Use the remainder theorem to find P(2) for P(x)=-x^3+3x^2+6.
Specifically, give the quotient and the remainder for the associated division and the value of P(2).

Answer:

shaded area ≈ 69.53 cm²

Step-by-step explanation:

the shaded area (A) is calculated as

A = area of square - area of circle

area of square = 18² = 324

area of circle = πr² ( r is the radius )

the diameter of the circle = 18 , so r = 18 ÷ 2 = 9

area of circle = π × 9² = 81π

then

A = 324 - 81π ≈ 69.53 cm² ( to 2 decimal places )

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

<95141404393>

Answer:

Let's denote the original cost of the season train ticket as "x".

According to the given information, a reduction of $33.10 corresponds to a 10% reduction in the original cost. We can set up the following equation to represent this:

10% of x = $33.10

To solve for x, we need to convert 10% to decimal form, which is 0.10. We can rewrite the equation as:

0.10 * x = $33.10

Simplifying the equation, we have:

0.10x = $33.10

To isolate x, we divide both sides of the equation by 0.10:

x = $33.10 / 0.10

x = $331.00

Therefore, the original cost of the season train ticket is $331.00.

Step-by-step explanation:

Answer:

[tex]a_n=3n-16[/tex]

Step-by-step explanation:

[tex]a_n=a_1+(n-1)d\\\\a_8=a_1+(8-1)d\rightarrow 8=a_1+7d\\a_{20}=a_1+(20-1)d\rightarrow 44=a_1+19d[/tex]

[tex]-36=-12d\\3=d[/tex]

[tex]8=a_1+7(3)\\8=a_1+21\\-13=a_1[/tex]

[tex]a_n=-13+(n-1)(3)\\a_n=-13+3n-3\\a_n=3n-16[/tex]

[tex]|\Omega|=19+28+21+29=97\\|A|=19+28+21=68\\\\P(A)=\dfrac{68}{97}[/tex]

The 95% confidence interval for the total percentage of national park visitors who support supporting endangered species is approximately 33.3% to 52.7%.

To calculate the 95% confidence interval for the percentage of national park visitors who support supporting endangered species, we can use the formula:

Confidence Interval = Sample proportion ± (Critical value * Standard error)

Given that 43% of a sample of 100 visitors believe that additional funds should be used to preserve endangered species, the sample proportion is 0.43.

To calculate the standard error, we use the formula:

Standard Error = sqrt((p * (1 - p)) / n)

where p is the sample proportion and n is the sample size. In this case, p = 0.43 and n = 100.

Standard Error = sqrt((0.43 * (1 - 0.43)) / 100) ≈ 0.0495

The critical value for a 95% confidence interval can be obtained from a standard normal distribution table. For a 95% confidence level, the critical value is approximately 1.96.

Now we can calculate the confidence interval:

Confidence Interval = 0.43 ± (1.96 * 0.0495)

Confidence Interval = 0.43 ± 0.097

The lower bound of the confidence interval is 0.43 - 0.097 = 0.333

The upper bound of the confidence interval is 0.43 + 0.097 = 0.527

Therefore, the 95% confidence interval for the total percentage of national park visitors who support supporting endangered species is approximately 33.3% to 52.7%.

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The volume of the given cylinder is 2543 cubic yards.

For the given cylinder,

Height of the cylinder  = 10 yard

Radius of cylinder = 9 yard yard

Then we have to calculate the volume of this cylinder.

Since we know that,

Volume of the cylinder  = πr²h

Where,

r represents radius of cylinder = 9 yard

h represents height of cylinder = 10 yard

Noe therefore,

Volume of the cylinder = π(9)²(10)

                                       = 3.14x 81 x 10

                                       = 2543 cubic yards

Thus,

⇒ Volume = 2543 cubic yards.

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Unless we restrict its domain, a quadratic function doesn't have the inverse.

Answer: 180

Step-by-step explanation:

Use the order of operations: PEMDAS

Parenthesis

Exponents

Multiplication/Division

Addition/Subtraction

3² x (-2)³ x 5               >There is nothing to simplify within parenthesis

                                   >Exponents are next in Order of Operations

(3)(3) x (-2)(-2) x 5       >This is the exponents expanded

9 x 4 x 5                      >Multiply from left to right

36 x 5

180

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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Answer: The rental cost of each movie is $2 and each video game is approximately $5.5

Step-by-step explanation:

Let's assume the rental cost per movie is "m" and the rental cost per video game is "v". We can set up a system of linear equations based on the given information.

