Point Tis on line segment SU. Given TU = 4x + 1, SU = 8, and ST = 3x,determine the numerical length of TU.

Answer:

x^2+x + 1/4

Step-by-step explanation:

x^2+x

Take the coefficient of x

1

divide by 2

1/2

Square it

(1/2)^2 = 1/4

Add this to make a perfect square trinomial

Answer:

<3=75°

Step-by-step explanation:

Angle 3 and angle 2x+95 are supplementary( supplementary angles add up to 180°)

So <3+2x+95=180

<3+2x=180-95

<3+2x=85( let's call this equation 1)

Next, angle 5 and angle 8x+71 are opposite angles (opposite angles are equal) therefore <5=8x+71

Now, <3 and <5 are co-interior angles(co-interior angles are supplementary)

So <3+8x+71=180

<3+8x=180-71=109

Thus, <3+8x=109(let's call this equation 2)

Now solving equation 1 and 2 simultaneously:

Make <3 the subject of equation 1

<3=85-2x

Put <3=85-2x into equation 2

85-2x+8x=109

6x=24

x=24/6=4

Now, remember that angle 2x+95 becomes

2(4)+95

8+95=103°

Therefore<3=180-105=75°

Answer:

a

Step-by-step explanation:

1. <dfh=<ehg
2. fh=hg
3. <dhf=<hgf

Answer:

  about 4.097 seconds

Step-by-step explanation:

The vertical velocity is ...

  (35 m/s)sin(35°) ≈ 20.075 m/s

When the projectile reaches the level from which it was launched (ground level), its final velocity will be the opposite of its initial velocity. Thus, the change in velocity is ...

  -20.075 -(20.075) = -40.150 . . . . m/s

The acceleration is provided by gravity, which is -9.8 m/s², so the time required is ...

  t = Δv/a = (-40.150 m/s)/(9.8 m/s²) ≈ 4.097 s

Answer:

Correct option: "No, a probability of about 0.20 would be assigned using the relative frequency method if selection is equally likely."

Step-by-step explanation:

The assumption made is that all the 5 different packages are equally likely, i.e. the probability of selecting a package is .

The probability distribution is shown below.

According to the probability distribution:

• The probability of a person preferring design 1 is,

• The probability of a person preferring design 2 is,

• The probability of a person preferring design 3 is,

• The probability of a person preferring design 4 is,

• The probability of a person preferring design 1 is,

So it can be seen that the probability of preferring any of the 5 designs are not same.

Thus, the designs are not equally likely.

The correct option is "No, a probability of about 0.20 would be assigned using the relative frequency method if selection is equally likely."

The selection Probability determined using the relative frequency method do not match the assigned probabilities, suggesting that the data do not confirm the belief that one design is as likely to be selected as another.

The given data can be used to calculate the relative frequencies of each package design selected by the consumers.

To determine the selection probabilities using the relative frequency method, divide the number of times a design was preferred by the total number of consumers.

For example, for design 1, the selection probability would be 10/100 = 0.1.

Similarly, for design 2, the selection probability would be 5/100 = 0.05.

The selection probabilities for designs 3, 4, and 5 would be 0.3, 0.4, and 0.15 respectively.

Comparing these probabilities to the assigned probabilities, it can be observed that the assigned probabilities do not match the observed relative frequencies, indicating that the data do not confirm the belief that one design is just as likely to be selected as another.

Learn more about Probability here:

brainly.com/question/22962752

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