Kadir, Chandran and Ping Wei participated in a Science quiz. The number of questions they had answered was in the ratio 4:6:3. Chandran had answered 30 questions. Calculate the total number of questions Kadir amd Ping Wei had answered. ​

Problem 6, part c)

The tickmarks indicate the sides are the same length. This triangle is isosceles.

The two base angles are always opposite the congruent sides. One base angle is 25, so the other base angle must be 25 as well (base angles are congruent for isosceles triangles).

The three angles of this triangle are

25, 25 and 4x+2

Add those three angles up, set the result equal to 180, and solve for x

4x+2+25+25 = 180

4x+52 = 180

4x = 180-52

4x = 128

x = 128/4

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

Problem 7, part a)

We use the same idea as with the last problem above. This works because this triangle is also isosceles (due to the tickmarks).

The three angles of this triangle are

(4x+1), (4x+1) and (5x-4)

note how (4x+1) shows up twice because it is a base angle

Add up those angles and set it equal to 180 to solve for x

(4x+1) + (4x+1) + (5x-4) = 180

13x - 2 = 180

13x = 180+2

13x = 182

x = 182/13

x = 14

Using this x value, we can find angle F

angle F = 5x-4

angle F = 5*14-4

angle F = 70-4

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

Problem 7, part b)

We'll use the x value found back in part a) above.

angle D = 4x+1

angle D = 4*14+1

angle D = 56+1

Angle E is also 57, since D and E are congruent base angles

note how D+E+F = 57+57+66 = 180 to help confirm our answers

The correct answer is A. Mean

Explanation:

In the analysis of numerical data, means refers to the average value. This is found by adding all the values, in this case, all the salaries and then dividing the total by the total of values, in this case, 235. This sample statistic is affected by each of the values that are added, due to this, if a value changes or was corrected, the mean needs to be revised. Also, this does not occur in the case of the minimum (lowest value), the median (value in the middle), or in the mode (most frequent value.)

Answer:

Step-by-step explanation:

Given the equation of a plane in rectangular coordinates to be y = 4x.

The cylindrical coordinates of the axis is as given below;

x = rcosθ

y = rsinθ

z = z

Since there is no z coordinate in the equation of the plane given, we will only substitute x = rcosθ and y = rsinθ into the equation y = 4x and simply the result as shown;

y = 4x

rsinθ = 4( rcosθ)

rsinθ = 4rcosθ

sinθ = 4cosθ

sinθ - 4cosθ = 0

Hence the equation for the plane in cylindrical coordinate is expressed as sinθ - 4cosθ = 0

The equation of the plane y=4x in cylindrical coordinates is,  [tex]sin\theta-4cos\theta=0[/tex]

To find the equation of plane in cylindrical coordinates,

We have to substitute ,

                      [tex]x=rcos\theta\\\\y=rsin\theta\\\\z=z[/tex]

Given equation of plane is, [tex]y=4x[/tex]

Substitute values in equation of plane.

                   [tex]rsin\theta=4(rcos\theta)\\\\sin\theta=4cos\theta\\\\sin\theta-4cos\theta=0[/tex]

Learn more about the equation of plane here:

https://brainly.com/question/8629643

a = 85 10cent coins

b = 117 20cent coins

a = 10c coins

b = 20c coins

$31.90 = c3190

a + b = 202 => a = 202 - b

10a + 20b = 3190

10(202 - b) + 20b = 3190

2020 - 10b + 20b = 3190

10b = 3190 - 2020

10b = 1170

b = 117 (20cent coins)

a = 202 - 117

= 85 (10cent coins)

Answer:

[tex]321_{10} = 101000001_{2}[/tex]

[tex]1023_{10} = 1111111111_2[/tex]

[tex]100632_{10} = 11000100100011000_{2}[/tex]

Step-by-step explanation:

Given

a) 321

b) 1023

c) 100632

Required

Convert to decimal

To convert each of these to binary, we have to divide the quotient by 2 and we take note of the remainder;

Solving (a)

321 / 2 = 160 R 1

160 / 2 = 80 R 0

80 / 2 = 40 R 0

40 / 2 = 20 R 0

20 / 2 = 10 R 0

10 / 2 = 5 R 0

5 / 2 = 2 R 1

2 / 2 = 1 R 0

1 / 2 = 0 R 1

Hence;

[tex]321_{10} = 101000001_{2}[/tex]

Solving (b)

