A book store had 30816 exercise books which were paclced in cartons each carton contained 24 exercise books the mass of an empty carton was 2kg and a full carton 12kg

Answer:

5.5

Step-by-step explanation:

[tex] \frac{1}{6 - d} = \frac{1}{d - 5} \\ \\ \therefore \: 6 - d = d - 5 \\ \\ 6 + 5 = d + d \\ \\ 11 = 2d \\ \\ d = \frac{11}{2} \\ \\ d = 5.5[/tex]

Answer:

$2182.13

Step-by-step explanation:

Simple interest (I) is calculated as

I = [tex]\frac{PRT}{100}[/tex] ( P is principal, R is rate of interest, T is time in years )

Here P = $34,500 , R = 6.9 and T = [tex]\frac{11}{12}[/tex] , then

I = [tex]\frac{34500(6.9)(\frac{11}{12}) }{100}[/tex]

  = 345 × 6.9 × [tex]\frac{11}{12}[/tex]

  = $2182.13

Answer:

x = 1, y = 2 , z = 3

Step-by-step explanation:

[tex]6x\:+\:2y\:-4z\:=\:-2 \ \ \ \ \ \ \ \ \ -----( 1 ) \:\\\\-3x-4y\:+2z\:=\:-5 \ \ \ \ \ \ ------( 2 ) \:\\\\4x-\:6y\:+3z\:=\:1 \ \ \ \ \ \ \ \ \ \ \ \ ------- ( 3 ) \\\\( 2 ) \times 2=> -6x -8y + 4z = -10 \ \ \ \ \ \ \ -----( 4)[/tex]

Now add ( 1 ) and  (4)

[tex]6x +2y -4z = - 2\\\\-6x-8y - 4z = -10\\\\=>0x -6y + 0 = - 12\\\\-6y = -12[/tex]

y = 2

Now multiply ( 1 ) by  2 and (3) by 3

[tex](1) \times 2 => 12x + 4y -8z = -4\\\\(3) \times 3 => 12x -18y +9z = 3\\\\Subtract \ the \ equation : ( 1) - ( 3) => 0x +22y -17z = -7[/tex] ------ ( 5 )

Substitute y = 2 in ( 5 ) :

[tex]22(2) - 17z = - 7\\\\ 44 - 17z = - 7\\\\ -17z = - 7 - 44\\\\ -17z = -51\\\\[/tex]

z = 3

Substitute z = 3 and y = 2 in ( 1 ) :

[tex]6x + 2y - 4z = - 2\\\\6x + 2( 2) -4( 3) = -2\\\\6x + 4 - 12 = -2\\\\6x - 8 = - 2\\\\6x = - 2 + 8 \\\\6x = 6\\[/tex]

x = 1

Answer:

it says round to the nearest 10th so it wouldn't be 81, it would be 81.8%

Answer: 15.3 cm

Step-by-step explanation:

The actual length of the line in question is 1.53km.

The scale is 10 cm to 1 km.

You can therefore use direct proportion to solve this.

Assume the length on the drawing is x:

10cm  :   1km

x cm  :   1.53 km

Cross multiply:

x = 15.3 cm

Answer:

2+3+4+6 = 15 parts

Village B gets 3 of 15 parts

3/15 * 30000 = 6000 bags

Village C gets 4 of 15 parts

4/15 * 6000 = 8000 bags

Answer:

each "share" needs "15" (2+3+4+6) "portions/bags"

2000 distributions

A-4000 bags/80000 kg

B-6000 bags/120000 kg

C-8000 bags/1680000 kg

D-12000 bags/240000 kg

Step-by-step explanation:

9514 1404 393

Answer:

  0.261 ohm

Step-by-step explanation:

If the radius increases by a factor of 0.7/0.4= 7/4, the square of this factor is (7/4)^2 = 49/16. The inverse of this square is 16/49, which is the factor by which the resistance changed.

