1 and 2 are a linear pair, and 2 and 3 are vertical angles. m 2=(5+4 y) and m 3=(6 y-25). what is m 1

Answer:

1.)- B. 5/12

2)- A. 7/9

Step-by-step explanation:

Answer:

$800,000 because she will need to save for 20 years times $40,000

Step-by-step explanation:

Silvia wants to retire at 65 and live on $40,000 a year.

She wants to live till 85 and retire at 65 years.

So, number of years to save = [tex]85 -65= 20[/tex]

And she needs to save [tex]40000\times20=800000[/tex]

Hence, she must save 800,000.

A-Town is conducting a survey using a random sample method by dividing the population into neighborhoods and surveying random households in each, which ensures each household has an equal chance of being selected and provides a representative sample.

A-Town's approach to determining the number of cell phones in each household through a survey is an example of a random sample. The method involves dividing the population into neighborhoods and surveying a random selection of households within each area. This technique helps to ensure that every household has an equal chance of being selected, which should provide a representative sample of the town's population. Such methods are necessary to obtain reliable data that reflects the true distribution and characteristics of the target population without regional bias.

Using a representative sample is crucial in research and polling to measure accurately public opinion or collect data on phenomena. As in the given example where the market research firm surveys 500 randomly selected residents to estimate the percentage of adults with cell phones, the firm employs statistical measures like confidence intervals to infer about the entire population's cell phone ownership based on the sample data. Moreover, the concept of probability sampling is also important for achieving a sample that can be generalized to the whole population with reasonable accuracy.

Case 1: If the letter z is distinctly different

If we have the letter z which is distinctly different than the other "z", then we have five letters in the word F U Z Z Y and the number of arrangements would be = 5*4*3*2*1 =5! = 120 different arrangements

Case 2: If the letter Z is interchangeable

If the letter "Z" is interchangeable with the other "z" then we have 2 letters which cancel out each other that would be represented by 2*1 = 2! = 2

So, the number of arrangements in this case would be 5!/2! = 5*4*3*2*1/2*1 = 60 arrangements

To express that Jake is younger than Sophie who is 14, we use the inequality j < 14, where j symbolizes Jake's age in years.

The question is asking for an inequality that represents Jake's age compared to Sophie's age. Since we are told that Jake is younger than Sophie and Sophie is 14 years old, we can use an inequality symbol to express this relationship. The appropriate inequality is j < 14, where j represents Jake's age in years. The symbol < means 'less than,' which correctly compares Jake's age to Sophie's, indicating that Jake's age is less than 14 years.

Answer: The Work done to move the object is  [tex]=23.15 \text { foot pounds }[/tex]

Step-by-step explanation:

Given;

Force F=3 [tex]l b s[/tex]

Vectors of F= (3,-1)

Moves object to a distance=9 [tex]f t s[/tex]

Let A and B be the displacements Vectors

A= (0,-5)

B= (6,-2)

To Find:

Work done in foot-pounds

Solution:

Work done [tex]W=F \times D[/tex]

Direction of force vector= (3,-1)  (i, j)  

                                        =3i-j

Unit of force vector [tex]=\sqrt{3^{2}+\left(-1^{2}\right)}[/tex]

                                 [tex]=\sqrt{9+1}[/tex]

Force vector=(Force/Unit Vector)Direction of  force vectors

                   F=[tex]3 / \sqrt{10} \times(3 i-j)[/tex]

Direction of motion vector= (B-A)  

                                          = (6,-2)-(0,-5) x i,j)

                                          =(6-0),(-2-5) x (i, j)

                                          =(6,-7) x (i, j)

                                          =6i-7j

Unit of motion vector [tex]=\sqrt{6^{2}+\left(-7^{2}\right)}[/tex]

                                   [tex]=\sqrt{36+49}[/tex]

                                   [tex]=\sqrt{85}[/tex]

Motion Vector= (Distance moved by the object/Unit motion vector) × (Direction of motion vectors)

                        [tex]D=9 / \sqrt{85} \times(6 i-7 j)[/tex]

Workdone [tex]W=F \times D[/tex]

                  [tex]= [3/ \sqrt{10} \times (3i-j)] \times [9/ \sqrt{85} \times (6i-7j)][/tex]

                  [tex]= [3/ \sqrt{10} \times 9/ \sqrt{85}] \times [(3i-j)  \times(6i-7j)][/tex]

