A committee consisting of
4

faculty members and
5

students is to be formed. Every committee position has the same duties and voting rights. There are
12

faculty members and
15

students eligible to serve on the committee. In how many ways can the committee be formed?

Answer: the answer would be choice A

Step-by-step explanation: it passes through the origin making it a proportional relationship

Answer:

true

Step-by-step explanation:

false because it would just be 2y+4y -1y*2=6

5y*2=6

divide 2

5y+1=6

5y=5

divide 5 to each

then then the answer is 1

Answer:

True

Step-by-step explanation:

Solve the equation for Y by finding a, b, and of the quadratic then applying the quadratic formula.

The leading coefficient is a negative value (-3) so the graph goes down on the right side.

This makes either Graph B or C correct.

Now because the degree ( exponent ) (the ^4) is even both ends of the graph go in the same direction.

This makes Graph B the correct answer.

Answer:

The leading coefficient is a negative value (-3) so the graph goes down on the right side.

This makes either Graph B or C correct.

Now because the degree ( exponent ) (the ^4) is even both ends of the graph go in the same direction.

This makes Graph B the correct answer.

The ratio of the lengths of EF and BC is 2:1. The correct answer is (EF, BC), where the length of EF is twice the length of BC.

The ratio of the lengths of two segments is given as 2:1. We can set up a proportion and find that the length of one segment is twice the length of the other.

In this question, the ratio of the lengths of two segments is given as 2:1. We are asked to find the lengths of the two segments, which are represented by two choices: (EF, BC) and (AD, IH). To solve this problem, we can set up a proportion. Let's assume that EF and BC represent the lengths of the segments, and we can write the proportion as:

[tex]\frac {EF}{BC} =\frac {2}{1}[/tex]

To solve for the lengths, we can cross multiply:

[tex]EF \times 1 = BC \times 2[/tex]

[tex]EF = 2 \times BC[/tex]

So, the length of EF is twice the length of BC. Therefore, the correct answer is (EF, BC), where the length of EF is twice the length of BC.

Final answer:

The student's question deals with the concept of ratios and similar triangles in High School level Mathematics. Without additional context to the specific figures and points mentioned, a precise answer cannot be given. Typically, in similar triangles, corresponding side lengths are proportional, allowing calculation of unknown lengths when a ratio is provided.

Explanation:

The question refers to finding a ratio of lengths related to geometrical figures. Since ratios and proportions frequently deal with lengths and geometry, and the provided examples reference triangles, circles, and other geometric shapes, this question is most closely related to the subject of Mathematics. The use of similar triangles to find unknown lengths is a typical high school-level geometry problem.

Based on the information given in the question, it seems we are required to use the property that states the ratios of corresponding sides of similar triangles are equal. To answer the student's question specifically, we'd need more context to the figures in question, such as circle C with center F and point F', or the configuration of the triangles abc and a'b'c'.

For instance, if we have two similar triangles, with corresponding side lengths in a ratio of 2:1, this means that if one triangle has a side length of 'x', the similar triangle's corresponding side length would be '2x'. To answer the student's query correctly, however, additional information on which particular sides of the named points are being inquired about is necessary.

[tex]\cos x=0\\\\x=\dfrac{\pi}{2}+k\pi, k\in\mathbb{Z}[/tex]

The x-values where cos(x) = 0 occur at x = π/2 + nπ, where n is any integer.

To determine the x-values where cos(x) equals 0, we refer to the unit circle, where the cosine of an angle represents the x-coordinate of the corresponding point on the circle.

The cosine function equals 0 at angles where the x-coordinate is 0, which occurs at specific points on the unit circle:

Additionally, cosine is a periodic function with a period of 2π, meaning these values will repeat every 2π. Thus, the general solution for x where cos(x) = 0 is:

x = π/2 + nπ, where n is any integer.

For example: when n=0, x = π/2; when n=1, x = 3π/2; and so on.