The resistance of the larger wire is ...

  (16/49)(0.80 ohm) ≈ 0.261 ohm

Answer:

A = 41.4°

Step-by-step explanation:

Reference angle = A

Length of Adjacent side = 6

Length of Hypotenuse = 8

Apply the trigonometric function, CAH.

Cos A = Adj/Hyp

Substitute

[tex] Cos(A) = \frac{6}{8} [/tex]

[tex] A = Cos^{-1}(\frac{6}{8}) [/tex]

A = 41.4° (approximated to the nearest tenth)

Answer:

x = 1 and y = 1

Step-by-step explanation:

You can eliminate x first to get the value of y which is 1 and then replace it in one of the equations.

Answer:

4. (2, 3)

5. (0, 1)

7. (-1, 2)

Step-by-step explanation:

I hope this helps! Have a nice dayy! :)

You're very close. Choices D and E are two of the three answers. The third answer is choice G (-1,2)

If you plug the coordinates of the points into the inequality, you should get a true statement.

For instance, let's try the coordinates of choice G

[tex]-2x + 3y\ge 3\\\\-2(-1) + 3(2)\ge 3\\\\2 + 6\ge 3\\\\8\ge 3\\\\[/tex]

Which is true since 8 is indeed greater than 3. That verifies point G is a solution point. A similar story happens with points D and E as well.

----------

If you tried something like choice A, then,

[tex]-2x + 3y\ge 3\\\\-2*(2) + 3(-3)\ge 3\\\\-4 - 9\ge 3\\\\-13\ge 3\\\\[/tex]

Which is false because -13 is not greater than 3, and -13 is not equal to 3 either. So choice A is a non-answer. You should find that choices B, C, and F are also non-answers.

----------

The graph is below. Notice how points D, E and G are either in the blue shaded region or on the boundary. The boundary line is solid (due to the "or equal to" as part of the inequality sign), so points on the solid boundary line are part of the solution set. The graph is a quick way to visually confirm the answers. I used GeoGebra to make the graph.

So that's why the 3 answers are D, E and G.

Answer:

The area is 91 cm²

Step-by-step explanation:

The shape is a kite.

area of a kite = ½(p*q)

Where, p and q are the diagonals of the kite.

p = 13 cm

q = 7 + 7 = 14 cm

The area of the kite = ½(13 * 14)

= ½(182)

Area = 91 cm²

Answer:

Profit = Selling price - Variable cost  

Formulas:  

F2 =SUMPRODUCT(B2:E2,$B$16:$E$16) copy to F2:F12, F14  

Optimal solution: The company should produce the following quantities (in pounds) of the four varieties of nuts.  

Whole = 1000  

Cluster = 500  

Crunch = 80  

Roasted = 200  

Total profit = $ 2913.20

Step-by-step explanation:

[tex]\huge\textsf{Hey there!}[/tex]

[tex]\large\textsf{Guide}\downarrow[/tex]

[tex]\large\textsf{Penny: 1 cent} \\\large\textsf{Nickel: 5 cents}\\\large\textsf{Dime: 10 cents}\\\large\textsf{Quarter: 25 cents}\\\large\textsf{Half dollar: 50 cents}\\\large\textsf{1 bill = 1 dollar}[/tex]

[tex]\large\textsf{6 dimes:}\downarrow[/tex]

[tex]\large\textsf{= 10 + 10 + 10 + 10 + 10 + 10}[/tex]

[tex]\large\textsf{= 20 + 20 + 20}[/tex]

[tex]\large\textsf{= 40 + 20}[/tex]

[tex]\large\textsf{= \bf 60}[/tex]

[tex]\large\textsf{6 dimes = \bf 60 cents}[/tex]

[tex]\large\textsf{8 nickels}[/tex]

[tex]\large\textsf{= 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5}[/tex]

[tex]\large\textsf{= 10 + 10 + 10 + 10}[/tex]

