraction - from left to right).

First, we will simplify any calculations within parentheses:

4(-2)² + 8(-2) + 3(-2) + 6

(-2)² is equal to (-2) * (-2), which is 4:

4 * 4 + 8(-2) + 3(-2) + 6

Next, we perform the multiplication:

4 * 4 = 16

Now, we have:

16 + 8(-2) + 3(-2) + 6

Next, we continue with the multiplication:

8(-2) = -16

3(-2) = -6

Now, we have:

16 + (-16) + (-6) + 6

Finally, we simplify the addition and subtraction from left to right:

16 + (-16) = 0

0 + (-6) = -6

-6 + 6 = 0

Therefore, the expression 4(-2)² + 8(-2) + 3(-2) + 6 simplifies to 0.

In the given expression, "2" represents that each new year the profits double with respect to the previous year. So the correct answer is D) that each new year the profits double with respect to the previous year.

In the given expression, the variable "t" represents the number of years that have passed since the initial investment was made. The expression 1,000,000 × 2t calculates the profit obtained after "t" years.

Therefore, the correct answer is D) that each new year the profits double with respect to the previous year.

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The profit obtained after t years of

have made an initial investment of

$1,000,000 is given by the expression:

1,000,000 × 2t

What does the number 2 represent in the

previous expression?

A) the profits obtained in the second year

B) the profits obtained in the last year

C) that every new year the profits are cut in half

D) that each new year the profits double with respect to the previous year

Mis disculpas por la respuesta anterior, cometí un error en la explicación. La respuesta correcta es la opción D. La expresión 1.000.000 × 2t indica que cada nuevo año las ganancias se duplican con respecto al año anterior.

                                                                                     En la expresión, el número 2 indica que las ganancias se duplican cada año con respecto al año anterior. La expresión 1.000.000 × 2t significa que la inversión inicial de un millón de dólares se multiplica por 2 elevado a la potencia de t, donde t es el número de años que han pasado.Cuando t=1, se refiere al primer año después de la inversión, y la ganancia sería 1.000.000 dividido por 2=1, es decir, dos millones. Esto significa que las ganancias del segundo año (opción A) serían de 2.000.000 de dólares.En general, las ganancias del año anterior se duplican cada año subsiguiente. Por lo tanto, la D es la opción correcta porque significa que las ganancias se duplican cada año con respecto al año anterior.

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The factored form of the expression 12a - b is simply 12a - b.

We have,

The concept used in the expression 12a - b is that of combining like terms. When we have an algebraic expression like this, the goal is typically to simplify or rewrite it in a more concise form.

In this case, 12a and -b are two terms in the expression.

The concept of combining like terms allows us to combine these terms together if they have the same variable(s) raised to the same power(s).

The expression 12a - b cannot be factored further using simple algebraic techniques.

Factoring typically involves breaking down an expression into its constituent factors, such as common factors or binomial factors.

However, in the case of 12a - b,

There are no common factors or binomial factors that can be extracted.

Therefore,

The factored form of the expression 12a - b is simply 12a - b.

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Answer:

$60

Step-by-step explanation:

Based on the regression equation, the best prediction for the price of a 70-pound container of detergent can be found by substituting x = 70 into the equation:

y^ = 0.86x + 0.52

y^ = 0.86(70) + 0.52

y^ = 60.2 + 0.52

y^ ≈ $60.72

Therefore, the best prediction for the price of a 70-pound container of detergent is approximately $60.72. However, since we are dealing with prices, it is reasonable to round this value to the nearest dollar, which would be $61. But since none of the answers are 61 it would be $60.

The rate at which the surface area of the sphere is increasing is 16π cm^2/s.(option-c)

To find the rate at which the area of a sphere increases when its radius is increasing at a given rate, we can use the formula for the surface area of a sphere, which is A =[tex]4πr^2[/tex], where r is the radius of the sphere and A is its surface area. We can then differentiate this with respect to time t to find the rate of change of area with respect to time, which is given as dA/dt.