Hence, the x-values where cos(x) = 0 are expressed as x = π/2 + nπ for any integer n.

Answer:

Step-by-step explanation:

2 x w x l + 2 x l x h + 2 x h x w

* is times  2*5*7+2*7*4+2*4*5 =

= 70+56+40=166 cm

Hope it helps

Answer:

The smaller diameter is [tex]3.9\ cm[/tex]

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

The diameter of the circle is equal to BD

Applying the Pythagoras Theorem

[tex]BD^{2} =BE^{2} +DE^{2}[/tex]

substitute the given values

[tex]BD^{2} =3^{2} +2.5^{2}\\ BD^{2} =15.25\\ BD=3.9\ cm[/tex]

Answer:

3.9

Step-by-step explanation:

use Pythagorean Theorem

plus i took the test :)

Answer:

I see this

"Which relation is a function?

A {(-3,4),(-3,8),(6,8)}

B {(6,4),(-3,8),(6,8)}

C {(-3,4),(3,-8),(3,8)}

D {(-3,4),(3,5),(-3,8)}"

So the answer is none of these.

Please make sure you have the correct problem.

Step-by-step explanation:

A set of points is a function if you have all your x's are different.  That is, all the x's must be distinct. There can be no value of x that appears more than once.

If you look at choice A, this is not a function because the first two points share the same x, which is -3.

Choice B is not a function because the first and last point share the same x, which is 6.

Choice C is not a function because the last two points share the same x, which is 3.

Choice D is not a function because the first and last choice share the same x, which is -3.

None of your choices show a function.

If you don't have that choice you might want to verify you written the problem correctly.

This is what I see:

"Which relation is a function?

A {(-3,4),(-3,8),(6,8)}

B {(6,4),(-3,8),(6,8)}

C {(-3,4),(3,-8),(3,8)}

D {(-3,4),(3,5),(-3,8)}"

Answer:

  $557.51

Step-by-step explanation:

A financial calculator tells you the payments are ...

  on $80,000 at 4.75%: $417.32

  on $20,000 at 7.525%: $140.19

Then the total monthly payment is ...

  $417.32 +140.19 = $557.51

_____

You can use the amortization formula to find the payment (A) on principal P at interest rate r for t years to be ...

  A = P(r/12)/(1 -(1+r/12)^(-12t))

I find it takes fewer keystrokes to enter the numbers into a financial calculator. Both give the same result.

Final answer:

Troy's total mortgage payment can be found by calculating the monthly payment for the first mortgage at 80% of the home price with an interest rate of 4.75% and the second mortgage at 20% of the home price with a 7.525% interest rate, then combining these two payments. However, exact figures require the use of an amortization formula or an online mortgage calculator.

Explanation:

To calculate Troy's total mortgage payment for an 80/20 mortgage on a $100,000 house, we need to separate the calculations for the first mortgage (80%) and the second mortgage (20%) because they have different interest rates.

First Mortgage Calculation:

The first mortgage is 80% of the home price, which amounts to $80,000. With an interest rate of 4.75%, his monthly payment can be calculated using the formula for a fixed-rate mortgage.

Second Mortgage Calculation:

The second mortgage is 20% of the home price, equal to $20,000. With a higher interest rate of 7.525%, we again use the formula for a fixed-rate mortgage to find the monthly payment.

Without the actual formula or financial calculator, we cannot compute the exact monthly payments here. Typically, you would use the amortization formula or an online mortgage calculator to find the monthly payments for each part of the mortgage, and then sum them up for the total monthly payment.

Combining the Payments:

Once the monthly payments for both mortgages are calculated, they are added together to determine Troy's total monthly mortgage payment.