[tex]\mathsf{= 20 + 20}[/tex]

[tex]\large\textsf{= \bf 40}[/tex]

[tex]\large\textsf{8 nickels = \bf 40 cents}[/tex]

[tex]\large\textsf{3 one dollar bills}[/tex]

[tex]\large\textsf{= 1 + 1 + 1}[/tex]

[tex]\large\textsf{= 2 + 1 }[/tex]

[tex]\large\textsf{= \bf 3}[/tex]

[tex]\large\textsf{3 one dollar bills = \bf 3 dollars}[/tex]

[tex]\large\textsf{NOW LETS SOLVE FOR YOUR EQUATION}[/tex]

[tex]\large\textsf{3.00 + 0.60 + 0.40}[/tex]

[tex]\large\textsf{= 3.60 + 0.40 }[/tex]

[tex]\large\textsf{= \bf \$4}[/tex]

[tex]\boxed{\boxed{\large\textsf{Therefore, your answer is: \huge \bf \$4}}}\huge\checkmark[/tex]

[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

1)  2/20 x 200 = 1/10 x 200 = 20

2) 3/20 x 200 = 30

3) 4/20 x 200 = 1/5 x 200 = 40

4) 5/20 x 200 = 1/4 x 200 = 50

5) 18/20 = 9/10 x 200 = 180

The answers are as follows part A = 30m+15  part B =3m+15+27m

and partC = 30m+15

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition,substraction, multiplication and division.

Part A:- Two expressions that are equivalent to the given expressions are:-

3m   +   15   +   27m

30m  +   15

Part B:  Show that one of your expressions in Part A is equivalent to the given expression using algebraic properties.

3  (  m   +   5    +   9m   )

Open the bracket by multiplying 3 by what is in the bracket

3m   +   15   +   27m

Part C: Show that your other expression from Part A is equivalent to the given expression by substituting a number for m.

3   (  m    +   5   +   9m  )

Open the bracket by multiplying 3 by what is in the bracket

3m    +    15    +     27m

Collect like terms together

3m    +     27m  +   15

=   30m   +    15

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Answer: [tex]14\ ft[/tex]

Step-by-step explanation:

Given

Length of rectangle is [tex]6\ ft[/tex]

Perimeter must be greater than 40 ft

Suppose l and w be the length and width of the rectangle

[tex]\Rightarrow \text{Perimeter P=}2(l+w)\\\Rightarrow P\geq 40\\\Rightarrow 2(l+w)\geq40\\\Rightarrow l+w\geq20\\\Rightarrow w\geq20-6\\\Rightarrow w\geq14\ ft[/tex]

So, the smallest width can be [tex]14\ ft[/tex]

Answer:

62

Step-by-step explanation:

t=digit in the tens place

u=digit in the units place

t=3*u

original number=t*10+u

number with reversed digits=u*10+t

u*10+t=t*10+u-36

u*10+(3*u)=(3*u)*10+u-36

10u+3u-30u-u=-36

-18u=-36

u=2

t=3*u=6

Original number = 62

Check the solution:

6=3*2 ok

26=62-36 ok

Answer:

9 hundreds that is the answer

Answer:

460 is part of the confidence interval, which means that we cannot say that there is significant evidence that the mean mathematics SAT score for entering freshmen class is greater than 460

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.99}{2} = 0.005[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.005 = 0.995[/tex], so Z = 2.575.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 2.575\frac{101}{\sqrt{90}} = 27.4[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 436 - 27.4 = 408.6.

The upper end of the interval is the sample mean added to M. So it is 436 + 27.4 = 463.4.

460 is part of the confidence interval, which means that we cannot say that there is significant evidence that the mean mathematics SAT score for entering freshmen class is greater than 460

Answer:

20°

Step-by-step explanation:

perpendicular from the center on a chord of a circle always bisects the chord.