                  [tex]= [3/3.1623 \times 9/9.2195] \times [(3\times6) + ((-1) \times (-7))][/tex]

                  [tex]= [0.94867 \times 0.97619] \times [18+7][/tex]

                  [tex]=23.15 \text { foot pounds }[/tex]

Result:

   Work done to move an object [tex]=23.15 \text { foot pounds }[/tex]

Answer:

[tex]W = 25.617\,lbf\cdot ft[/tex]

Step-by-step explanation:

The work done to move the object is:

[tex]W = F \cdot s \cdot \cos \alpha[/tex]

The angle of the force with respect to change in the position vector is:

[tex]\alpha = \tan^{-1}\left(-\frac{7}{6} \right) - \tan^{-1}\left(-\frac{1}{3} \right)[/tex]

[tex]\alpha \approx 18.415^{\textdegree}[/tex]

The magnitude of the work done is:

[tex]W = (3\,lbf)\cdot (9\,ft)\cdot \cos 18.415^{\textdegree}[/tex]

[tex]W = 25.617\,lbf\cdot ft[/tex]

Using the combination formula, 21 different 5-person committees can be chosen from a group of 7 students.

To determine how many different 5-person committees can be chosen from a group of 7 students, we use the concept of combinations, specifically the combination formula which is defined as:

C(n, k) = n! / [k! * (n - k)!]

where n is the total number of items to choose from, k is the number of items to choose, and the exclamation point represents a factorial, which is the product of all positive integers up to that number.

Applying this to the given problem, we have:

C(7, 5) = 7! / [5! * (7 - 5)!]

This simplifies to:

C(7, 5) = (7 * 6) / (2 * 1)

Therefore, C(7, 5) = 21.

There are 21 different 5-person committees that can be formed from 7 students.

Using a quadratic function, it is found that it will take 5.17 seconds for the javelin to hit the ground.

Considering meters as the measure of height, it is given by:

h(t) = -4.9t² + v(0)t + h(0).

In which:

In this problem, we have that v(0) = 25, h(0) = 1.6, hence:

h(t) = -4.9t² + 25t + 1.6

It hits the ground when h(t) = 0, hence:

-4.9t² + 25t + 1.6 = 0

4.9t² - 25t - 1.6 = 0.

Which is a quadratic function with coefficients a = 4.9, b = -25, c = -1.6. Hence:

[tex]\Delta = (-25)^2 - 4(4.9)(-1.6) = 656.36[/tex]

[tex]x_1 = \frac{25 + \sqrt{656.36}}{9.8} = 5.17[/tex]

[tex]x_2 = \frac{25 - \sqrt{656.36}}{9.8} = -0.06[/tex]

For time we want the positive value, hence, it will take 5.17 seconds for the javelin to hit the ground.

More can be learned about quadratic functions at https://brainly.com/question/24737967

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Answer:

  1 13/20

Step-by-step explanation:

You want the total of distances walked to be the length of the hike:

  2 1/10 + 1 1/4 + (left to walk) = 5

Then the amount left to walk is the difference ...

  left to walk = 5 - 2 1/10 - 1 1/4

___

You are expected to know how to do arithmetic with mixed numbers, and/or to be able to use a calculator for the purpose.

  5 - 2 1/10 - 1 1/4

  = (5 -2 -1/10) - 1 1/4

  = 2 9/10 - 1 1/4

  = (2 -1) + (9/10 -1/4)

  = 1 + (9/10 -1/4)

  = 1 + (18/20 - 5/20)

  = 1 13/20 . . . miles left to walk

___

Using a calculator:

  5 -2.1 -1.25 = 1.65 = 1 65/100 = 1 13/20

Since, it is given that the pentagon ABCDE is congruent to pentagon FGHIJ.

By being congruent, the corresponding angles and sides are equal.

Therefore, [tex]\angle A = \angle F[/tex], [tex]\angle B = \angle G[/tex], [tex]\angle C = \angle H[/tex], [tex]\angle D= \angle I[/tex], [tex]\angle E = \angle J[/tex].

By using [tex]\angle A = \angle F[/tex]

So, [tex]100^\circ = \angle 1[/tex]

Therefore, the measure of angle 1 is 100 degrees.

So, Option B is the correct answer.