The Fox TV network is considering replacing one of its prime-time crime investigation shows with a new family-oriented comedy show. Before a final decision is made, network executives commission a sample of 400 viewers. After viewing the comedy, 250 indicated they would watch the new show and suggested it replace the crime investigation show.


(a) Estimate the value of the population proportion. (Round your answer to 3 decimal places.)

Estimated population proportion

(b)
Develop a 95 percent confidence interval for the population proportion. (Round your answers to 3 decimal places.)

Answer:

Step-by-step explanation:

Answer:

It's C.

Step-by-step explanation:

Note. x^2 + 6x - 40 = (x + 10)(x - 4) so we have

     x - 16                    1

----------------        +  ---------

(x + 10)(x - 4)          (x + 10)

=   x - 16  + (x - 4)            2x - 20

   --------------------  =     -----------------------

    (x + 10)(x - 4)            x^2 + 4x - 40

Answer:

y=4

Step-by-step explanation:

Slope equal 0 means you have a horizontal line. Horizontal lines are all of the form y=a where a is the constant you have to figure out. Our horizontal line goes through (2,4) and the coordinate there is 4 so the line is y=4.

The equation in slope-intercept form that describes a line through (2, 4) with slope 0 is y = 4 .

The equation of a straight line in the form y = mx + c where m is the slope of the line and c is its y-intercept is known as the slope-intercept form. Here both the slope (m) and y-intercept (c) have real values. It is known as slope-intercept form as it gives the definition of both the slope and y-intercept.

It is given that the line passes through (2,4) and it has slope 0 .

Thus, general equation of straight line is y = mx + c

Slope(m) = 0

∴ y = c

The y-coordinate of the point is 4 , so c = 4

Thus, the equation of a straight line in slope-intercept form is -

  y = 0*(x) + 4

∴ y = 4 .

Therefore, the equation in slope-intercept form that describes a line through (2, 4) with slope 0 is y = 4 .

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Answer:

The number of black T-shirts in 110 experiments is 20.

Step-by-step explanation:

It is given that in 55 trials of the experiment, a black T-shirt was drawn 10 times.

Formula of probability:

[tex]P=\frac{\text{Favorable outcomes}}{\text{Total number of outcomes}}[/tex]

Since 55 trials of the experiment, a black T-shirt was drawn 10 times, therefore the probability of getting black T-shirts in 1 experiment is

[tex]P=\frac{10}{55}[/tex]

[tex]P=\frac{2}{11}[/tex]

The number of black T-shirts that would be drawn in 110 times is

[tex]T=\frac{2}{11}\times 110=20[/tex]

Therefore the number of black T-shirts in 110 experiments is 20.

Answer:

  Obtuse

Step-by-step explanation:

The sum of squares of the short sides is 130, so is less than the square of the long side. The long side (12) is longer than it would need to be for a right triangle, so the largest angle is bigger than 90°.

The triangle is obtuse.

_____

A triangle solver app or calculator can confirm this. Note angle C is about 96°, an obtuse angle.

Answer:

KM = 10.68; angle K= 55; angle M=35  

Step-by-step explanation:

Using Law of Cosine, you can find KM. Then using Law of Sines, you can find the angle of M. Find the sum of angle M and 90. Then subtract the total of that to 180 to fine angle K.  (sidenote: your angle K should be bigger then angle M since the side measurement of K is larger than M.)

A correct option is option (b).

Given,

[tex]KL=6.2\\LM=8.7\\KM=x(let)[/tex]

Trigonometric ratios:

The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.

The given triangle is right angle triangle then

[tex]KM^2=LM^2+KL^2\\KM=\sqrt{(8.7)^2+(6.2)^2}\\KM=\sqrt{114.13}\\ KM=10.68[/tex]

Now, calculate the angles.