From the first month:

5m + 2v = 21 ----(1)

From the second month:

3m + 8v = 50 ----(2)

To solve the system of equations:

5m + 2v = 21 ----(1)

3m + 8v = 50 ----(2)

We can multiply equation (1) by 4 to make the coefficients of "m" the same:

4(5m + 2v) = 4(21)

20m + 8v = 84 ----(3)

Now, subtract equation (2) from equation (3):

(20m + 8v) - (3m + 8v) = 84 - 50

20m - 3m + 8v - 8v = 34

17m = 34

Divide both sides of the equation by 17:

m = 34 / 17

m = 2

Now that we have the value of "m," we can substitute it back into either equation (1) or (2) to solve for "v." Let's use equation (1):

5(2) + 2v = 21

10 + 2v = 21

2v = 21 - 10

2v = 11

v = 11 / 2

v = 5.5

Therefore, the solution to the system of equations is:

m = 2 and v = 5.5

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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The exact value of expression sin 9π/4 is,

⇒ sin 9π/4 = 1 / √2

We have to given that;

Expression to find exact value is,

⇒ sin 9π/4

Now, WE can change it into degree as,

⇒ 9π/4

⇒ 9 × 180 / 4

⇒ 9 × 45

⇒ 405 degree

Hence, We get;

⇒ sin 9π/4

⇒ sin 405°

⇒ sin (360 + 45°)

⇒ sin 45°

⇒ 1 / √2

Thus, The exact value of expression sin 9π/4 is,

⇒ sin 9π/4 = 1 / √2

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Answer:

[tex]\overline{LP}=77[/tex]

Step-by-step explanation:

Given [tex]\Delta LMQ\sim\Delta LNP[/tex], then [tex]\overline{LN}=\overline{LM}+\overline{MN}=8+14=22[/tex]. This will help us find [tex]\overline{LQ}[/tex] since we know the length of [tex]\overline{QP}[/tex]:

[tex]\displaystyle \frac{\overline{LM}}{\overline{LM}+\overline{MN}}=\frac{\overline{LQ}}{\overline{LQ}+\overline{QP}}\\\\\frac{8}{8+14}=\frac{\overline{LQ}}{\overline{LQ}+49}\\\\\frac{8}{22}=\frac{\overline{LQ}}{\overline{LQ}+49}\\\\8(\overline{LQ}+49)=22\overline{LQ}\\\\8\overline{LQ}+392=22\overline{LQ}\\\\392=14\overline{LQ}\\\\28=\overline{LQ}[/tex]

Therefore:

[tex]\overline{LP}=\overline{LQ}+\overline{QP}=28+49=77[/tex]

The rate of growth of the plant is 2 centimeters per week.

Calculate the change in height divided by the change in time (weeks) to find the plant's growth rate.

To calculate the rate of growth of the plant, we need to determine the change in height per week.

Given:

Initial height = 4 cm

Final height = 12 cm

Weeks = 4

To find the rate of growth, we can use the formula:

Rate of growth = (Final height - Initial height) / Weeks

Substituting the given values into the formula:

Rate of growth = (12 cm - 4 cm) / 4 weeks

Rate of growth = 8 cm / 4 weeks

Rate of growth = 2 cm/week

Therefore, the rate of growth of the plant is 2 centimeters per week.

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Answer:

We can get 10 cheeseburgers.

Step-by-step explanation:

To find out how many cheeseburgers we can buy if:

we can divide the money we have by the cost of each cheeseburger.

To make the division simpler, we can multiply both numbers by 10.

$25 / $2.50 = $250 / $25

From this form of the division, we can clearly see that the amount of money we have is 10 times the cost of one burger because it is 25 with a 0 on the end, which is the result of multiplying by 10.

Therefore, we can get 10 cheeseburgers.

Answer:

швлалалаось.чллслслслсб вщлалс

The tangent from the external point are equal, so the x value is 3 units.

7) The measure of the arc XW is 180-105=75

8) The measure of the arc VWY is 105+75+85 = 265

9) We know that, tangent from the external point are equal

In circle C, AB=AD

26=8x+2

8x=24

x=24/8

x=3 units

10) 9x-3=7x+5

9x-7x=5+3

2x=8

x=8/2

x=4

Therefore, the tangent from the external point are equal, so the x value is 3 units.

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The value of x in the expression is 66/114.

Let's begin by addressing the issue in detail:

Emma runs 12 km, hence the time it takes her to complete that distance is 12/x hours.

Emma cycles 26 kilometers at a speed that is 10 kilometers per hour faster than she runs.

Her cycling pace is therefore (x + 10) km/hr. Her cycle distance is 26 kilometers, which can be calculated as 26/(x + 10) hours.

Emma's total time spent cycling and running is 22 hours and 48 minutes. By dividing 48 minutes by 60, we can translate it to hours: 48/60 = 0.8 hours.