AR=BR

∴m arcAC=m arc BC=20°

Answer:

ans:

Match the metric measurement on the left with an equivalent unit of measurement on the right are as follows;

0.3 hectoliter       3 deciliters

0.03 liters             30 milliliters

30 centimeter     3 Deciliters

3000 Milliliters    0.3 Decaliters

A standard unit of measurement is a quantifiable language that describes the magnitude of the quantity.

Match the metric measurement on the left with an equivalent unit of measurement on the right is determined in the following steps given below.

1. 0.3 hectoliter = 0.3 × 10 = 3 deciliters

2. 0.03 liters = 0.03 × 1000 = 30 mililiters

3. 3 Centiliters = 0.3 Deciliters then 30 centimeter = 3 Deciliters

4. 3000 Milliliters = 0.3 Decaliters

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Answer:

C.-37/7

Step-by-step explanation:

Given the following data;

Points (x, y) = (5, -6)

Slope, m = -1/7

Mathematically, the equation of a straight line is given by the formula;

y = mx + c

Where;

m is the slope.

x and y are the points

c is the intercept.

To find the y-intercept of the line, we would use the following formula;

y - y1 = m(x - x1)

y - (-6) = -⅐(x - 5)

y + 6 = -⅐x + 5/7

y = -⅐x + (5/7 - 6)

y = -⅐x - 37/7 = mx + c

Therefore, y-intercept (c) = -37/7

Answer:

s(t) = 160/3  ( 1 - e^(-3t / 200) )

Step-by-step explanation:

volume of pure water in tank  = 1000 L

Brine contains 0.04kg of salt/L

Inflow rate of Brine containing 0.04kg of salt/L = 5L/min

Brine containing 0.06 kg of salt/L

Inflow rate of Brine containing 0.06 kg of salt/L = 10L/min

Solution is thoroughly mixed and drains from tank at 15L/min

a) Determine the amount of salt is in the tank after t minutes

rate of salt entering = 0.2 + 0.6 = 0.8 kg/min

rate of salt leaving = s/1000 * 15

amount of salt at time (t) = s(t)

initial condition s( 0 ) = 0

ds/dt = 0.8 - 15s/1000 = 0.8 - 3s/200

200 ds/dt = ( 160 - 3s )

-200/3  In ( 160 - 3s ) = t + c

Given that ;  t = 0 , s = 0    

c =  - 200/3  In ( 160 )

∴  -200/3  In ( 160 - 3s ) = t - 200/3  In ( 160 )

- 200/3  [ In ( 60 - 3s ) - In ( 160 ) ] = t

therefore:  

In ( 160 - 3s / 160 ) = -3t/200

= ( 160 - 3s / 160 ) = e ^ (-3t/200 )

Hence amount of salt in tank after t minutes

s(t) = 160/3  ( 1 - e^(-3t / 200) )

Answer:

4)8 goats, 3 hens.

Step-by-step explanation:

8*4=32

3*2=6

32+6=38

Answer:

a. The mean is 4.5 and the standard deviation is 0.3818.

b. 4.5

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 4.5 and a standard deviation of 2.291.

This means that [tex]\mu = 4.5, \sigma = 2.291[/tex]

a. Find the mean and the standard deviation of the resulting distribution of sample means for n=36.

By the Central Limit Theorem, the mean is 4.5 and the standard deviation is [tex]s = \frac{2.291}{\sqrt{36}} = 0.3818[/tex]

The mean is 4.5 and the standard deviation is 0.3818.

b. The mean of the resulting distribution of the sample means is:________

By the Central Limit Theorem, 4.5.

Answer:

{2,4,6}

Step-by-step explanation:

Hope it helps you

Answer:

17

Step-by-step explanation:

Properties used:-

All sides of rhombus are equal therefore in the triangles

EQUAL SIDE OPPOSITE TO ANGLES, ANGLES BECOME EQUAL

then we use alternate interior angles

Then we get,

3x-11=x+23

2x=34

x=17