Answer:

  a. x^4 +2x^2 -6

  b. 2x^5 +x^4 +4x^3 +2x^2 -12x -6

  c. 6x^5 +3x^4 +12x^3 +6x^2 -36x -18

  d. the area of one piece is 1/3 the area of the board

Step-by-step explanation:

a. The length of each piece will be 1/3 the length of the board. Divide each of the coefficients of the length polynomial by 3:

  piece length = (1/3)(board length) = (1/3)(3x^4 +6x^2 -18) = x^4 +2x^2 -6

__

b. The area is the product of length and width.

  piece area = (width)×(piece length) = (2x +1)(x^4 +2x^2 -6)

  piece area = 2x^5 +x^4 +4x^3 +2x^2 -12x -6

__

d. The board area is 3 times the area of one piece. The area of one piece is 1/3 the area of the board.

__

c. board area = 3×(piece area) = 6x^5 +3x^4 +12x^3 +6x^2 -36x -18

Answer:

  1231 km/h

Step-by-step explanation:

The average speed is given by ...

  average speed = (total distance)/(total time)

The total time will be the sum of times down and back, each of which is given by ...

  time = distance/speed

Going to Mexico, the time required was ...

  time down = (2000 km)/(1600 km/h) = 1.25 h

Coming back, the time required was ...

  time back = (2000 km)/(1000 km/h) = 2.00 h

Then the average speed is ...

  average speed = (2000 km + 2000 km)/(1.25 h +2.00 h) = 4000/3.25 km/h

  ≈ 1231 km/h

_____

Comment on average speed

The value we computed was ...

  2/(1/s1 + 1/s2) . . . . where s1 and s2 are the speeds over the same distance

This is the harmonic mean of two numbers (the two speeds). The harmonic mean of n numbers is ...

  harmonic mean = n/(1/a1 +1/a2 +1/a3 + ... + 1/an)

This mean generally finds less use than the typical arithmetic mean or geometric mean.

  arithmetic mean = (a1 + a2 + a3 + ... + an)/n

  geometric mean = (a1·a2·a3·...·an)^(1/n)

Answer:

  4:9 ≠ 6:13

Step-by-step explanation:

The ratios of corresponding segments will be equal if DE || BC. Yana can compare AD:AB versus AE:AC. She will find they're not equal, as expressed by ...

  4 : 9 ≠ 6 : 13

Answer:

4:9 ≠ 6:13

Step-by-step explanation:

Given,

In triangle ABC,

D ∈ AB, E ∈ AC,

Also, AD = 4 unit, DB = 5 unit, AE = 6 unit, EC = 7 units,

Suppose,

DE ║ BC,

[tex]\because \frac{AD}{AB}=\frac{AD}{AD + DB}=\frac{4}{9}[/tex]

[tex]\frac{AE}{AC}=\frac{AE}{AE+EC}=\frac{6}{6+7}=\frac{6}{13}[/tex]

[tex]\implies \frac{AD}{AB}\neq \frac{AE}{AC}[/tex]

Because,

[tex]\frac{4}{9}\neq \frac{6}{13}[/tex]

Which is a contradiction. ( if a line joining two points of two sides of a triangle is parallel to third sides then the resultant triangles have proportional corresponding sides )

Hence, DE is not parallel to segment BC.

A reflection along parallel line l and m is the same as a translation

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.

A composition of reflection over two parallel lines is the same as a translation, hence:

Find out more on translation at: https://brainly.com/question/12861087

Answer:

-81

Step-by-step explanation:

b=a+3

Subtract 3 from each side

b=a+3

b-3 = a+3-3

b-3 =a

Then subtract b from each side

b-b-3 = a-b

-3 = a-b

We want (a-b) ^4

We know a-b = -3

(-3) ^4

-81

He drives 55 miles per hour for x hours. You want to multiply the number of hours by his speed , so you have 55x.

Then you want to subtract that from the total miles he has to drive.

The equation is Y = 385 - 55x

Answer:

  22 ft/s

Step-by-step explanation:

15 mph is 1/4 of 60 mph. At 1/4 the speed, the car will travel 1/4 as far in a second.

