Q1.

Diaries are sold in boxes of 12

Pencils are sold in boxes of 10

Rulers are sold in boxes of 6

A teacher wants to buy the same number of diaries, pencils and rulers.

Work out the smallest number of boxes of each item he could buy.

boxes of diaries

boxes of pencils

boxes of rulers

Tebal

Two shaped are merged so

One is square and the other is trapezoid so,

AREA OF SQUARE=4*4

=16

AREA OF TRAPEZOID=(2+4)x4/2

So,rhe answer will be

12+16=28

HOPE IT IS HELPFUL

Answer: 28 units^2

Step-by-step explanation:

You basically have a square and a trapezoid merged together

4*4=16 for the square

(2+4)*4/2=12 for the trapezoid

so

12+16=28 is your answer

Answer:

C: x = 10

Step-by-step explanation:

PO = QR (so having equal central angles)

Now

4x-11 = 2x+9

4x-2x = 9+11

2x = 20

Dividing both sides by 2

x = 10

Answer:

x=10

Step-by-step explanation:

2x+9=4x-11

-2x      -2x

9=2x-11

+11  +11

20=2x

:2     :2

x=10

Answer:

z=1/9w

Step-by-step explanation:

Equation w = 9z best describes the proportional relationship between w and z.

Data has been given
w = 18   45   81
z  =  2     5     9

proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense that are they directly proportional or inversely proportional to each other.

Clearly from the data as z increases w increases so it implies w is directly proportional to z.
w ∝ z
w = kz - - - - - -  (1)
Where k is proportionality constant.
From data put w = 18 and z = 2
18=k*2
k=18/2
k=9
put k in equation w =kz
w = 9z
It shows that w is directly proportional to z by the constant of proportionality 9.

Thus equation w = 9z best describes the proportional relationship between w and z.

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Answer:

24?

Step-by-step explanation:

Answer:

4 1/2 meters is equal to 4.5

Step-by-step explanation:

This is the correct answer to 4 1/2 meters. :)

Answer:

a) [tex]\frac{(8)(30.23)^2}{20.09} \leq \sigma^2 \leq \frac{(8)(30.23)^2}{1.65}[/tex]

[tex] 363.90 \leq \sigma^2 \leq 4430.80[/tex]

Now we just take square root on both sides of the interval and we got:

[tex] 19.08 \leq \sigma \leq 66.56[/tex]

b) For this case we are 98% confidence that the true deviation for the population of interest is between 19.08 and 66.56

Step-by-step explanation:

423.6, 487.3, 453.2, 402.9, 483.0, 477.7, 442.3, 418.4, 459.0

Part a

The confidence interval for the population variance is given by the following formula:

[tex]\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}[/tex]

On this case we need to find the sample standard deviation with the following formula:

[tex]s=sqrt{\frac{\sum_{i=1}^8 (x_i -\bar x)^2}{n-1}}

And in order to find the sample mean we just need to use this formula:

[tex]\bar x =\frac{\sum_{i=1}^n x_i}{n}[/tex]

The sample deviation for this case is s=30.23

The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:

[tex]df=n-1=9-1=8[/tex]

The Confidence interval is 0.98 or 98%, the value of [tex]\alpha=0.02[/tex] and [tex]\alpha/2 =0.01[/tex], and the critical values are:

[tex]\chi^2_{\alpha/2}=20.09[/tex]

[tex]\chi^2_{1- \alpha/2}=1.65[/tex]

And replacing into the formula for the interval we got:

[tex]\frac{(8)(30.23)^2}{20.09} \leq \sigma^2 \leq \frac{(8)(30.23)^2}{1.65}[/tex]

[tex] 363.90 \leq \sigma^2 \leq 4430.80[/tex]

Now we just take square root on both sides of the interval and we got:

[tex] 19.08 \leq \sigma \leq 66.56[/tex]

Part b

For this case we are 98% confidence that the true deviation for the population of interest is between 19.08 and 66.56

Answer:

6*3 = 18 candies - Ahmad

6*4 = 24 candies - Zara

6*5 = 30 candies - Bilal

Step-by-step explanation:

3+4+5= 12 parts

72 : 12 = 6 candies is one part

6*3 = 18 candies - Ahmad

6*4 = 24 candies - Zara

6*5 = 30 candies - Bilal

Answer:

my butt

Step-by-step explanation:

my poop

dxhfhdjdjsjajalalalalqlqlqlalalal

Answer:

XY = 5268

Step-by-step explanation:

XY = XZ (originating from the same point)

85b+83=91b-283

85b-91b=-283-83

-6b=-366

Dividing both sides by -6

b = 61

Now

XY = 85b+83

= 85(61)+83

= 5268

Answer:

28 are large or blue.

Step-by-step explanation:

In this case they ask us how many are big or blue, that is, either of the two characteristics are valid, they tell us the following things in the statement:

17 large and blue, that is, 17 comply with what they ask us, since they are blue or large.

3 small and blue, that is 3 since they are blue, and we must take them into account.

8 large and red, you have to add 8 more because there are 8 large ones here.

12 small and red, none of them meet the requested characteristics, that is, they are in total:

17 + 3 + 8 = 28

28 are large or blue.

Answer:

y = x/6 - 17/6

Step-by-step explanation:

     x - 6y = 17

<=>6y = x - 17  

<=> y  =x/6 - 17/6

Hope this helps!

Answer:

by finding something to factor it by

Answer:

1) first eliminate constant (number without variable) you eliminate constant by doing the inverse operation (if constant is being added, then subtract) (if constant is being subtracted, then add it)

ex: if  x+9=32

subtract 9 from both sides to get rid of it

x=23

2) if there is another constant but this constant is being multiplied/divided then do the opposite operation to remove it

you could multiply by 3 on both sides:

x+9=69

x=60

Answer:

22 is the answer but which country are you from

Answer:

22

Step-by-step explanation:

Answer:

-6ab^3sqrtac^2 option b

Step-by-step explanation:

i just did it

Answer:

Step-by-step explanation:

Answer:

  D.  129°

Step-by-step explanation:

Angles XZY and XZV form a linear pair, so are supplementary.

 angle XZV = 180° -51° = 129°

Answer:

8

Step-by-step explanation:

[tex] a = 1 - \sqrt{2} [/tex]

[tex] (a - \dfrac{1}{a})^3 = [/tex]

[tex] = (\dfrac{a^2}{a} - \dfrac{1}{a})^3 [/tex]

[tex] = (\dfrac{a^2 - 1}{a})^3 [/tex]

[tex] = (\dfrac{(a + 1)(a - 1)}{a})^3 [/tex]

[tex] = (\dfrac{(1 - \sqrt{2} + 1)(1 - \sqrt{2} - 1)}{a})^3 [/tex]

[tex]= (\dfrac{(2 - \sqrt{2})(-\sqrt{2})}{1 - \sqrt{2}})^3[/tex]

[tex]= (\dfrac{(-2\sqrt{2} + \sqrt{2}\sqrt{2}}{1 - \sqrt{2}})^3[/tex]

[tex]= (\dfrac{2 - 2\sqrt{2}}{1 - \sqrt{2}})^3[/tex]

[tex]= (\dfrac{2(1 - \sqrt{2})}{1 - \sqrt{2}})^3[/tex]

[tex] = 2^3 [/tex]

[tex] = 8 [/tex]

Answer: [tex]x = \frac{35}{2}[/tex] or [tex]x = 17.5[/tex]



Step-by-step explanation:

[tex]\frac{4}{7} = \frac{10}{x}[/tex]

[tex]\frac{4x}{4} = \frac{70}{4}[/tex]

[tex]x = \frac{35}{2}[/tex]

or [tex]x = 17.5[/tex]

Answer:

cos(β)  = √6/3

Step-by-step explanation:

Given  β lies in the fourth quadrant and sin (β) = -√3/3

we know that the trigonometry formula

sin²(β)+cos²(β) = 1

cos²(β) = 1- sin²(β)

cos²(β) = 1- ( -√3/3)²

           = [tex]1-\frac{3}{9} } } =\frac{6}{9}[/tex]

cos(β) =  √6/9 = √6/3

we Know that β lies in the fourth quadrant  so cos(β) is Positive

cos(β)  = √6/3

Answer:

a) margin of error ME = 5.77

b) Margin of error becomes smaller

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

x+/-ME

Where margin of error ME = zr/√n

a)

Given that;

Mean = x

Standard deviation r = 25

Number of samples n = 72

Confidence interval = 95%

z(at 95% confidence) = 1.96

Substituting the values we have;

ME = 1.96(25/√72)

ME = 1.96(2.946278254943)

ME = 5.774705379690

ME = 5.77

b)

For n = 89

ME = 1.96(25/√89)

ME = 1.96(2.649994700015)

ME = 5.193989612031

ME = 5.19

5.19 is smaller than 5.77 in a) above. So,

Margin of error becomes smaller

Answer:

4.8 * 10^15 Newton

Step-by-step explanation:

Electric field is electric force  created by a unit charge. Mathematically it is defined as

Electric field = electric force /charge in coulomb  _____(1)

given

Electric field =  1.2 * 10^6 N/C

charge = 4.0 * 10^9 C

substituting above value in equation 1 we have

1.2 * 10^6 N/C =  electric force/4.0 * 10^9 C

=> 1.2 * 10^6 N/C * 4.0 * 10^9 C = electric force

=> electric force = 4.8 * 10^15

Thus, electric force acting on the toner particle is 4.8 * 10^15 Newton

Answer:

Step-by-step explanation:If you choose any 3 of the 7 vertices, you can connect them with lines to create a unique triangle.

So, the question becomes "In how many different ways can we select 3 vertices from 7 vertices?"

Since the order in which we select the 3 vertices does not matter, we can use COMBINATIONS.

We can select 3 vertices from 7 vertices in 7C3 ways.

Answer:

Step-by-step explanation:

Just integrate r(t) with respect to t  

Integrate r(t) dt = 400t -(4t^2)/2 + C

                      = 400t -4t^2 + C

where C is a constant

then replace the above answer with 30 and 0, then do subtraction for both answers

hence the amount of water flows during first 30 mins is

=   {400*30 - 4*(30)^2 + C} - {400*0 - 4*(0)^2 + C}

=  12000 - 3600

=   8400 liters

The amount of water that flows from the tank during the first 30 minutes is 8,400Liters.

Based on the information definite integral will be use to find the amount of water.

Using this formula

[tex]\int_{a}^{b} r(t) dt\\\\\\Where:\\r(t)=400-8t\\\\\\ \int_{a}^{b} r(t) dt\ = \int_{0}^{30} (400-8t) dt\\\\\\\\ \int_{a}^{b} r(t) dt\ = (400t-8t^2/2)_{0}^{30}\\\\\\\\ = (400t-4t^2)_{0}^{30}\\\\\\\\=(400\times30)-4(30)^2\\\\\\=12,000-4(900)\\\\\\=12,000-3,600\\\\\\=8,400\ liters\\[/tex]

Inconclusion the amount of water that flows from the tank during the first 30 minutes is 8,400Liters.

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Answer:

  (x, y, z) = (1, -3, 1)

Step-by-step explanation:

Any number of calculators and/or web sites can be used to solve this system of equations. It can be helpful to familiarize yourself with your graphing calculator's capabilities in this area. The solution from one such site is shown below:

  (x, y, z) = (1, -3, 1)

__

Both y and z show up in these equations with coefficients that have a magnitude of 1. This means you can easily use one of those equations to create a substitution for y or for z.

Using the first equation to write an expression for z, we have ...

  z = 4x +3y +6

Substituting that into the second and third equations gives ...

  6x -y +3(4x +3y +6) = 12   ⇒   18x +8y = -6

  8x +2y +4(4x +3y +6) = 6   ⇒  24x +14y = -18

Now, we can subtract 4 times the first equation from 3 times the second to eliminate x:

  3(24x +14y) -4(18x +8y) = 3(-18) -4(-6)

  10y = -30

  y = -3

Substituting into the first equation (of the equations in x and y), we have ...