Given that the radius of the sphere increases at the rate of 0.4 cm/s, we can find the rate of change of area as follows:

- Differentiate the surface area formula with respect to time t:

dA/dt = d/dt [tex](4πr^2)[/tex]

- Use the chain rule to differentiate[tex]r^2[/tex]with respect to time t:

d/dt (r^2) = 2r (dr/dt)

- Substitute the value of dr/dt given as 0.4 cm/s, and the radius value as 5 cm:

dA/dt = 4π(5)^2 (2 × 0.4)

- Simplify the expression to get the rate of change of area with respect to time:

dA/dt = 16π [tex]cm^2/s[/tex]

(option-c)

Answer:

Step-by-step explanation:

Answer:

x = 9 and y = 4

Step-by-step explanation:

-2x + 7y = 10    (call this equation '1')

x - 3y = -3      (call this '2')

multiply '2' by 2:

2x - 6y = -6  (call this '3')

add '1' and '3':

(-2x + 7y = 10)  +  (2x - 6y = -6)

0x + y = 4

y = 4

sub that back into '1':

-2x + 7y = 10

-2x + 7(4) = 10

-2x + 28 = 10

-2x = 10 - 28 = -18

x = -18/-2 = 9

sub both y = 4 and x =9 into '2' to check if everything adds up:

x - 3y = -3

9 - 3(4) = 9 - 12 = -3

so x = 9 and y = 4

Answer:

5.25 feet tall

Step-by-step explanation:

Doug's height / Doug's shadow = Statue's height / Statue's shadow

x / 3.5 = 12 / 8

Cross-multiplying:

8x = 3.5 * 12

8x = 42

Dividing both sides by 8:

x = 42 / 8

x ≈ 5.25

Answer:

d)  171.8°

e)  72

f)  60°

Step-by-step explanation:

The Polygon Interior Angle Theorem states that measure of the interior angle of a regular polygon with n sides is [(n - 2) · 180°] / 2.

The number of sides of a 44-gon is n = 44. Therefore, the measure of its interior angle is:

[tex]\begin{aligned}\textsf{Interior angles of a 44-agon}&=\dfrac{(44-2) \cdot 180^{\circ}}{44}\\\\&=\dfrac{42\cdot 180^{\circ}}{44}\\\\&=\dfrac{7560^{\circ}}{44}\\\\&=171.8^{\circ}\;\sf(nearest\;tenth)\end{aligned}[/tex]

Therefore, the interior angle of a 44-gon is 171.8°.

[tex]\hrulefill[/tex]

The Polygon Interior Angle Theorem states that measure of the interior angle of a regular polygon with n sides is [(n - 2) · 180°] / 2.

Given the interior angle of a regular polygon is 175°, then:

[tex]\begin{aligned} \textsf{Interior angle}&=175^{\circ}\\\\\implies \dfrac{(n-2) \cdot 180^{\circ}}{n}&=175^{\circ}\\\\(n-2)\cdot 180^{\circ}&=175^{\circ}n\\\\180^{\circ}n-360^{\circ}&=175^{\circ}n\\\\5^{\circ}n&=360^{\circ}\\\\n&=72\end{aligned}[/tex]

Therefore, the number of sides of the regular polygon is 72.

[tex]\hrulefill[/tex]

According the the Polygon Exterior Angles Theorem, the sum of the measures of the exterior angles of a polygon is 360°.

Therefore, to find exterior angle of a regular hexagon, divide 360° by the number of sides:

[tex]\begin{aligned}\sf Exterior\;angle&=\dfrac{360^{\circ}}{\sf Number\;of\;sides}\\\\&=\dfrac{360^{\circ}}{6}\\\\&=60^{\circ}\end{aligned}[/tex]

Therefore, the exterior angle of a regular hexagon is 60°.

