Q1. Which of the following are well-defined sets?
(a) All the colors in the rainbow.

(b) All the points that lie on a straight line.

(c) All the honest members in the family.

(d) All the consonants of the English alphabet.

(e) All the tall boys of the school.

(f) All the efficient doctors of the hospital.

(g) All the hardworking teachers in a school.

(h) All the prime numbers less than 100.

(i) All the letters in the word GEOMETRY.

Answer:

Step-by-step explanation:

x=180-59-41

x=80

Answer: 80°

Step-by-step explanation:

The sum of all angles in a triangle is always 180°

so 59° + 41° + x ° = 180°

or x = 180 - 41 - 59 = 80

Answer:

Length = 3 inches

Width = 7 Inches

Step-by-step explanation:

The shape of a postcard = Rectangle

L = Length

W = Width

A postcard has a perimeter of 20 inches.

Formula for perimeter of a rectangle = 2L + 2W

Hence:

2L + 2W = 20.... Equation 1

Its area is 21 square inches.

The formula for Area of a rectangle = LW

Hence:

LW = 21

L = 21/W

We substitute 21/W for L in Equation 1

2L + 2W = 20.... Equation 1

2(21/W) + 2W = 20

42/W + 2W = 20

Multiply both sides by W

42 + 2W² = 20W

2W² - 20W + 42 = 0

2W - 14W - 6W + 42 = 0

(2W - 6)( W - 7) = 0

2W - 6 = 0

2W = 6

W = 6/2 = 3

W - 7 = 0

W = 7 inches

Solving for L

L = 21/W

W = 7

L = 21/7

L = 3 inches

The dimensions of the postcard are:

Length = 3 inches

Width = 7 Inches

Answer:

1

Step-by-step explanation:

27 - {18 + (16 ÷ (2 x 3 - 4))}

27 - {18 + (16 ÷ (6 - 4))}

27 - {18 + (16 ÷ 2)}

27 - {18 + 8}

27 - 26 = 1

Answer:

[tex]HI=HJ=\sqrt{30}[/tex]units

[tex]\angle I=45^{\circ}[/tex]

Step-by-step explanation:

We are given that

[tex]\angle J=45^{\circ}[/tex]

[tex]JI=2\sqrt{15}[/tex]units

We know that

[tex]sin\theta=\frac{Perpendicular\;side}{hypotenuse}[/tex]

Using the formula

[tex]sin45=\frac{HI}{2\sqrt{15}}[/tex]

[tex]\frac{1}{\sqrt{2}}\times 2\sqrt{15}=HI[/tex]

Where [tex]sin45^{\circ}=\frac{1}{\sqrt{2}}[/tex]

[tex]\frac{2\sqrt{15}\times \sqrt{2}}{\sqrt{2}\times \sqrt{2}}=HI[/tex]

By using rationalization

[tex]HI=\sqrt{30}[/tex] units

[tex]Cos45=\frac{HJ}{2\sqrt{15}}[/tex]

Using the formula

[tex]cos\theta=\frac{base}{hypotenuse}[/tex]

[tex]\frac{1}{\sqrt{2}}\times 2\sqrt{15}=HJ[/tex]

[tex]\frac{2\sqrt{15}\times \sqrt{2}}{\sqrt{2}\times \sqrt{2}}=HJ[/tex]

[tex]HJ=\sqrt{30}[/tex] units

When two sides are equal then angle made by two equal sides are equal

Therefore,

[tex]\angle J=\angle I=45^{\circ}[/tex]

Answer:

y=-7

Step-by-step explanation:

first, you want variables on one side, numbers on the other side of the equation.

4y+4=2y-10

*plus ten on both side to get rid of -10*

4y+14=2y

*minus 4y on each side to get rid of 4y*

14=-2y

*divide by -2 on each side to get the value of just one y itself*

y=-7

I think the answer is,

[tex] - 5[/tex]

sorry if I'm wrong :(

Answer:

(y+2)= -3(x-7)

Step-by-step explanation:

We can use the slope-intercept formula to write this equation. The slope-intercept form of a linear equation is:  

y = m x + b

 Where  m  is the slope and  b  is the y-intercept value.

We can substitute the slope into the formula giving:

y = − 3 x + b

Next, we can substitute the values from the points in the problem for  x  and  y  and solve for  b :

− 2 = ( − 3x 7 ) + b  

− 2 =  − 21 + b

21 − 2 = 21  − 21 + b

 19 = 0 + b

19 = b

We can now substitute the slope from the problem and the value for  b  we calculated into the formula to write the equation.

y = − 3 x + 19

Another process is to use the point-slope formula. The point-slope formula states:

 ( y − y 1 ) = m ( x − x 1 )

 Where  m  is the slope and  ( x 1 , y1 )  is a point the line passes through.