[tex]\angle m=sinm\\=\frac{P}{H}\\ =\frac{6.2}{10.6}\\ m=35[/tex]

Again,

[tex]\angle k=sink\\=\frac{P}{H}\\ =\frac{8.7}{10.6}\\ k=55[/tex]

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The value of the missing angle x° in the diagram is: 63°

By the concept of opposite angles, we know that opposite angles are defined as the angles directly opposite each other where two lines cross.

Thus:

∠ACB = 63°

Similarly, we can say that:

x° = 63°

This is because angle x is also an opposite angles to ∠ACB from the given diagram

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Answer:

3

Step-by-step explanation:

lim(t→∞) [t ln(1 + 3/t) ]

If we evaluate the limit, we get:

∞ ln(1 + 3/∞)

∞ ln(1 + 0)

∞ 0

This is undetermined.  To apply L'Hopital's rule, we need to rewrite this so the limit evaluates to ∞/∞ or 0/0.

lim(t→∞) [t ln(1 + 3/t) ]

lim(t→∞) [ln(1 + 3/t) / (1/t)]

This evaluates to 0/0.  We can simplify a little with u substitution:

lim(u→0) [ln(1 + 3u) / u]

Applying L'Hopital's rule:

lim(u→0) [1/(1 + 3u) × 3 / 1]

lim(u→0) [3 / (1 + 3u)]

3 / (1 + 0)

3

L'Hospital's Rule is a technique used to evaluate limits of indeterminate forms. It involves differentiating the numerator and denominator separately and then taking the limit again. The process is repeated until a determinate form is obtained.

L'Hospital's Rule is a technique used to evaluate limits of indeterminate forms. An indeterminate form is an expression that does not have a unique value when evaluating the limit. To use L'Hospital's Rule, we differentiate the numerator and denominator separately and then take the limit again. If the new limit is still indeterminate, we repeat the process until we get a determinate form.

For example, let's say we have the limit lim(x → 0) (sin(x) / x). This is an indeterminate form since both the numerator and denominator approach 0. Applying L'Hospital's Rule, we differentiate sin(x) and x, giving us lim(x → 0) (cos(x) / 1). Since the new limit is determinate, we can simply evaluate it as cos(0) / 1, which equals 1.

Answer:

73.5 kJ

Step-by-step explanation:

Mass of butane = 185 g

Heat of vaporization for butane = 23.1 kJ/mol

Molar mass of butane = 58.12 g/mol

Number of moles of butane = [tex]\frac{\text{Mass of butane}}{\text{Molar mass of butane}}=\frac{185}{58.12}=3.18\ moles[/tex]

Energy required for burning 185 g of butane = 3.18×23.1 = 73.5 kJ

∴ Energy is required to vaporize 185 g of butane at its boiling point is 73.5 kJ

The square root property seems to be another name for completing the square

x^2 + 5x + 6 = 0

We move the constant to the other side

x^2 + 5x = -6

We square half the linear coefficient and add that to both sides

x^2 + 5x + (5/2)^2 = -6 + 25/4

Now the left side is a perfect square,

(x + 5/2)^2 = 1/4

Here's the square root property part, we take the square root of both sides, remembering the ±

x + 5/2 = ± 1/2

x = -5/2 ± 1/2

Answer: x = -3 or x=-2

We check by plugging in these values to the original equation, and they work.

------

x^2 + 6x = 16

Again we add half the linear coefficient, squared, to both sides

x^2 + 6x + 3^2 = 16 + 9

(x + 3)^2 = 25

Here comes the square root property, taking the square root of both sides:

x + 3 = ±5

x = -3 ± 5

x = 2 or x = -8

Again we check by substitution, and they both work

Answer: x = 2 or x = -8

The given line is y = 3x - 5 after adding Y and subtracting 5 from both sides.

The slope of this given line is 3.

Therefore, the slope of the perpendicular line is -1/3, as it must be the negative reciprocal.

The general form of a line equation in slope intercept form is y = Mx+B where M is the slope and B is the intercept.