Answer:

4. a. 171.818°

b. 72 sides

c. 60°

Step-by-step explanation:

d. The interior angle of a regular polygon with n sides can be calculated using the formula:

[tex]\bold{Interior Angle =\frac{ (n-2) * 180\°}{n}}[/tex]

For a regular 44-gon, the interior angle would be:

[tex]\bold{Interior Angle =\frac{ (44-2) * 180\°}{44}=171.818^o}[/tex]

[tex]\hrulefill[/tex]

e. The number of sides in a regular polygon with an interior angle of 175° can be found using the formula:

[tex]\bold{n = \frac{360\° }{180\° - Interior \:Angle}}[/tex]

For an interior angle of 175°, the number of sides would be:

substituting Value,

[tex]\bold{n =\frac{ 360\° }{ 180\° - 175\°} = \frac{360\° }{ 5\° }= 72 \:sides}[/tex]

[tex]\hrulefill[/tex]

f.

The sum of the exterior angles of any polygon is always 360°.

Since a regular hexagon has six sides,
n=6

exterior angle would be [tex]\bold{\frac{360\° }{ n}}[/tex]

substituting value,

exterior angle=[tex]\bold{\frac{360\° }{ 6}=60\°}[/tex]

[tex]\hrulefill[/tex]

Answer:

c

Step-by-step explanation:

we know he spends 10$ on shirts but not how much he spends on shorts. Since we know he has $50 to spend, we can buy shorts up to the $50 limit including $50. The only inequality that includes $50 is c

C, 10+ 4.5x ≤ 50

Happy to help, have a great day! :)

Answer:

Step-by-step explanation:

Given midsegment EF = (4x+6) and base segment BC = (9x+4) of a trapezoid with base AD = 3, you want the value of x and the lengths of the two segments EF and BC.

The midsegment parallel to the base segment is the average of the lengths of the parallel bases.

  4x +6 = 1/2((9x +4) +3))

  8x +12 = 9x +7 . . . . . . . . . multiply by 2 and simplify

  5 = x . . . . . . . . . . . . subtract 8x+7

Using this value of x, we find the lengths of the segments to be ...

  EF = 4·5 +6 = 26

  BC = 9·5 +4 = 49

  (BC +AD)/2 = EF

  (49 +3)/2 = 52/2 = 26 . . . . as required

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The coordinates of midpoint P are P(-1/2, 3/2) and coordinates of midpoint Q are Q(-3/2, -4).

To find the coordinates of the midpoints P and Q of sides AB and AC, we can use the midpoint formula.

The midpoint formula states that the coordinates of the midpoint of a line segment between two points (x1, y1) and (x2, y2) are given by:

Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)

Using this formula, we can find the coordinates of P and Q as follows:

Coordinates of midpoint P:

P = ((2 + (-3)) / 2, (-1 + 4) / 2)

= (-1/2, 3/2)

Therefore, the coordinates of midpoint P are P(-1/2, 3/2).

Coordinates of midpoint Q:

Q = ((2 + (-5)) / 2, (-1 + (-7)) / 2)

= (-3/2, -4)

Therefore, the coordinates of midpoint Q are Q(-3/2, -4).

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Let the points A(2,-1), B(-3,4), and C(-5,-7) be the vertices of triangle A B C. Let P and Q be the midpoints of the sides AB and AC respectively. Find the coordinates of P and Q. (2 marks)

The cash cycle, also known as the operating cycle or cash conversion cycle, is a financial metric that measures the time it takes for a company to convert its investments in inventory and other resources into cash flow from sales. It provides insight into the efficiency of a company's working capital management.