Substituting the slope and values from the points in the problem gives:

(y − − 2 ) = − 3 (x-7)

( y + 2 ) =  − 3 ( x − 7 )

Answer:

16

Step-by-step explanation:

Answer:

-1/6

Step-by-step explanation:

(-1/4)/(3/2)=(-1/4)(2/3)=-2/12=-1/6

Answer:

Step-by-step explanation:

There's no "solving" to be done because its an expression, but im assuming the question wants you to factor.

[tex]b^4-3b^3-10b^2[/tex]

First, factor out a b^2

[tex]b^2(b^2-3b-10)[/tex]

Factor the trinomial. What two numbers multiply to equal -10 but add to equal -3? They are -5 and +2

[tex]b^2((b-5)(b+2))[/tex]

Answer:

540/90=6

and is 6 cm

height is 6 cm

Answer: x - 5.6 = 76.9

Step-by-step explanation:

The number June thought of would give a result of 76.9 if 5.6 were subtracted from it.

Assume that number is x.

If you subtract 5.6 from x, you would get 76.9.

Equation is therefore:

x - 5.6 = 76.9

Solving for x would make x:

x - 5.6 = 76.9

x = 76.9 + 5.6

x = 82.5

Answer:

Each result is equally likely.

The sample space has 36 different outcomes.

Explanation:

A number cube has 6 sides, and there are 2 number cubes so there are 36 possible outcomes because 6² = 36

Answer:

Each result is equally likely.

The sample space has 36 different outcomes.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given that:

Each small square on a grid represents 1 unit

Base of triangle = 5 1/2 units = 11/2

Area of triangle = 19 1/4 unit² = 77/4

The Area, A of a triangle is obtained thus :

77/4 = 1/2 * 11/2 * h

77/4 = 11/4 * h

h = 77/4 ÷ 11/4

h = 77/4 * 4 /11

h = 7 units

Answer: 20

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

Divide each term by 8 and simplify

Answer:

the answer is false

Step-by-step explanation:

just cause it is

Answer:

a = 1/2 (b) (h)

Step-by-step explanation:

Use Pythagorean theorem for sub triangle on the left: 8^2 + h^2 = 22^2

Use Pythagorean again for sub triangle on the right: x^2 + h^2= 31^2

Find your base: 8+x=b

Find entire area: a = 1/2 (b) (h)

Answer:

operaciones : 600×3= 1800÷5=360.

Step-by-step explanation:

y entonces cada amigo tendra que pagar 360 ya que eran 3 amigos y iban a pagar 600 cada uno pero ahora son 5 asi que deben de pagar 360

answer 10,000 Because if you round thirteen to the nearest ten thousand it's ten thousand

Explanation

because 10,000 is the first 10,000 you can ever get to

Answer:

y = 6/5x - 2 (or y = 1.2x - 2)

Step-by-step explanation:

To find the slope-intercept form ( = mx + b) you need to rearrange the equation of the line:

Step 1 - Add 18x to both sides

15y = 18x - 30

Step 2 - Divide both sides by 15.

y = 6/5x - 2

Answer:

1844

Step-by-step explanation:

For polling firm survey on voters, the smallest sample size which is required to obtain the desired margin of error, is 1850.

The probability or the chances of error while choosing or calculating a sample in a survey is called the margin of error.

[tex]MOE=z\times\dfrac{\sigma}{\sqrt{n}}[/tex]

Here, z is the critical value and n is the sample size.

Here, a polling firm wants to use a one-sample z interval to estimate, the number of proportion of voters in a country plan on voting for a certain candidate.

The margin of error for this test is 3% or 0.03 and the confidence interval is 99 percent.

The z value on the confidence interval of 99 percent is 2.576. Here, the standard deviation for this survey is 50 percent, or 0.50.

Put the value in the above formula as,

[tex]0.03=(2.576)\times\dfrac{0.5}{\sqrt{n}}\\n\approx1850[/tex]

Hence, for polling firm survey on voters, the smallest sample size which is required to obtain the desired margin of error, is 1850.

Learn more about the margin of error here;

https://brainly.com/question/10218601

Answer:

-1/3

Step-by-step explanation:

It's going 1 down and 3 across

Answer:

289300 miles/72 hours * 1.60934 km/mile* 1 hour/3600 seconds = 1.48 km/second. Answer 6: To get average speed, we divide the total distance by the total time it takes to travel that distance. If we assume the distance to the moon is 238,900 miles then we divide by 72 hours to get roughly 3318 mph.

Step-by-step explanation:

Hope this helps!!

Answer:

KR

Step-by-step explanation:

First, you can see the right angle and the 30 degrees. Those are the same, so we can flip the triangle on the right to match the one on the left. The line that is similar is KR.