Solving for B is: B = y- Mx

So the intercept of the perpendicular line with slope M=-1/3 and passing through (x=4, y=-3) is

y M * x

B = -3 - (-1/3)*4 =

-3 + 1/3*4 = <-- subtracting the negative is the same as adding the positive; definition of subtraction

-3 + 4/3 = <-- multiplies the fractions first per order of mixed operations

-9/3 + 4/3 <-- common denominator is 3

= -5/3

So the equation of the perpendicular line is y = -1/3X + -5/3 = -1/3X-5/3

Notice when X=4, y = -1/3(4) - 5/3 = -4/3 - 5/3 = -9/3 = -3 as expected

Answer:

1) x = 6.6.

2) x = 6.1.

Step-by-step explanation:

1) In this triangle, the hypotenuse is given, which is 8 units, and the angle is given, which is 35 degrees. The base is unknown. To find the base, following ratio will be used:

cos θ = Base/Hypotenuse.

cos 35 = x/8.

x = 8*cos 35.

x = 6.6 units (to the nearest tenth)!!!

2) In this triangle, the base is given by 12, and the angle is given by 27 degrees. The perpendicular is unknown. To find the perpendicular in this case, tangent formula will be used:

tan θ = Perpendicular/Base

tan 27 = x/12.

x = 12*tan 27.

x = 6.1 units (to the nearest tenth)!!!

Answer:

1).  x = 6.55 units

2).x = 2.55 units

Step-by-step explanation:

1). To find the value of x

From the given figure 1 we can see a right angled triangle with hypotenuse is 8 units

Cos 35 = Adjacent side/Hypotenuse

 = x/8

x = 8 * Cos 35

 = 8 * 0.8196

 = 6.55

2). To find the value of x

From the figure we can write,

Tan 27 = Opposite side/Adjacent side

 = x/12

x = 12 * Tan 27

 = 12 * 0.509

 = 2.55 units

Answer:

  cos(θ) = -3/5

Step-by-step explanation:

The cosine of the reference angle (in the first quadrant) is ...

  cos(θ) = √(1 -sin(θ)²) = √(1 -(4/5)²) = √(1 -16/25) = √((25-16)/25)

  = √(9/25) = 3/5 . . . . in the first quadrant

In the second quadrant, the cosine is negative, so the answer is ...

  cos(θ) = -3/5

Answer:

Correct arrangement of equation of displacement to find a is as follows;

1-  Vt - d = 1/2 a t^2 (^ represents exponent i.e. t square as given in equation)

2- 2(Vt - d ) = a t^2

3- a = 2(Vt - d )/ t^2   (keep in mind, 2(Vt - d) whole divided by  t^2)

Step-by-step explanation:

1-  In the first equation, Vt is taken to the left side of the equation (keep in mind, original equation of displacement used for reference as given in question) and multiplied by -1 on the both sides of the equation.

2- In the second equation, 2 is multiplied on the both sides.

3- Multiply t^2 on both sides of the equation, We will get a in correct arrangement, which is required to find.

Answer:

The area of the two-dimensional cross section is 30 feet²

Step-by-step explanation:

* Lets explain what is the right triangular prism

- The right triangular prism has five faces

- Two right triangular bases (cross sections)

- Three rectangular faces

- Its volume V = area of its base × its height

- Its surface area SA = the sum of the areas of the five faces

- The area of the triangular bases = 1/2 × base of Δ × height of Δ

* Lets solve the problem

- ABCFED is a right triangular prism

- Its two parallel bases are ABC and DEF

- Its bases are congruent right triangles

∴ AB = DE , BC = EF , AC = DF

∵ AB = 5 feet

∴ DE = 5 feet

- The two-dimensional cross section that is parallel to face ABC

  is the face DEF

∵ Δ DEF is right triangle , where angle E is a right angle

∴ DE and EF are the base and the height of Δ DEF

∵ DE = 5 feet ⇒ proved

∵ EF = 12 feet ⇒ given

∴ The area of Δ DEF = 1/2 × 5 × 12 = 30 feet²

∵ The two-dimensional cross section that is parallel to face ABC

  is the face DEF

* The area of the two-dimensional cross section is 30 feet²

Answer:

The area of the cross section is 30 feet².