  1/4×(88 ft/s) = 22 ft/s

Answer:

22 ft/s

Step-by-step explanation:

At 60 mph a car travels  88 feet per second. There are 22 feet per second that a car  travels at 15 mph.

Answer:

C. 24.1 ft

Step-by-step explanation:

The side of the wall making the tilt of 75° will represent the hypotenuse

The height of the wall will be represented by the side opposite to the angle 75°

Apply the relationship for sine of angle Ф

Formula to use is ;

Sin Ф=  length of opposite side÷hypotenuse

SinФ=O/H

Sin 75°=O/25

0.96592582628=O/25

O=0.96592582628×25 =24.1 ft

Option 24.1 ft

1. Identify the given information:

   - Length of the wall (hypotenuse, [tex]\( c \)[/tex]) = 25 feet
   - Angle [tex](\( \theta \))[/tex] with the ground = 75°

2. Recall the sine function:
   - Sine of an angle [tex](\( \sin \theta \))[/tex] is the ratio of the length of the opposite side to the hypotenuse.
   - Mathematically, [tex]\( \sin \theta = \frac{\text{opposite}}{\text{hypotenuse}} \)[/tex].

3. Set up the equation using the sine function:
   [tex]\[ \sin(75^\circ) = \frac{\text{height}}{25} \][/tex]

4. Solve for the height:
   - Multiply both sides by 25 to isolate the height.
   [tex]\[ \text{height} = 25 \times \sin(75^\circ) \][/tex]

5. Calculate [tex]\( \sin(75^\circ) \)[/tex]:
   - This value is approximately 0.9659.

6. Substitute [tex]\( \sin(75^\circ) \)[/tex] into the equation:
   [tex]\[ \text{height} = 25 \times 0.9659 \][/tex]
   [tex]\[ \text{height} \approx 24.148 \][/tex]

7. Determine the closest option:
   - The options given are 25.9 ft, 6.5 ft, 24.1 ft, 93.3 ft.
   - The calculated height is approximately 24.148 feet.
   - The closest option is 24.1 ft.

Answer:

n/m = 1.5 is direct variation

v = 1/3 bh is joint variation

y = -7 is constant

vw = -18 is inverse variation

Step-by-step explanation:

* Lets explain the types of variation

- Direct variation is a relationship between two variables that can be

 expressed by an equation in which one variable is equal to a constant

 times the other

# Ex: the equation of a direct variation y = kx , where k is a constant

- Inverse variation is a relationship between two variables in which their

 product is a constant.

- When one variable increases the other decreases in proportion so

 that their product is unchanged

# Ex: the equation of a inverse variation y = k/x , where k is a constant

- Joint variation is a variation where a quantity varies directly as the

 product of two or more other quantities

# Ex: If z varies jointly with respect to x and y, the equation will be of

  the form z = kxy , where k is a constant

- The constant function is a function whose output value (y) is the

  same for every input value (x)

* Lets solve the problem

∵ n/m = 1.5 ⇒ multiply both sides by m

∴ n = 1.5 m

∵ The equation in the shape of y = kx

∴ n/m = 1.5 is direct variation

∵ v = 1/3 bh

∵ 1/3 is a constant

∴ v is varies directly with b and h

∴ v = 1/3 bh is joint variation

∵ y = -7

∴ All output will be -7 for any input values

∴ y = -7 is constant

∵ vw = -18

∵ -18 is constant

∵ The product of the two variables is constant

∴ vw = -18 is inverse variation

Chris would need to drive 650 miles for the two plans to cost the same.

Further Explanation:

Let d = distance traveled in miles

Plan 1 will have an initial fee of $65 and a cost of $0.80 per mile driven. Therefore, the total cost to drive a distance of d will be:

total cost = $65 + ($ 0.80 × d)

Plan 2 will have no initial fee but has a cost of $0.90 per mile drive. The total cost, then, to drive a distance of d will be:

total cost = $0.90 × d

If the two costs are the same, then:

$65 + ($ 0.80 × d) = $0.90 × d

The distance driven, d, can then be solved algebraically.