1023 / 2 = 511 R 1

511 / 2 = 255 R 1

255 / 2 = 127 R 1

127 / 2 = 63 R 1

63 / 2 = 31 R 1

31 / 2 = 15 R 1

15 / 2 = 7 R 1

7 / 2 = 3 R 1

3 / 2 = 1 R 1

1 / 2 = 0 R 1

Hence;

[tex]1023_{10} = 1111111111_2[/tex]

Solving (c)

100632 / 2 = 50316 R 0

50316 / 2 = 25158 R 0

25158 / 2 = 12579 R 0

12579 / 2 = 6289 R 1

6289 / 2 = 3144 R 1

3144 / 2 = 1572 R 0

1572 / 2 = 786 R 0

786 / 2 = 393 R 0

393 / 2 = 196 R 1

196 / 2 = 98 R 0

98 / 2 = 49 R 0

49 / 2 = 24 R 1

24 / 2 = 12 R 0

12 / 2 = 6 R 0

6 / 2 = 3 R 0

3 / 2 = 1 R 1

1 / 2 = 0 R 1

Hence;

[tex]100632_{10} = 11000100100011000_{2}[/tex]

Answer:

5 miles.

Step-by-step explanation:

We would be using the Pythagoras Theorem to solve for this.

I have attached a diagram to better help you to better understand my explanation this.

The shortest distance from her playground to her house = Hypotenuse

Pythagoras Theorem for a triangle =

c² = a² + b²

Where c = Hypotenuse

a = 3 miles due west

b = 4 miles north

c² = 3² + 4²

c² = 9 + 16

c² = 25

c = √25

c = 5 miles

Therefore, the shortest distance to Alicia's home from the playground is 5 miles.

Answer:

y=ax+b

y=5(-6)+28=-2

a

Answer:

Step-by-step explanation:

Hello, please consider the following.

We will multiply the numerator and denominator by

[tex]3-\sqrt{3}[/tex] to get rid of the root in the denominator.

Let's do it!

[tex]\begin{aligned}\dfrac{\sqrt{12}}{\sqrt{3}+3}&=\dfrac{\sqrt{2^2*3}*(3-\sqrt{3})}{(3+\sqrt{3})*(3-\sqrt{3})}\\\\&=\dfrac{2\sqrt{3}*(3-\sqrt{3})}{3^2-\sqrt{3}^2}\\\\&=\dfrac{2\sqrt{3}*(3-\sqrt{3})}{9-3}\\\\&=\dfrac{2\sqrt{3}*(3-\sqrt{3})}{6}\\\\&=\dfrac{6\sqrt{3}}{6}-\dfrac{2*3}{6}\\\\&=\sqrt{3}-1\\\\\large &\boxed{=-1+\sqrt{3}}\\\end{aligned}[/tex]

Thank you

Step-by-step explanation:

Here,

[tex] = \frac{ \sqrt{12} }{ \sqrt{3} + 3} [/tex]

is given.

Now, rationalizing it,

[tex] = \frac{ \sqrt{12} }{ \sqrt{3} + 3} \times \frac{ \sqrt{3} - 3 }{ \sqrt{3} - 3} [/tex]

now, simplifying it,

[tex] = \frac{ \sqrt{12 } \times \sqrt{3 } - 3 }{( { \sqrt{3} )}^{2} - 9} [/tex]

or, simplifying it we get,

[tex] = \frac{3}{ - 6} [/tex]

= 1/ -2

Hope it helps...

I assumed you are referring to the Net (take away by the seller after removing their commissions).

Answer:

Selling price

Step-by-step explanation:

To determine what amount goes to the seller, we multiply the selling price of a commodity in question by the percentage (commissions) to the seller.

Note that the resulting amount is the value of the commission paid to the seller, the actual net is gotten by substracting the selling price from the commission paid.

Answer:

picked

Step-by-step explanation:

It is the only one that sounds correct.

Answer:

hi,

i think the answer can be picked

Step-by-step explanation:

picked is the answer

Answer:

value of the variable: 3/2

perimeter: 84 feet

Step-by-step explanation:

Let's find the value of the variable first:

It is a square, so all 4 sides are the same (have the same length)

This means, 3(2f + 4) = 12f + 3

Simplify it,

6f + 12 = 12f + 3

6f = 9

f = 3/2

So, the variable f = 3/2!

Let's find the perimeter:

First, we find the value of one side of the square

12f + 3 is a side

because f = 3/2, we know that the one side of a square is 18 + 3 ft, which is 21 ft

Like I said, all 4 sides are the same in a square, so we can just calculate the length of 1 side, and multiply it by 4!

so 21 * 4 = 84!

The perimeter of this square is 84 feet!