The cash cycle can be calculated using the following formula:

Cash Cycle = Inventory Conversion Period + Receivables Conversion Period - Payables Conversion Period

1. Inventory Conversion Period (ICP):

ICP measures the average number of days it takes for the company to convert its raw materials into finished goods. It is calculated as:

ICP = (Average Inventory / Cost of Goods Sold) x Number of Days in a Year

Average Inventory = (Opening Inventory + Closing Inventory) / 2

Cost of Goods Sold = Total Sales - Closing Inventory

2. Receivables Conversion Period (RCP):

RCP measures the average number of days it takes for the company to collect payment from its customers. It is calculated as:

RCP = (Average Receivables / Total Sales) x Number of Days in a Year

Average Receivables = (Opening Receivables + Closing Receivables) / 2

Opening Receivables = Total Sales x Percentage of Sales on Credit

Closing Receivables = Total Sales x Percentage of Sales on Credit - Collections

3. Payables Conversion Period (PCP):

PCP measures the average number of days it takes for the company to pay its suppliers. It is calculated as:

PCP = (Average Payables / Total Purchases) x Number of Days in a Year

Average Payables = (Opening Payables + Closing Payables) / 2

Opening Payables = Total Purchases x Percentage of Purchases on Credit

Closing Payables = Total Purchases x Percentage of Purchases on Credit - Payments

Now, let's calculate the cash cycle using the provided information:

Given data:

Opening balances:

Raw material: ₹1,00,000

WIP: ₹45,000

Finished goods: ₹1,35,000

Debtors: ₹6,00,000

Creditors: ₹8,60,000

Closing balances:

Raw material: ₹2,00,000

WIP: ₹65,000

Finished goods: ₹1,25,000

Debtors: ₹5,45,000

Creditors: ₹9,75,000

Costs incurred during the year:

Manufacturing costs: ₹11,60,000

Excise duty: ₹18,80,000

Selling and distribution expenses: ₹6,20,000

Admin. overheads: ₹2,00,000

Total sales: ₹2,01,96,800

Total purchases: ₹1,46,00,000

Percentage of sales on credit: 40%

Percentage of purchases on credit: 70%

1. Calculate the Inventory Conversion Period (ICP):

Average Inventory = (Opening Inventory + Closing Inventory) / 2

Opening Inventory = Raw Material + WIP + Finished Goods

Closing Inventory = Raw Material + WIP + Finished Goods

Opening Inventory = ₹1,00,000 + ₹45,000 + ₹1,35,000 = ₹2,80,000

Closing Inventory = ₹2,00,000 + ₹65,000 + ₹1,25,000 = ₹3,90,000

Average Inventory = (₹2,80,000 + ₹3,90,000) / 2 = ₹3,35,000

Cost of Goods Sold = Total Sales - Closing Inventory

Cost of Goods Sold = ₹2,01,96,800 -

The shop initially has 0.884 jars of jam

The probability that both customers chose strawberry jam, is 0.25.

a) Let's assume the number of jars of strawberry jam is 3x and the number of jars of raspberry jam is x.

So, the total number of jars of jam in the shop is 3x + x = 4x.

According to the given information, the probability that both customers select strawberry jam is 11/20.

So, the probability of the first customer selecting a jar of strawberry jam = (3x/4x) = 3/4,

and the probability of the second customer

=  ((3x-1)/(4x-1)).

Now, (3/4) ((3x-1)/(4x-1)) = 11/20

(3/4) ((3x-1)/(4x-1)) = 11/20

20(3/4) ((3x-1)/(4x-1)) = 11

15 (3x-1) = 44  (4x-1)

45x - 15 = 176x - 44

176x - 45x = 44 - 15

131x = 29

x ≈ 29/131

Therefore, the value of x is 0.221

To find the initial number of jars of jam in the shop, we can substitute this value of x into the equation:

4x =  0.884

b) The probability of the first customer selecting strawberry jam is

= (3x)/(4x)

= 3/4.