Combining like terms:

$65 = $0.90d - $0.80d

$65 = $0.10d

Solving for d:

d = $65/$0.10

d = 650 miles

To check the answer, solve for the total cost of Plan 1 and Plan 2 and see if they are equal.

Plan 1:

total cost = $65 + ($0.80 x 650)

total cost = $65 + $520

total cost = $585

Plan 2:

total cost = $0.90 x 650

total cost = $585

Since both plans cost the same, then the distance 650 mi is correct.

Learn More

Keywords: word problem, total cost

Answer:

  9 rolls

Step-by-step explanation:

The perimeter of the room measures 2(19' +12') = 62', so the area of the walls is ...

  (62 ft)(8.5 ft) = 527 ft²

We know that 8 rolls will cover 8×60 ft² = 480 ft², and 9 rolls will cover 540 ft², so we will need 9 rolls to cover the walls.

Answer:

  339π in³

Step-by-step explanation:

The amount of water is the difference between the volume of the cylinder and the volume of the ball. The appropriate volume formulas are ...

  cylinder V = πr²h

  sphere V = (4/3)πr³

For the given numbers, the volumes are ...

  cylinder V = π(5 in)²(15 in) = 375π in³

  sphere V = (4/3)π(3 in)³ = 36π in³

The water volume is the difference of these ...

  water volume = cylinder V - sphere V

     = 375π in³ - 36π in³ = 339π in³

Answer:

Step-by-step explanation:

This is a geometric sequence so the standard formula for a recursive geometric sequence is

[tex]a_{n}=a_{0}*r^{n-1}[/tex]

We know the heights and the number of bounces needed to achieve that height, but in order to write the recursive formula we need r.

The value of r is found by dividing each value of a bounce by the one before it.  In other words, bounce 1 divided by the starting height gives a value of r=240/300 so r = .8

Bounce 2 divided by bounce 1: 192/240 = .8

So r = .8

Therefore, the formula is

[tex]a_{n}=a_{0}(.8)^{n-1)[/tex] where

aₙ is the height of the ball after the nth bounce,

a₀ is the starting height of the ball,

.8 is the rebound percentage, and

n-1 is the number of bounces minus 1

The first problem basically asks us to find n when the starting height is 175 and the bounce height is less than 8.  I used 7.  Here is the formula filled in with our info:

[tex]7=175(.8)^{n-1}[/tex]

and we need to solve for n.  That requires that we take the natural log of both sides.  Here are the steps:

First, divide both sides by 175 to get

[tex].04=(.8)^{n-1}[/tex]

Next, take the natural log of both sides:

[tex]ln(.04)=ln((.8)^{n-1})[/tex]

The power rule of logs says that we can bring the exponent down in front of the log:

[tex]ln(.04)=n-1(ln(.8))[/tex]

Finding the natural logs of those decimals gives us:

[tex]-3.218876=-.223144(n-1)[/tex]

Divide both sides by -.223144 to get your n-1 value:

n - 1 = 14.4251067

That means that, since the ball is not bouncing 14.425 times, it bounces 14 times to achieve a height less than 8.  Let's see how much less than 8 by checking our answer.  To do this, we will solve for aₙ when x = 14:

[tex]a_{n}=175(.8)^{14}[/tex]

This gives us a height at bounce 14 of 7.697 cm, just under 8!

Now for the next part, we want to use a starting value of 250 and .8 as the rebound height.  We want to find a₄, the height of the 4th bounce.