Step-by-step explanation:

The area is 30, because you want to multiply 5 and 12, then multiply that by 1/2 to find the area of a right triangle.

Answer: (-1.5, -0.5)

Step-by-step explanation:

Answer:

  C. 615.7536 square inches

Step-by-step explanation:

The formula for the area of a circle is ...

  A = πr²

Fill in the given numbers and do the arithmetic.

  A = 3.1416×(14 in)² = 615.7536 in²

_____

Comment on the value of pi

We are interested to see that recent problems require use of a value of pi that has 5 significant digits, instead of 3 (as in 3.14). The only problem in this scenario is that the answer is now reported to 7 significant figures, so is still wrong. The correct 7-digit answer to this problem is 615.7522 in². It would be obtained by using a 7- or 8-digit value for pi: 3.141593 or 3.1415927 and rounding appropriately.

Answer:

Step-by-step explanation:

The equation is y = 225 - 60x

y is the distance from Seattle

x is the number of driving hours.

At the start of the journey, x = 0.

y = 225 - 60*0

Therefore he has 225 miles to go.

====================

The change for every hour is the slope of the equation, which is - 60.

So the answer to the second part is - 60

Answer:

The distance was 225 miles when be began driving. The change in Milan's distance from Seattle for each hour he drives is -60.

Step-by-step explanation:

Consider the provided equation.

225 - 60x = y

Where x is the time and y is distance.

For part (A):

When she begins the drive, x = 0.

Substitute the value of x in the provided equation.

y = 225 - 60(0)

y = 225

Hence, the distance was 225 miles when be began driving.

Part (B)

The slope intercept form is: y = mx + c

Where m is the slope and c is the y intercept.

By comparing the provided equation with the slope intercept form it can be conclude that the slope is -60 or the rate of change of distance with respect to x is -60

The change for every hour is the slope of the equation, which is - 60.

Hence, the change in Milan's distance from Seattle for each hour he drives is -60.

Answer:

2

Step-by-step explanation:

Consider two functions:

[tex]y=\sin x[/tex] and [tex]y=\sin 2x[/tex]

The period of each function is

[tex]2\pi[/tex] and [tex]\pi[/tex]

This means that the graph of the function [tex]y=\sin x[/tex] (red graph) intersects by the horizontal line [tex]y=\frac{1}{2}[/tex] twice and the graph of the function [tex]y=\sin 2x[/tex] intersects by the horizontal line [tex]y=\frac{1}{2}[/tex] four times (blue graph) for [tex]x\in [0,2\pi ).[/tex]

So the equation [tex]\sin \theta=\dfrac{1}{2}[/tex] has 2 solutions and  the equation [tex]\sin 2\theta=\dfrac{1}{2}[/tex] has 4 solutions. Thus, the difference is 2.

Answer:

[tex]\large\boxed{\bold{Q1.}\ \overline{WX},\ \overline{XY},\ \overline{YW}}\\\boxed{\bold{Q2.}\ \angle P,\ \angle Q,\ \angle R}[/tex]

Step-by-step explanation:

The longest side is opposite the largest angle, and the shortest is opposite the smallest one.

The largest angle lies opposite the longest side, and the smallest is opposite the smallest side.

Q1.

Calculate m∠Y.

We know: Measures of angles of triangle add up to 180°.

m∠Y + m∠W + m∠X = 180°

Substitute given angles:

m∠Y + 51° + 90° = 180°

m∠Y + 141° = 180°      substitute 141° from both sides

m∠Y = 39°

39° < 51° < 90° → XW < XY < YW

Q2.

RQ < PR < PQ → ∠P < ∠Q < ∠R

Answer:

please ignore my answer

Answer:

0, 6 = x

Step-by-step explanation:

I hope you can see how and if this was alot of help to you, and as always, I am joyous to assist anyone at any time.