We can now formulate an equation to express the entire amount of time spent:

12/x + 26/(x + 10) = 22.8

To get rid of the denominators and solve this equation, multiply both sides by x(x + 10).

12(x + 10) + 26x = 22.8x(x + 10)

To make the calculation easier:

12x + 120 + 26x = 22.8x² + 228x

Combining comparable phrases

38x + 120 = 22.8x² + 228x

Changing the equation's order:

22.8x² + 228x - 38x - 120 = 0

22.8x² + 190x - 120 = 0

By dividing the equation by 0.4, the coefficients are made simpler:

57x² + 475x - 300 = 0

Solving the equation by x = (-b ± √(b² - 4ac)) / (2a),

x = (-475 ± √(475² - 4 * 57 * -300)) / (2 * 57)

Simplifying further:

x = (-475 ± √(225625 + 68400)) / 114

x = (-475 ± √293025) / 114

x = (-475 ± 541) / 114

Now, we can calculate the two possible solutions:

x₁ = (-475 + 541) / 114

x₁ = 66 / 114

x₁ ≈ 0.579

x₂ = (-475 - 541) / 114

x₂ = -1016 / 114

x₂ ≈ -8.912

Take x = 66/114

Hence the value of x in the expression is 66/114.

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Answer:

  see below

Step-by-step explanation:

You want the piecewise function that gives straight line segments between domain boundary points (-8, 5), (-2, -9), (1, -2), (8, 4).

The two-point equation for the slope of a line is ...

  m = (y2 -y1)/(x2 -x1)

For the first pair of points, the slope is ...

  m = (-9 -5)/(-2 -(-8)) = -14/6 = -7/3

The attached calculator image shows the computation of slope for the other two segments. Those slopes are 7/3 and 6/7.

The slope-intercept form of the equation for a line can be rearranged to give the y-intercept:

  y = mx + b

  b = y - mx

In the attached, we used the (x1, y1) point for each segment. For the first segment, the y-intercept is ...

  b = 5 -(-7/3)(-8) = -41/3

The other two y-intercepts are computed to be -13/3 and -20/7.

The piecewise function that models the given data is ...

  [tex]\boxed{y=\begin{cases}-\dfrac{7}{3}x-\dfrac{41}{3}\quad&-8\le x\le-2\\\\\dfrac{7}{3}x-\dfrac{13}{3}\quad&-2 < x\le1\\\\\dfrac{6}{7}x-\dfrac{20}{7}\quad&1 < x\le8\end{cases}}[/tex]

__

Additional comment

There is nothing in this problem statement that requires the function be continuous. However, we have made it so this function is continuous in the region where it is defined.

The same repetitive computations are handled nicely by a spreadsheet.

<95141404393>

A) Area of figure is,

⇒ A = 3π (3 + √73) + 4.5π

B) Area of figure is,

A = 89 feet²

We can simplify as;

A) In figure A,

It is make with one cone and one semicircle.

Hence, Area of cone is,

A = πr (r + √h² + r²)

A = π × 3 (3 + √8² + 3²)

A = 3π (3 + √64 + 9

A = 3π (3 + √73)

And, Area of semicircle is,

⇒ A = 1/2 (π × 3²)

⇒ A = 4.5π

Hence, Total area is,

⇒ A = 3π (3 + √73) + 4.5π

B) Figure B is make with a trapezoid and triangle.

Area of trapezoid is,

A = 1/2 (7 + 13) × 5

A = 20 × 5 / 2

A = 50 feet²

And, Area of triangle is,

A = 1/2 × 6 × 13

A = 39 feet²

Hence, We get;

Area of figure is,

A = 50 + 39

A = 89 feet²

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a)

Shape 1 area is 753.8 cm³.

Shape 2 area 14.13 cm².

b)

Shape 1 area is 50 ft³.

Shape 2 area is 24 ft².

We have,

a)

The composite figure has a cone and a semicircle.

So,

Area of cone = 1/3πr²h = 1/3 x 3.14 x 3 x 3 x 8 = 753.8 cm³

Area of semicircle = 1/2 x πr² = 1/2 x 3.14 x 3 x 3 = 14.13 cm²

b)

The composite figure has a trapezium and a triangle.

Area of the trapezium

= 1/2 x ( sum of the parallel side) x h

= 1/2 x (7 + 13) x 5

= 1/2 x 20 x 5

= 10 x 5

= 50 ft³

Area of the triangle.

= 1/2 x base x height

= 1/2 x 6 x 8

= 3 x 8

= 24 ft²

Thus,

a)

Shape 1 area is 753.8 cm³.