[tex]a_{4}=250(.8)^{4-1}[/tex]

which simplifies to

[tex]a_{4}=250(.8)^3[/tex]

Do the math on that to find the height of the 4th bounce from a starting height of 250 cm is 128 cm

Answer:

First case

   Recursive formula: [tex]h_n = 0.8 \times h_{n-1}[/tex]

   Explicit formula: [tex]h_n = 300 \times 0.8^{n-1}[/tex]

Second case: 15 bounces are needed

Third case: 128 cm

Step-by-step explanation:

Let's call h to he height of the ball

From the table, the rate is computed as follows:

r = 240/300 = 192/240 = 153.6/192 =  122.88/153.6 = 98.3/122.88 = 0.8

Which means this is a geometric sequence (all quotients are equal).

Recursive formula:

[tex]h_0 = 300[/tex]

[tex]h_n = r \times h_{n-1}[/tex]

[tex]h_n = 0.8 \times h_{n-1}[/tex]

where n refers to the number of bounces

Explicit formula:

[tex]h_n = h_0 \times r^{n-1}[/tex]

[tex]h_n = 300 \times 0.8^{n-1}[/tex]

If this ball is dropped from a height of 175 cm, then

[tex]h_n = 175 \times 0.8^{n-1}[/tex]

If the height must be 8 cm or less:

[tex]8 = 175 \times 0.8^{n-1}[/tex]

[tex]8/175 = 0.8^{n-1}[/tex]

[tex]ln(8/175) = (n-1) ln(0.8)[/tex]

[tex]n = 1 + \frac{ln(8/175)}{ln(0.8)}[/tex]

[tex]n = 14.83[/tex]

which means that 15 bounces are needed.

If this ball is dropped from a height of 250 cm, then

[tex]h_n = 250 \times 0.8^{n-1}[/tex]

For the fourth bounce the height will be:

[tex]h_4 = 250 \times 0.8^{4-1}[/tex]

[tex]h_4 = 128[/tex]

Check the picture below.

[tex]\bf \textit{surface area of a cone}\\\\ SA=\pi r\sqrt{r^2+h^2}+\pi r^2\qquad \implies SA=\pi (8)\sqrt{164}+ \pi (8)^2 \\\\\\ SA=8\pi \sqrt{164}+ 64\pi \implies \stackrel{\pi =3.14~\hfill }{SA\approx 522.65296}\implies \stackrel{\textit{rounded up}}{SA=522.65}[/tex]

Answer:

522.75 yards2 is correct.

Step-by-step explanation:

Answer:

Part a) 0.63

Part b) 0.22

Part c) 0.68

Step-by-step explanation:

The individual probabilities are calculated as

1) Probability of scoring in first attempt = 70%

2) Probability of missing in first attempt = 30%

3)  Probability of scoring in second attempt provided she scores in first attempt = 90%

4)  Probability  of missing in second attempt provided she scores in first attempt = 10%

5) Probability of scoring in 2nd attempt provided she misses in ist attempt = 50%

6)  Probability of missing in 2nd attempt provided she misses in ist attempt = 50%

Part a)

probability of making the throw exactly  both the times = [tex]P(ist)\times P (2nd)[/tex]

Applying values we get

probability of making the throw exactly  both the times= [tex]0.7\times 0.9=0.63[/tex]

Part b)

She will make it exactly once if

1) She scores in first attempt and misses second

2) She misses in first attempt and scores in  the second attempt

Probability of case 1 = [tex]0.7\times 0.1=0.07[/tex]

Probability of case 2 =[tex] 0.3 \times 0.5 =0.15[/tex]

Thus probability She will make it exactly once equals [tex] 0.15+0.07=0.22[/tex]

Part c)

It is a case of conditional probability

Now by Bayes theorem we have

[tex]P(B|A)=\frac{P(B\cap A)}{P(A)}[/tex]

P(B|A) is the probability of scoring in second attempt provided that she has scored only once

P(B) is the probability of scoring exactly once

Given that she makes it exactly once [tex]\therefore P(A)=0.22[/tex]

[tex]P(B\cap A)=0.15[/tex]

using these values we have

[tex]P(B|A)=\frac{0.15}{0.22}\\\\P(B|A)=0.68[/tex]

Answer:

[tex]\large\boxed{\text{Nine over eighteen}}[/tex]

Step-by-step explanation:

In this question, we're trying to find the probability of picking a person that is a male or a doctor.