Final answer:

The probability that Alice wins the coin-flipping game is 2/3, or approximately 66.67%. This is calculated by summing the infinite geometric series of her winning probabilities over multiple rounds.

Explanation:

The student has asked about the probability that Alice wins a coin-flipping game against Bob where Alice needs a heads to win, and Bob requires a tails to win. Each has a turn to flip the coin if the previous person does not win.

Probability is the measure of the likelihood that an event will occur. To calculate Alice's probability of winning, we consider that she has the first opportunity to win with a 50% chance (heads). If she does not get heads, Bob has a turn, also with a 50% chance (tails), but this does not directly affect Alice's probability. What affects Alice's chances are the subsequent rounds where she will have another opportunity to flip the coin if Bob does not win on his turn.

To calculate her total probability of winning, we can sum up the probabilities of her winning on the first turn, plus the probability of her winning after each complete set of turns:

Alice's probability of winning on the first turn is simply 0.5 (50% for getting heads).

If both fail their first attempt, the game starts over with the same conditions, so the probability of Alice winning on the second set of turns is (0.5 x 0.5 x 0.5), since both need to fail their first flip (0.5 x 0.5) and then Alice must succeed on her second try (x 0.5).

This pattern continues indefinitely, with each complete set of turns reducing Alice's additional chance of victory by a factor of (0.5 x 0.5).

Thus, the sum of this geometric series gives us the total probability of Alice winning:

P(Alice) = 0.5 + ([tex](0.5^3[/tex]x[tex]0.5^5)[/tex] + ... = 0.5 / (1 - (0.5^2)) = 0.5 / (0.75) = 2/3

Alice has a 2/3 (approximately 66.67%) chance of winning the game.

Answer:

  5/3 m/s

Step-by-step explanation:

Antonio's speed in the 400 m dash was ...

  (400 m)/(80 s) = 5 m/s

Antonio's speed in the hurdles was ...

  (400 m)/(120 s) = 3 1/3 m/s

His speed in the dash was ...

  (5 -3 1/3) m/s = 1 2/3 m/s = 5/3 m/s

faster than in the hurdles.

There are three ways to buy 66 cookies with packaging options of single cookies, or packages of 11 or 33. They are two packages of 33, six packages of 11, or sixty-six single cookies.

To find out how many ways you can buy 66 cookies using single cookies, or packages of 11 or 33, we can set up a problem using combinations of these quantities. As we know, 66 is a multiple of both 11 and 33, so we'll want to find out how many packages of 11 and how many packages of 33 can be combined without exceeding 66.

Firstly, since 33 is exactly half of 66, we can have either two packages of 33 or zero packages of 33. If we choose two packages of 33, then we have no need for additional cookies. If we choose zero packages of 33, we can then use six packages of 11 to make up the total because 6 x 11 = 66. There's also the option of buying 66 single cookies, although that tends to be inefficient.

So, our possibilities are:

Thus, there are three ways to buy 66 cookies given the packaging constraints.

Answer:

Measure of <QTS = 20°

Measure or minor arc QS = 40°

Step-by-step explanation:

From the figure we can see a circle with center U.

To find the measure of <QTS

m<QTS = m<QPS   [Angles subtended by same arc are equal]

Therefore m<QTS = 20°

To find the measure of minor arc QS

Measure or minor arc QS = 2 * m<QPS

 = 2 * 20 = 40°

Measure or minor arc QS = 40°

Answer:

A) m∠QTS = 20°

B) The degree measure of minor arc QS is 40°

C) The degree measure of arc QTS is 320°

Step-by-step explanation:

* Lets revise some facts about the circle

- The inscribed angle in a circle is the angle whose vertex lies on the

 circumference of the circle and its sides are the chords in the circle

- Each inscribed angle subtended by an opposite arc to its vertex

- The measure of the arc is twice the measure of the inscribed angle

  subtended by this arc

- The measures of the inscribed angles subtended by the same arcs

  are equal

- The measure of the circle is 360°

* Lets solve the problem

- In circle U

A)

