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2 years ago

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A sample of 75 concrete blocks had a mean mass of 38.3 kg with a standard deviation of 0.6 kg.

1 answer:

Scilla [17]2 years ago

8 0

The answer will be a

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Jenna eats dinner at a restaurant. Her bill is $14.50 Jenna pays her bill and leaves a tip. Write an inequality to represent the

Sophie [7]

Answer:

Step-by-step explanation:

x>14.50+y

7 0

2 years ago

A store sells 8 colors of balloons with at least 28 of each color. How many different combinations of 28 balloons can be chosen?

Len [333]

Answer:

(a) $Selection = 6724520$

(b) $At\ most\ 12 = 6553976$

(c) $At\ most\ 8 = 6066720$

(d) $At\ most\ 12\ red\ and\ at\ most\ 8\ blue = 5896638$

Step-by-step explanation:

Given

$Colors = 8$

$Balloons = 28$ --- at least

Solving (a): 28 combinations

From the question, we understand that; a combination of 28 is to be selected. Because the order is not important, we make use of combination.

Also, because repetition is allowed; different balloons of the same kind can be selected over and over again.

So:

$n => 28 + 8-1$ $= 35$

$r = 28$

$Selection = ^{35}^C_{28$

$Selection = \frac{35!}{(35 - 28)!28!}$

$Selection = \frac{35!}{7!28!}$

$Selection = \frac{35*34*33*32*31*30*29*28!}{7!28!}$

$Selection = \frac{35*34*33*32*31*30*29}{7!}$

$Selection = \frac{35*34*33*32*31*30*29}{7*6*5*4*3*2*1}$

$Selection = \frac{33891580800}{5040}$

$Selection = 6724520$

Solving (b): At most 12 red balloons

First, we calculate the ways of selecting at least 13 balloons

Out of the 28 balloons, there are 15 balloons remaining (i.e. 28 - 13)

So:

$n => 15 + 8 -1 = 22$

$r = 15$

Selection of at least 13 =

$At\ least\ 13 = ^{22}C_{15}$

$At\ least\ 13 = \frac{22!}{(22-15)!15!}$

$At\ least\ 13 = \frac{22!}{7!15!}$

$At\ least\ 13 = 170544$

Ways of selecting at most 12 =

$At\ most\ 12 = Total - At\ least\ 13$ --- Complement rule

$At\ most\ 12 = 6724520- 170544$

$At\ most\ 12 = 6553976$

Solving (c): At most 8 blue balloons

First, we calculate the ways of selecting at least 9 balloons

Out of the 28 balloons, there are 19 balloons remaining (i.e. 28 - 9)

So:

$n => 19+ 8 -1 = 26$

$r = 19$

Selection of at least 9 =

$At\ least\ 9 = ^{26}C_{19}$

$At\ least\ 9 = \frac{26!}{(26-19)!19!}$

$At\ least\ 9 = \frac{26!}{7!19!}$

$At\ least\ 9 = 657800$

Ways of selecting at most 8 =

$At\ most\ 8 = Total - At\ least\ 9$ --- Complement rule

$At\ most\ 8 = 6724520- 657800$

$At\ most\ 8 = 6066720$

Solving (d): 12 red and 8 blue balloons

First, we calculate the ways for selecting 13 red balloons and 9 blue balloons

Out of the 28 balloons, there are 6 balloons remaining (i.e. 28 - 13 - 9)

So:

$n =6+6-1 = 11$

$r = 6$

Selection =

$^{11}C_6 = \frac{11!}{(11-6)!6!}$

$^{11}C_6 = \frac{11!}{5!6!}$

$^{11}C_6 = 462$

Using inclusion/exclusion rule of two sets:

$Selection = At\ most\ 12 + At\ most\ 8 - (12\ red\ and\ 8\ blue)$

$Only\ 12\ red\ and\ only\ 8\ blue\ = 170544+ 657800- 462$

$Only\ 12\ red\ and\ only\ 8\ blue\ = 827882$

$At\ most\ 12\ red\ and\ at\ most\ 8\ blue = Total - Only\ 12\ red\ and\ only\ 8\ blue$

$At\ most\ 12\ red\ and\ at\ most\ 8\ blue = 6724520 - 827882$

$At\ most\ 12\ red\ and\ at\ most\ 8\ blue = 5896638$

3 0

2 years ago

On a coordinate plane, parallelogram H I J K is shown. Point H is at (negative 2, 2), point I is at (4, 3), point J is at (4, ne

nasty-shy [4]

HIJK is a parallelogram because the midpoint of both diagonals is

(1 , 0), which means the diagonals bisect each other

Step-by-step explanation:

If (x , y) is the mid-point of a segment whose end points are $(x_{1},y_{1})$ and $(x_{2},y_{2})$ then,

$x=\frac{x_{1}+x_{2}}{2}$

$y=\frac{y_{1}+y_{2}}{2}$

In a parallelogram, its diagonals intersect each other at their mid-points

that means its diagonals bisect each other

∵ HIJK is a quadrilateral

∵ HJ and IK are its diagonals

∵ H = (-2 , 2)

∵ J = (4 , -2)

- Find the mid point of HJ

∵ $M_{HJ}=(\frac{-2+4}{2},\frac{2+-2}{2})$

∴ $M_{HJ}=(\frac{2}{2},\frac{0}{2})$

∴ $M_{HJ}=(1,0)$

∴ The mid-point of HJ is (1 , 0)

∵ I = (4 , 3)

∵ K = (-2 , -3)

- Find the mid point of IK

∵ $M_{IK}=(\frac{4+-2}{2},\frac{3+-3}{2})$

∴ $M_{IK}=(\frac{2}{2},\frac{0}{2})$

∴ $M_{IK}=(1,0)$

∴ The mid-point of IK is (1 , 0)

∵ The mid-points of HJ and IK are equal

∴ HJ and IK bisects each other

∴ HIJK is a parallelogram because its diagonals bisect each other

HIJK is a parallelogram because the midpoint of both diagonals is

(1 , 0), which means the diagonals bisect each other

Learn more:

You can learn more about parallelogram in brainly.com/question/6779145

#LearnwithBrainly

6 0

2 years ago

Read 2 more answers

On a coordinate plane, a straight line with a negative slope, labeled f of x, crosses the y-axis at (0, 4), and the x-axis at (4

Inga [223]

Answer: 1 f of 3 = 2 f of 2 = negative

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

In winter, the price of apples suddenly went up by \$0.75$0.75dollar sign, 0, point, 75 per pound. Sam bought 333 pounds of appl

DanielleElmas [232]

Your formula would be 3(p+0.75)=5.88

Because you have 3 pounds and 0.75 for each.

Solving the equation by distributing, you will get P=1.21

Hope this helps!

4 0

2 years ago

Read 2 more answers