Shape 2 area 14.13 cm².

b)

Shape 1 area is 50 ft³.

Shape 2 area is 24 ft².

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Answer:

49pi cm^2

Step-by-step explanation:

The area of a circle is pi(r)^2

To find our radius, we need to divide the diameter by 2.

14 / 2 = 7

Lets plug that into our equation:

pi(7)^2

Simplify:

pi(49)

rearrange:

49pi

WAIT, we need units!

49pi cm^2

~~~Harsha~~~

Answer:
-328

Step-by-step explanation:

Simply use BODMAS or BIDMAS; this is the order of your operations. It is an acronym that tells you what to do in what order

Brackets: there are no brackets, move on to indices/order

Indices/Order: for the first step, do 5^2, which is 25, and √49, which is 7. The equation is no 12-5*9(7)-25

Division/Multiplication: For this step, multiply 5, 9 and 7 to get 315. The equation is now 12-315-25

Addition/subtraction: For the final step, just solve 12-315-25 in the traditional left to right way, which is -328.

I have grouped addition and subtraction as well as division and multiplication together because they are done at the same time; if a question has either both addition and subtraction or division and multiplication, just solve these parts from left to right. Division is not superior to multiplication and, likewise, addition is not above subtraction.

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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The 95% confidence interval for the mean number of delivery orders on a Friday night is 36 to 60 orders.

The confidence interval for the mean number of delivery orders on a Friday night is constructed assuming a 95% confidence level.

Given data:

Sample mean (x) = 48 orders

The margin of error (E) = 12 orders

To calculate the confidence interval, we'll use the formula:

Confidence Interval = x ± E

Substituting the values:

Confidence Interval = 48 ± 12

The lower limit of the confidence interval:

Lower Limit = 48 - 12 = 36

The upper limit of the confidence interval:

Upper Limit = 48 + 12 = 60

Therefore, the 95% confidence interval for the mean number of delivery orders on a Friday night is 36 to 60 orders.

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Complete question:

In Boston, A Popular Restaurant Recently Added A Delivery Option. In Reviewing The Sales For This New Delivery Service, The Restaurant Found The Mean Delivery Orders In A Random Sample Of Friday Nights Was X¯=48 Orders, With A Margin Of Error Of 12 Orders. Construct A Confidence Interval For The Mean Number Of Delivery Orders On A Friday Night.

Answer:

3

Step-by-step explanation:

To find the z-score for a data value of 155 in a normal distribution with a mean of 137 and a standard deviation of 6, you can use the formula:

z = (x - μ) / σ

where:

x is the data value,

μ is the mean, and

σ is the standard deviation.

Plugging in the values, we have:

z = (155 - 137) / 6

Calculating this expression:

z = 18 / 6 = 3

The volume of the extra space in the box is 9.0 cubic inches.

To estimate the volume of the extra space in the box, we shall find the difference between the volume of the box and the volume of the cracker tower.

First, volume of the box:

The volume can be calculated as the product of the height, length, and width (we assume the width is the same as the side length since it is a square prism):

Box volume = height * length * width

Given:

height = 8 inches

side length = 2 inches

Box volume = 8 * 2  * 2

= 32  in³

Next, the volume of the cracker tower:

The tower of the cracker is cylindrical, so we shall use the formula for the volume of a cylinder to estimate the volume:

Tower volume = π * (radius²) * height

Given:

height = 7.9 inches

diameter = 1.9 inches

radius = diameter / 2 = 1.9  / 2 = 0.95

Tower volume = π * (0.95)² * 7.9

≈ 22.994 in³ (rounded to three decimal places)

Then, the volume of the extra space in the box:

Volume of the extra space = Tower volume - Box volume:

= 32 in³ - 22.994 in³

≈ 9.006 in³ (rounded to three decimal places)

Therefore, the volume of the extra space in the box = 9.0 in³.

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Based on the supply graph and demand graph shown above, the price at the point of equilibrium is $ 30.

Demand refers to quantity of a commodity that the consumers are willing to, able to purchase at a given price during a given period of time. Supply refers to quantity of a commodity that the producers are willing to, able to offer for sale at a given price during a given period of time.

Demand curve slopes downward due to inverse relationship between price and quantity demanded whereas supply curve slopes upward due to direct relationship between quantity supplied and price. When both demand and supply curve intersect with each other balance is achieved. Intersection point between demand and supply curve is known as equilibrium.

At this point when prices are equal is known as equilibrium price and when quantiy demanded or supplied are equal it is known as equilibrium quantity. When we combine the given graph. Equilibrium is achieved at a point when price is equal to $ 30 and quantity is equal to 20 units.

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