∵ ∠QPS is an inscribed angle subtended by arc QS

∵ ∠QTS is an inscribed angle subtended by arc QS

∴ m∠QPS = m∠QTS

∵ m∠QPS = 20°

∴ m∠QTS = 20°

B)

- Lets find the measure of the arc QS

∵ ∠QPS is an inscribed angle subtended by arc QS

∵ The measure of the arc is twice the measure of the inscribed angle

  subtended by this arc

∴ Measure of arc QS = 2 × m∠QPS

∵ m∠QPS = 20°

∴ Measure of arc QS = 2 × 20° = 40°

∴ The degree measure of minor arc QS is 40°

C)

∵ The arc QTS is an major arc

∵ The sum of the major arc QTS and the minor arc QS equals the

   measure of the circle

∵ The measure of the circle is 360°

∴ m of major arc QTS + m of minor arc QS = 360°

∵ m of minor arc QS = 40°

∴ m of major arc QTS + 40° = 360°

- Subtract 40° from both sides

∴ m of major arc QTS = 320°

∴ The degree measure of arc QTS is 320°

Step-by-step explanation:

1 can is to 10 liters as x cans is to 35 liters.

Write a proportion:

1 / 10 = x / 35

Cross multiply:

10x = 35

Divide:

x = 3.5

It takes 3.5 cans.

Answer:

The ratio of the reaming apples to peaches is 3 : 4

Step-by-step explanation:

* Lets solve the problem

- There are 300 apples and peaches

- The ratio of the number of apples to the number of peaches is 7 : 8

- To find the the numbers of apples and peaches add the terms of the

  ratio and then divide the total number of apples and peaches by this

  sum and then multiply each terms of the ratio by this quotient

∵ The ratio of apples to peaches = 7 : 8

∴ apple : peach : sum

      7     :     8    :    15

       ?    :       ?    :    300

∴ The number of apples = (300 ÷ 15) × 7 = 20 × 7 = 140 apples

∴ The number of peaches = (300 ÷ 15) × 8 = 20 × 8 = 160 peaches

- 50 apples and 40 peaches are sold

∴ The remaining number of apples = 140 - 50 = 90 apples

∴ The remaining numbers of peaches = 160 - 40 = 120 peaches

- To find the ratio simplify the numbers to its simplest form

∵ There are 90 apples and 120 peaches

∴ apple : peach

      90  :   120      ⇒ divided both by 10

∴       9  :    12       ⇒ divide both by 3

∴       3  :     4    

∴ The ratio of the reaming apples to peaches is 3 : 4

The answer is:

The line that is parallel to the given line and passes through the point (4,32) is:

[tex]y=4x+16[/tex]

To solve the problem, we need to remember that parallel lines have the same slope, so, we need to find a line that has the same slope that the given line and it also pass through the point (4,32).

So, we are given the line:

[tex]y-1=4(x+3)\\\\y=4x+12+1\\\\y=4x+13[/tex]

So, we have that the line has a slope which is equal to "4".

Now, we have to find which of the given lines that have a slope equal to "4", also pass through the point (4,32), so, we need to evaluate it into the equations.

Therefore, evaluating we have:

Third line:

[tex]y=4x-16\\\\32=4*4-16=0\\32=0[/tex]

We can see that the equation is not satisfied, so the line does not pass through the point.

So, evaluating the fourth line, we have:

[tex]y=4x+16\\\\32=4*4+16=16+16=32\\\\32=32[/tex]

We can see that the equation is satisfied, so the line does pass through the point (4,32)

Hence, we have that the line that is parallel to the given line and passes through the point (4,32) is:

[tex]y=4x+16[/tex]

Have a nice day!

