What expressions are equivalent to 3x+5x+8 and 4x+4x

A random sample of 30 households was selected as part of a study on electricity usage, and the number of kilowatt-hours (kWh) wa

grin007 [14]

Answer:

The 98% confidence interval for the mean usage in the March quarter of 2006, in kWh, was (333.87, 416.13).

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 30 - 1 = 29

98% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 29 degrees of freedom(y-axis) and a confidence level of $1 - \frac{1 - 0.98}{2} = 0.99$ . So we have T = 2.462

The margin of error is:

$M = T\frac{s}{\sqrt{n}} = 2.462\frac{91.5}{\sqrt{30}} = 41.13$

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 375 - 41.13 = 333.87 kWh

The upper end of the interval is the sample mean added to M. So it is 375 + 41.13 = 416.13 kWh

The 98% confidence interval for the mean usage in the March quarter of 2006, in kWh, was (333.87, 416.13).

6 0

3 years ago

What is the value of z if z/4 = 12

Digiron [165]

Answer:

z = 48 :)

Step-by-step explanation:

z ÷ 4 = 12

So, all you need to do is multiply 12 by four, to get z- 48

hope this helped!

5 0

3 years ago

Read 2 more answers

The sum of the diagonals of a rhombus is 5√2.

Alex

Greetings!
Let ABCD be a rhombus
AC + BD = 5√2 cm

Area of ABCD = Ar△ABD + Ar △BCD
$= \frac{1}{2} \times BD \times AO + \frac{1}{2} \times BD \times OC$
$= \frac{1}{2} BD (AO + OC)$
$\frac{1}{2} BD \times AC$

$So, \frac{ BD \times AC}{2} = 4 \: cm {}^{2}$
$BD \times AC = 8$
$Now, AC + \: BD = 5 \sqrt{2}$

Squaring both sides, we get
$AC {}^{2} + BD {}^{2} + 2 AC.BD =50$
$AC {}^{2} + BD {}^{2} + 2 \times 8 = 50$
$AC {}^{2} + BD {}^{2} = 50 - 16$
$AC {}^{2} + BD {}^{2} = 34$

In △AOB, we have
$OA {}^{2} + OB {}^{2} =AB {}^{2}$
$( \frac{ AC }{2} ) {}^{2} + ( \frac{ BD}{2} ) {}^{2} = AB {}^{2}$
$\frac{ AC {}^{2} } {4} + \frac{ BD {}^{2} }{4} = AB {}^{2}$
$AC {}^{2} + BD {}^{2} = 4 AB {}^{2}$
$34 = 4 AB {}^{2}$

Square rooting both sides
$\sqrt{34} = 2 AB$
$Perimeter = 4 \: AB \\ = 2 \times 2 \: AB \\ = 2 \: \times \sqrt{34 } \\ = 2 \sqrt{34 \: } units$ .

Hope it helps!

7 0

3 years ago

A survey of 2,000 doctors showed that an average of 3 out of 5 doctors use brand X aspirin. How many doctors use brand X aspirin

VladimirAG [237]

This is a proportion problem that involves cross-multiplication
Set your problem up like so:
$\frac{x}{2,000}$ = $\frac{3}{5}$

Now cross multiply
2,000 x 3 = 6,000
now you're left with 5x = 6,000
Now divide by 5 on both sides
Answer is 1,200

7 0

3 years ago

A card is being drawn from a standard deck of playing cards. Find each probability.

EastWind [94]

These are 6 questions and 6 answers.

To find each probability we will use the definition of probability:

Probability = number of positive outcomes / number of total possible outcomes

1) P(Jack or ten)


Answer: 2/13 ≈ 0.12


Justification:

i) Positive outcomes: A standard deck of cards has 4 jacks and 4 tens, then those are 4 + 4 = 8 different positive outcomes.

ii) Possible outcomes: a standard deck of cards has 52 different cards, so, that is a total of 52 different possible outcomes

iii) Probability, P

P = number of positive outcomes / number of total possible outcomes

P = 8 / 52 = 2/13 ≈ 0.15

 2.P(red or black)


Answer: 1

Justification:

i) Positive outcomes

Half of the cards are red and half of the cards are black, so they both add for the total of the cards = 52

ii) Possible outcomes: 52 cards

iii) Probaility, P

P = number of positive outcomes / number of total possible outcomes

P = 52 / 52 = 1

 3.P(queen or club)


Answer: 4/13 ≈ 0.31

Justification:

i) Positive outcomes

There are 4 Queens.

There are 1/4 of 52 clubs = 1/4 × 52 = 13 clubs.

But you cannot add all of them, because one club is the Quenn of Clubs.

Then, the total number of different Queens and clubs is 4 + 13 - 1 = 16

ii) Possible outcomes: 52 different cards

iii) Probaility, P

P = number of positive outcomes / number of total possible outcomes

P = 16 /52 = 4 / 13 ≈ 0.31

 4.P(red or ace)


Answer: 7 / 13 ≈ 0.54

Justification:

i) Positive outcomes

Half of the cards are red: 26

There are 4 aces.

Since 2 aces are red, the number of different red and aces cards is: 26 + 4 - 2 = 28

ii) Possible outcomes: 52 different outcomes

iii) Probaility, P

P = number of positive outcomes / number of total possible outcomes

P = 28 / 52 = 7 / 13 ≈ 0.54

 5.P(diamond or black)


Answer: 1/2 = 0.5

Justification:

i) Positive outcomes

There are 52 / 4 = 13 diamonds

There are 26 black cards.

All the diamonds are black cards.

Then, the number of different diamond or black cards is 13 + 26 - 13 = 26

ii) Possible outcomes: 52 different cards.

iii) Probaility, P

P = number of positive outcomes / number of total possible outcomes

P = 26 / 52 = 1/2 = 0.5

6.P(face card or spade)

Answer: 11/26 ≈ 0.42

Justification:

i) Positive outcomes

Face cards are jacks, queens and kings. That is 3 × 4 = 12 different cards.

The spades are 13 cards.

Since, 3 of the faces are spade cards, the number of different cards of those types are 12 + 13 - 3 = 22

ii) Possible outcomes: 52 different cards

iii) Probaility, P

P = number of positive outcomes / number of total possible outcomes

P = 22 / 52 = 11 / 26 ≈ 0.42

4 0

2 years ago