I hope this helps! Please tell me if I did anything wrong, thank you and have a great day =D

Answer:

The values of r = -3/2 ,7

Step-by-step explanation:

2r2 - 11r - 21 = 0.

The is a quadratic equation in the form

2r²-11r -21= 0

Let's determine the value of r using factorization method

2r² -14r +3r -21= 0.

2r(r-7)+3(r-7)= 0

(2r+3)(r-7)= 0

2r+3= 0

2r= -3

r= -3/2

And

r-7= 0

r= 7

The values of r = -3/2 ,7

Answer:

The  95% confidence interval is [tex]0.1193 < p <0.4407[/tex]

Step-by-step explanation:

From the question we are told that

   The sample size is  [tex]m = 30[/tex]

   The sample proportion is  [tex]\r p = 0.28[/tex]

Given that the confidence interval is  95% then the level of significance is mathematically represented as

           [tex]\alpha = 100 - 95[/tex]

           [tex]\alpha = 5\%[/tex]

          [tex]\alpha = 0.05[/tex]

Next we obtain the critical value of the [tex]\frac{\alpha }{2}[/tex] from the normal distribution table, the value is

        [tex]Z_{\frac{ \alpha }{2} } = 1.96[/tex]

Generally the margin of error is mathematically represented as

       [tex]E = Z_{\frac{ \alpha }{2} } * \sqrt{\frac{ ( \r p (1 - \r p ))}{n} }[/tex]

=>    [tex]E = 1.96 * \sqrt{\frac{ (0.28 (1 - 0.28 ))}{ 30} }[/tex]

=>   [tex]E = 0.1607[/tex]

The  95% confidence interval is  

     [tex]\r p - E < p < \r p + E[/tex]

=> [tex]0.28 - 0.1607 < p < 0.28 + 0.1607[/tex]

=> [tex]0.1193 < p <0.4407[/tex]

Answer:

(b

Step-by-step explanation:

the line graph is showing this: x<10

Answer:

Option H (the third option)

Step-by-step explanation:

A person must be at least 10 years old.

Let the person's age be x years

therefore, he has to be x≥ 10 (the person's age has to be equal or more than 10 )

Answer:

ray

Step-by-step explanation:

ray is the answer because it starts with a startline but has no endpoint so it goes on for infinity.

Answer:

8

Step-by-step explanation:

Jason = 22

Taylor = x

Taylor is 8

Answer:

Step-by-step explanation:

From the question

P=2L+2W

where

L is the length

W is the width

To make W the subject move 2L to the left side of the equation

That's

2W = P - 2L

Divide both sides of 2 to make W stand alone

We have

[tex]W = \frac{P - 2L}{2} [/tex]

when

P = 70

L = 22

W is

[tex]W = \frac{70 - 2(22)}{2} \\ W = \frac{70 - 44}{2} \\ W = \frac{26}{2} [/tex]

We have the final answer as

Hope this helps you

Answer:

Width W = 13

Step-by-step explanation:

P = 2L + 2W

if the perimeter P = 70

and Length L = 22

find the Width W

P = 2L + 2W

70 = 2(22) + 2W

70 - 44 = 2W

26 = 2W

W = 26 / 2

W = 13

therefore,

the Width W = 13

check:

P = 2L + 2W

70 = 2(22) + 2(13)

70 = 44 + 26

70 = 70   --- OK

Answer:

14.6 feet

Step-by-step explanation:

Let A be the area of a square and S be the length of one of its sides.

The area of a square is A = S². We know A = 214 in this problem, so:

214 = S²

√214 = S

S ≈ 14.629 ≈ 14.6 feet (to the nearest tenth of a foot)

Answer:

AC = 10 units

Step-by-step explanation:

From the picture attached,

Triangle ABC is a right triangle.

Opposite side of the right angle B = Hypotenuse (AC)

and the other two legs are AB and BC

Pythagoras Theorem states

(hypotenuse)² = (leg 1)² + (leg 2)²

AC² = AB² + BC²

AC² = (6)² + (8)²

AC² = 36 + 64

AC² = 100

AC = √100

AC = 10

Therefore, length of the hypotenuse (AC) = 10 units will be the answer.

Answer: $139.23

Step-by-step explanation: Take 50% of original dress price and add price of shoes. Subtract 10% of that.