Answer:

y=4x+16

Step-by-step explanation:

Let us first rearrange the equation of the given line to be in the form y=mx+c. M gives the gradient of the line and c gives the y intercept.

y-1=4(x+3)

y-1=4x+12

y=4x+13

The gradient of parallel lines is equal. For the second line m=4

m=Δy/Δx

(y-32)/(x-4)=4

y-32=4(x-4)

y-32=4x-16

y= 4x+16

The equation of line 2 will be y=4x+16

Answer:

  10^2 . . . . see below for additional information or versions of the answer(s)

Step-by-step explanation:

You seem to want 10^exponent, where exponent is an even single digit, not zero.

We choose exponent = 2, so your expression is ...

  10^2

__

There are several versions of expanded form. One uses exponents. In that form, the expression above is the expanded form.

Another uses multipliers of 1, 10, 100, 1000, and so on. In that form, the expression expands as ...

  10^2 = 1×100

Another expanded form uses individual digits of the expanded form with others set to zero

  10^2 = 100

The standard form is ...

  10^2 = 100.

_____

We suppose your exponential expression might have another multiplier, such as 2.98:

To write an exponential expression with a base of 10 and an even exponent between 1 and 10, we can use 10^2 as an example. By multiplying the base by itself the number of times indicated by the exponent, we find that the expanded form is 10 × 10 = 100. Therefore, the standard form of the expression is 100.

a) The exponential expression with a base of 10 and an even number between 1 and 10 as the exponent would be:

102

b) To write the expression in expanded form, we would multiply the base (10) by itself the number of times indicated by the exponent (2):

10 × 10 = 100

The standard form of the expression would be 100.

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Answer:

your answer would be 4.5 cubic feet!!! HOPE I HELPED!!!!! good luck to anyone who needs this in the future

Step-by-step explanation:

The volume of the triangular prism is 44.52 cubic feet.

A prism is a three-dimensional object.

There are triangular prism and rectangular prism.

We have,

To find the volume of a triangular prism, we need to multiply the area of the base by the height of the prism.

The base of the triangular prism is a triangle with sides of lengths 2 ft, 2.5 ft, and 18 ft.

The perimeter of the base is the sum of the lengths of these sides, which is:

2 ft + 2.5 ft + 18 ft = 22.5 ft

To find the area of the base, we can use Heron's formula, which states that for a triangle with sides of lengths a, b, and c, the area is given by:

[tex]area = \sqrt{s(s-a)(s-b)(s-c)}[/tex]

where s is half the perimeter of the triangle:

s = (a + b + c) / 2

In this case, we have:

a = 2 ft, b = 2.5 ft, c = 18 ft

s = (2 ft + 2.5 ft + 18 ft) / 2

s = 11.25 ft

Plugging these values into the formula, we get:

[tex]area = \sqrt{11.25(11.25-2)(11.25-2.5)(11.25-18)}[/tex]

area = 14.84 ft^2

The volume of the triangular prism is:

volume = area of base x height

volume = 14.84 ft² x 3 ft

volume = 44.52 ft³

Thus,

The volume of the triangular prism is 44.52 cubic feet.

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Answer:

  A.  1 real root and 2 complex roots

Step-by-step explanation:

The one sign change among the coefficients tells you there is one positive real root. The rule of signs is inconclusive regarding the number of negative real roots. A graph shows there are none, so there are ...

  1 real root and 2 complex roots

The given polynomial F(X)=x3+4x2-16 can have either 3 real roots and 0 complex roots if the discriminant is greater than zero, or 1 real root and 2 complex roots if the discriminant is less than zero. The standard cubic formulas or numeric methods can be used to solve it.

The subject of your question is the roots of a cubic polynomial, a topic in mathematics. The given polynomial is not a quadratic equation, so the quadratic formula is not directly applicable. The roots of the polynomial F(X)=x3+4x2-16 can be complex or real numbers depending on the discriminant of the polynomial. If the discriminant of the polynomial is greater than zero, then there are 3 real roots and 0 complex roots, and if it is less than zero, there are 1 real root and 2 complex roots. Standard cubic formulas or numeric methods can be used to solve it, which is a more advanced topic usually covered in high school or college level algebra.

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