  18x +8(-3) = -6

  18x = 18

  x = 1

Finally, substituting into the equation for z gives ...

  z = 4(1) +3(-3) +6 = 1

The solution is (x, y, z) = (1, -3, 1).

___

The equations can also be solved using Cramer's rule, elimination, matrix methods, and other means. When solving by hand, the method of choice will often depend on what you're familiar with and what the coefficients are.

Answer:

7

Step-by-step explanation:

∑ᵢ₌₁³ (4 × (½)ⁱ⁻¹)

This is the sum of the first 3 terms of the sequence.

The first 3 terms are:

4 × (½)¹⁻¹ = 4

4 × (½)²⁻¹ = 2

4 × (½)³⁻¹ = 1

So the sum is:

∑ᵢ₌₁³ (4 × (½)ⁱ⁻¹) = 4 + 2 + 1 = 7

Answer: The system of equations is:

x + 2y + 2 = 4

y - 3z = 9

z = - 2

The solution is: x = -22; y = 15; z = -2;

Step-by-step explanation: ONe way of solving a system of equations is using the Gauss-Jordan Elimination.

The method consists in transforming the system into an augmented matrix, which is writing the system in form of a matrix and then into a Row Echelon Form, which satisfies the following conditions:

For this question, the matrix is a Row Echelon Form and is written as:

[tex]\left[\begin{array}{ccc}1&2&2\\0&1&3\\0&0&1\end{array}\right][/tex][tex]\left[\begin{array}{ccc}4\\9\\-2\end{array}\right][/tex]

or in system form:

x + 2y + 2z = 4

       y + 3z = 9

               z = -2

Now, to determine the variables:

z = -2

y + 3(-2) = 9

y = 15

x + 30 - 4 = 4

x = - 22

The solution is (-22,15,-2).

Answer:

(A)129 Pounds

Step-by-step explanation:

Let x be the number of 23% zink alloy

Therefore:

Since the total result is 516 pounds

The number of pounds of 42% zink alloy =516-x pounds

We then have the resulting equation:

0.23x+0.42(516-x)=0.3725*516

0.23x+216.72-0.42x=192.21

Colect like terms

0.23x-0.42x=192.21-216.72

-0.19x=-24.51

Divide both sides by 129

x=129 pounds

Therefore, the number of pounds of 23% zink alloy that must be mixed is 129 pounds.

Answer:

  0.78%

Step-by-step explanation:

The percentage tax rate required is t such that ...

  825t = 6.5 . . . . . milliions of dollars

  t = 6.5/825

As a percentage, ...

  t = 6.5/825 × 100% = 0.7878...% ≈ 0.78%

_____

Comment on rounding

Ordinarily, this value would be rounded to 0.79%. Property tax rates are often expressed in mils, or dollars per thousand. In that form, the tax rate would be 7.88‰ when rounded to two decimal places.

Answer:

The temperature difference in 5 minutes will be 12.38ºC

Step-by-step explanation:

The difference in temperature after t minutes is given by the following equation:

[tex]T(t) = T(0)(1-r)^{t}[/tex]

In which T(0) is the initial temperature and r is the decrease rate, as a decimal.

Decreases by 5% every minute.

This means that [tex]r = 0.05[/tex]

What will the temperature difference be in 5 minutes if it is currently 16°C

This is T(5) when [tex]T(0) = 16[/tex]

So

[tex]T(t) = T(0)(1-r)^{t}[/tex]

[tex]T(t) = 16(1-0.05)^{t}[/tex]

[tex]T(t) = 16*(0.95)^{t}[/tex]

[tex]T(5) = 16*(0.95)^{5} = 12.38[/tex]

The temperature difference in 5 minutes will be 12.38ºC

Answer:

5 times

Step-by-step explanation:

There is a 1/2 (50%) chance each time it is flipped that it will land on heads. Therefore, if flipped 10 times, 1/2 of 10 is 5