Therefore, the probability that both customers chose strawberry jam is:

= (3/4) x ((3x-1)/(4x-1))

= (3/4)  ((3 x 0.221 - 1)/(4 x 0.221 - 1))

= (3/4) ((3 x 0.221 - 1)/(4 x 0.221 - 1))

≈ 0.25

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[tex]-16=k\cdot2^2\\4k=-16\\k=-4[/tex]

Answer:

швлалалаось.чллслслслсб вщлалс

Hello!

it's a quadratic equation

x = (-b ± √(b² - 4ac))/2a

= (-(-5) ± √((-5)² - 4*1*(-7)))/(2*1)

= (5 ± √(25 + 28))/2

= (5 ± √53)/2

Hello !

Answer:

[tex]\large \boxed{\sf x= \dfrac{5\pm\pl\sqrt{53}}{2} }[/tex]

Step-by-step explanation:

This equation is a quadratic equation in the form ax²+bx+c=0

The solution of this equation is given by the quadratic formula :

[tex]\sf x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Here we have :

Let's replace a, b and c with their values in the quadratic formula :

[tex]\sf x=\dfrac{-(-5)\pm\sqrt{(-5)^2-4\times1\times(-7)}}{2\times 1} \\\sf x= \dfrac{5\pm\pl\sqrt{25+28}}{2} \\\boxed{\sf x= \dfrac{5\pm\pl\sqrt{53}}{2} }[/tex]

Have a nice day ;)

The probability that either event A or B will occur is 11/17.

We have,

The Addition Rule for Probability:

P(A U B) = P(A) + P(B) - P(A ∩ B),

where P(A U B) represents the probability of the union of events A and B, P(A) represents the probability of event A, P(B) represents the probability of event B, and P(A ∩ B) represents the probability of the intersection of events A and B.

Now,

P(A) = 9/17

P(B) = 2/17

There is no intersection of Q and B so,

P(A ∩ B) = 0

Now,

P(A U B) = P(A) + P(B) - P(A ∩ B),

Substituting the values.

P(A U B) = The probability that either event A or B will occur.

So,

P(A U B)

= 9/17 + 2/17 - 0

= 11/17

Thus,

The probability that either event A or B will occur is 11/17.

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The confidence interval is 0.559 < p < 0.641 and expected value is 0.600

To construct a confidence interval for the true population proportion, we can use the formula:

p ± Z * √((p × (1 - p)) / n)

Where:

p = sample proportion (336/560)

Z = critical value for the desired confidence level

95% confidence = Z-value of approximately 1.96

n = 560

Let's calculate the confidence interval:

p = 336/560 ≈ 0.600

Z ≈ 1.96 (for a 95% confidence level)

n = 560

Plugging these values into the formula:

p ± Z × √((p × (1 - p)) / n)

0.600 ± 1.96 × √((0.600 × (1 - 0.600)) / 560)

0.600 ± 1.96 × √((0.240) / 560)

0.600 ± 1.96 × √(0.0004285714)

0.600 ± 1.96 × 0.020709611

0.600 ± 0.040564459

The confidence interval is:

0.559 < p < 0.641

Therefore, the 95% confidence interval for the true population proportion of adults with children is 0.559 < p < 0.641.

For proportions, the expected value is simply the sample proportion, which is approximately 0.600.

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We can see that the number multiplied by t is 50. Therefore, the simplified expression is -6t^2 + 50t + 56, and the number multiplied by t is 50.

To simplify the given expression (8t - 6t^2) + 14(3t + 4), we first need to apply the distributive property by multiplying 14 with both terms inside the parentheses. This gives us:
8t - 6t^2 + 42t + 56
Now, we can combine like terms by adding the coefficients of the t and t^2 terms. The t^2 term has a coefficient of -6, and there are no other t^2 terms in the expression, so we can just bring it down as it is. The t term has a coefficient of 8 + 42 = 50, so we can simplify the expression further as:
-6t^2 + 50t + 56
From this expression, we can see that the number multiplied by t is 50. Therefore, the simplified expression is -6t^2 + 50t + 56, and the number multiplied by t is 50.

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