Answer:

[tex]2x^3+9x^2+16x+21[/tex]

Step-by-step explanation:

So we have the expression:

[tex](x+3)(2x^2+3x+7)[/tex]

Use the distribute property. Multiply each term on the right by (x+3):

[tex](2x^2)(x+3)+(3x)(x+3)+(7)(x+3)[/tex]

Distribute further:

[tex]=(2x^3+6x^2)+(3x^2+9x)+(7x+21)[/tex]

Combine like terms:

[tex]=(2x^3)+(6x^2+3x^2)+(9x+7x)+21\\=2x^3+9x^2+16x+21[/tex]

A polynomial in standard form has terms in descending order based on degree.

And we have that. Thus, we are done :)

Answer:

Step 2

Step-by-step explanation:

In step 2 the expression was 40+20 which would have been 60 but he might have thought addition sign was subtraction so he did 40-20 which is 20 so he is wrong made mistake in step 2

Answer:

Step-by-step explanation:

1. If x represents a number, then x^2 represents its square. If y represents a second number, then the sum of that square and the second number is ...

  x^2 + y

__

2. The difference of a number (n) and 7 is (n-7). Three times that difference is ...

  3(n - 7)

__

3. If x represents a number, then the product of 37 and a number is 37x. 9.85 less than that is ...

  37x - 9.85

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

Work Shown:

Multiply the first coefficient (6) and the last term (-7) to get -42. We need to find factors of -42 that add to -19

Turns out that those two numbers are -21 and 2, which you find by trial and error.

-21 * 2 = -42

-21 + 2 = -19

Break up -19x as -21x+2x and use the factor by grouping method

6x^2 - 19x - 7

6x^2 - 21x + 2x - 7

(6x^2 - 21x) + (2x - 7)

3x(2x - 7) + 1(2x - 7)

(3x+1)(2x-7)

The factorization represents the length*width, since this product is equal to the rectangle's area.

----------------------

Plug x = 15 into each factor

3x+1 = 3*15+1 = 46

2x-7 = 2*15-7 = 23

The length and width are 46 and 23

Answer:

hello your question is incomplete attached is the complete question

answer : 25/2 ( A )

Step-by-step explanation:

using Stokes' Theorem to calculate

F = 5yi + 7xj  + [tex]z^3 k[/tex]

line y = 5 - 2x

attached below is the remaining part of the solution to the question

Answer:

[tex](x+8)^2 = 86[/tex]

Step-by-step explanation:

Given

[tex]x^2 + 16x = 22[/tex]

Required

Determine an equivalent equation

[tex]x^2 + 16x = 22[/tex]

Get the coefficient of x

[tex]Coefficient = 16[/tex]

Divide this by 2

[tex]Result = \frac{16}{2}[/tex]

[tex]Result = 8[/tex]

Take its square

[tex]Result = 8^2[/tex]

[tex]Result = 64[/tex]

Add this to both sides of the equation

[tex]x^2 + 16x + 64 = 22 + 64[/tex]

[tex]x^2 + 16x + 64 = 86[/tex]

Expand the expression on the right hand side

[tex]x^2 + 8x + 8x + 64 = 86[/tex]

Factorize

[tex]x(x+8)+8(x+8) = 86[/tex]

[tex](x+8)(x+8) = 86[/tex]

[tex](x+8)^2 = 86[/tex]

Hence, the equivalent equation is [tex](x+8)^2 = 86[/tex]

Answer:

b/2-1 has a verbal phrase can be one minus the quotient of b and 2.

Answer: 20, 40, 60, 80, 100,....

Step-by-step explanation:

Given that :

It is possible to create teams of 4 for a relay race with no student leftover

Also,

It is possible to create teams of 5 for dodgeball with no student left over from the same class

To deduce the possible number of students in the class, then the number of students should be a multiple of both 4 and 5

Multiples of 4 include = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100,....

Multiples of 5 : 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100,....

Multiples common to both 4 and 5 : 20, 40, 60, 80, 100,....

Answer:

w=6

Step-by-step explanation:

Since the triangles are similar, we can use ratios to solve

4          3

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

8           w

4w = 3*8

4w = 24

Divide by 4

4w/4 = 24/4

w = 6

Answer:

As hard as this may seem, it's actually quite simple. Because these two figures are similar, their sides can be compared.

See how on the left side of both of the triangles the numbers are 4 and 8? This shows that the left triangle is twice as small as the right one, which means that if you multiply any of the sides of the triangle on the left by 2, you'll get the triangle on the right.

We can apply this to w. Look at the left triangle on the bottom and see how there is a 3. Well, we've already noticed how the triangle on the left just needs to be multiplied by 2 in order to get to the one on the right, so that's what we should do! When you multiply 3 by 2, you get 6 which is w.

So, long answer short, w is 6.