All categories

3 years ago

Use the distributive property to match equivalent expressions.

Mathematics

1 answer:

NeTakaya3 years ago

4 0

Answer:

<h3>By using the distributive property the matched equivalent expressions are</h3><h3>1) -7(-4+x) =28-7x </h3><h3>2) -7(4-x) =-28+7x </h3><h3>3) 7(4+x) =28+7x </h3><h3>4) 7(-4-x) =-28-7x </h3>

Step-by-step explanation:

Given that by using the distributive property to match the given equivalent expressions.

1) Given expression is -7(-4+x)

<h3>By Distributive property a(b+c)=ab+ac</h3>

-7(-4+x) =(-7)(-4)+(-7)(x)

=28-7x

2) Given expression is -7(4-x)

<h3>By Distributive property a(b+c)=ab+ac</h3>

-7(4-x) =(-7)(4)+(-7)(-x)

=-28+7x

3) Given expression is 7(4+x)

<h3>By Distributive property a(b+c)=ab+ac</h3>

7(4+x) =(7)(4)+(7)(x)

=28+7x

4) Given expression is 7(-4-x)

<h3>By Distributive property a(b+c)=ab+ac</h3>

7(-4-x) =(7)(-4)+(7)(-x)

=-28-7x

Hence the matched equivalent expressions are

1) -7(-4+x) =28-7x

2) -7(4-x) =-28+7x

3) 7(4+x) =28+7x

4) 7(-4-x) =-28-7x

You might be interested in

Halp me pls..<br> !!!!<br><br><br> :D I will be happy

pochemuha

The probability of multiple events happening is found by multiplying the probabilities of each event together.

$P_{d+even\ number}=P_{d}*P_{even}\\\\P_{d}=\frac{number\ of\ events}{total\ number\ of\ events}=\frac{(d)}{a,\ b,\ c,\ d,\ e)}=\frac{1}{5}\\\\P_{even}=\frac{number\ of\ events}{total\ number\ of\ events}=\frac{(2,\ 4,\ 6)}{(1,\ 2,\ 3,\ 4,\ 5,\ 6)}=\frac{3}{6}=\frac{1}{2}\\\\\frac{1}{5}*\frac{1}{2}=\boxed{\frac{1}{10}}$

So yes, 1/10 is the answer :)

5 0

3 years ago

A Pew Internet poll asked cell phone owners about how they used their cell phones. One question asked whether or not during the

EastWind [94]

Answer:

a) $\hat p=\frac{471}{1024}=0.460$

The standard error is given by:

$SE= \sqrt{\frac{\hat p(1-\hat p)}{n}}=\sqrt{\frac{0.460(1-0.460)}{1024}}=0.0156$

And the margin of error is given by:

$ME=z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}=1.96\sqrt{\frac{0.460(1-0.460)}{1024}}=0.0305$

b) The 99% confidence interval would be given by (0.429;0.491)

Step-by-step explanation:

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Data given and notation

n=1024 represent the random sample taken

X=471 represent the people responded that they had used their cell phone while in a store within the last 30 days to call a friend or family member for advice about a purchase they were considering

$\hat p=\frac{471}{1024}=0.460$ estimated proportion of people responded that they had used their cell phone while in a store within the last 30 days to call a friend or family member for advice about a purchase they were considering

p= population proportion of people responded that they had used their cell phone while in a store within the last 30 days to call a friend or family member for advice about a purchase they were considering

Part a

The confidence interval would be given by this formula

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

For the 95% confidence interval the value of $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.96$

The standard error is given by:

$SE= \sqrt{\frac{\hat p(1-\hat p)}{n}}=\sqrt{\frac{0.460(1-0.460)}{1024}}=0.0156$

And the margin of error is given by:

$ME=z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}=1.96\sqrt{\frac{0.460(1-0.460)}{1024}}=0.0305$

Part b

If we replace the values obtained we got:

$0.460-1.96\sqrt{\frac{0.460(1-0.460)}{1024}}=0.429$

$0.460+1.96\sqrt{\frac{0.460(1-0.460)}{1024}}=0.491$

The 99% confidence interval would be given by (0.429;0.491)

8 0

3 years ago

I need help with both of these

jeka57 [31]

Answer:

13x² - 19x + 23
-16x +17

Step-by-step explanation:

1 . (4x² - 9x + 16) + (7 + 9x² - 10x)

4x² - 9x + 16 + 7 + 9x² - 10x

13x² - 19x + 23

2 . (-2x + 6) - (14x - 11)

-2x + 6 - 14x + 11

-16x +17

8 0

3 years ago

Please help me expand theses and then help me factorise these brackets

melisa1 [442]

Answer:

-9xy+16x

Step-by-step explanation:

x(y-2) +3x(6-y) -7xy

Distribute

xy -2x +18x-3xy -7xy

Combine like terms

-9xy+16x

3 0

3 years ago

Read 2 more answers

Use the theoretical probability formula to solve the problem. Express the probability as a fraction

serg [7]

Answer:

c. 3 / 13

d. 2 / 13

Step-by-step explanation:

A deck of cards has 52 cards. There are cards of 4 suits- Spades, Hearts, Diamonds and Clubs.

So, there are 52/4= 13 cards of each suit.

Among these 13 cards, there are 3 picture cards or face cards as they are called. These are the Jack, Queen and King cards.

So, the number of total picture cards = 4*3 = 12

the number of cards are 52

theoretical probability formula: P = favorable events/ possible events

P = 12 / 52

P = 3 / 13

there are four aces and four sevens in the deck

so favorable events = 4 + 4 = 8

possible eventas = 52

P = 8 / 52

P = 2 / 13

4 0

3 years ago