We know that there are:

With the information above, we can find the probability.

Lets first find how many male nurses there are. To find this, we would get our total amount of nurses (15) and subtract it by 9, due to the fact that 9 of the nurses are female.

[tex]15-9=6[/tex]

This means that there are 6 male nurses.

6 would be added to our probability.

We're not done yet, we also need to add the chance of getting a doctor in our probability.

Since there's 3 doctors, we would just add 3 to our probability.

[tex]6+3=9[/tex]

Now, we need to find the total. When we add all together, we would get 18. This means that 18 would go on our denominator and 9 will go on our numerator.

This means that the chance of getting a male or a doctor would be [tex]\frac{9}{18}[/tex], or nine over eighteen.

Answer:

an=27(one third) - 1

thanks

The correct answer is:

                Option: B

   [tex]B.\ a_n=27(\dfrac{1}{3})^{n-1}[/tex]

We are given that the graph passes through (2,9) , (3,3) and (4,1)

Now, the function which models the graph is given by:

[tex]a_n=27(\dfrac{1}{3})^{n-1}[/tex]

when n=2 we have:

[tex]a_2=27(\dfrac{1}{3})^{2-1}\\\\i.e.\\\\a_2=27(\dfrac{1}{3})^1\\\\i.e.\\\\a_2=9[/tex]

when n=3 we have:

[tex]a_3=27(\dfrac{1}{3})^{3-1}\\\\i.e.\\\\a_3=27(\dfrac{1}{3})^2\\\\i.e.\\\\a_3=3[/tex]

when n=4 we have:

[tex]a_3=27(\dfrac{1}{3})^{4-1}\\\\i.e.\\\\a_3=27(\dfrac{1}{3})^3\\\\i.e.\\\\a_4=1[/tex]

Check the picture below.

Answer:

the point estimate of the true proportion of employees is 0.401

Step-by-step explanation:

Given data

plan A = ( 0.241 , 0.561 )

to find out

the point estimate for estimating the true proportion of employees who prefer that plan

solution

we know that given data 98% confidence interval for the proportion of employees who prefer plan A: (0.241, 0.561) so point estimate for estimating the true proportion o employees who prefer that plan is p^E

and we can say here  

lower limit = [tex]p^{-E}[/tex] = 0.241    ..............1

upper limit = [tex]p^{+E}[/tex]  = 0.561    ...............2

now add these two equations 1 and 2

=  [tex]p^{-E}[/tex] + [tex]p^{+E}[/tex]

=  [tex]p^{-E}[/tex] + [tex]p^{+E}[/tex]  = 0.241 + 0.561

2 p = 0.802

2p = 0.806

p = 0.401

So the point estimate of the true proportion of employees is 0.401

The point estimate in this scenario is 0.401, which is the estimated proportion of employees who prefer Plan A. This is calculated by averaging the lower and upper limits of the given 98% confidence interval.

The question is asking for the point estimate which is a single value used as an estimate of the population parameter. In a confidence interval, the point estimate is the mid-point or center of the interval. Here, the confidence interval given for the proportion of employees preferring Plan A is (0.241, 0.561). To find the point estimate, you average the two end values.

The formula for finding the point estimate is: (Lower limit + Upper limit) / 2.

Applying the values from your question: (0.241 + 0.561) / 2 = 0.401.

So, the point estimate, or the estimated true proportion of employees who prefer Plan A, is 0.401.

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Answer:

B

Step-by-step explanation:

The "value" of a function is the y-value.

Since we want negative y values, we look at "WHERE" the function is "UNDER" the y-axis.

Looking closely, it looks that function (the dip) is from x = -1 to x = 3

Hence, the function is negative at the interval  -1 ≤ x ≤ 3

B is correct.