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3 years ago

Solve the equation. 8b – 7 = 7b – 2

Mathematics

1 answer:

lidiya [134]3 years ago

8 0

<u> 8b - 7 = 7b - 2</u>

Subtract 7b from each side: b - 7 = -2

Add 7 to each side: <em> b = 5</em>

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Suppose you have a five dollar off coupon at a fabric store you buy a fabric that cost $10 per yard

Lunna [17]

<h3>Answer:</h3>

1.) 10x-5=y

2.) $85

3.) 5.25 yards of fabric.

<h3>Step-by-step explanation:</h3>

1.) To write an equation for this problem, we need to figure out what every value means:

the variable x, represents the amount of yards of fabric you can buy

the variable y, represents the total amount of money after you found out (x) or the amount of yards of fabric.

1 yard of fabric equals $10, and we have a $5 coupon (-5)

Our equation is:

10x-5=y

This equation represents the relationship between the total cost of fabric, and the amount that you can buy.

2. In order to solve this problem we need to use our equation, one value is given which is 9.

9 represents x, the amount of yards of fabric.

Substitute 9 into x:

10(9)-5=y

<h3>Solve:</h3>

90-5=y

85=y

85 represents the cost of 9 yards of fabric, including the $5 coupon.

3.) This problem is similar to #2, although it's flipped.

The value given is $47.50, which represents (y), the total amount of money after (x) was found out.

But, we need to figure out (x).

Substitute $47.50 into (y):

10(x)-5=$47.50

Next, we need to figure out x by solving the opposite.

Adding the coupon to our answer can represent 10(x).

$47.50+5=52.50

10(x)=52.50

Lastly, divide both sides of the equation by 10.

10(x) / 10=52.50 /10

x=5.25

5.25 represents the amount of yards of fabric purchased if you paid $47.50.

7 0

2 years ago

Wen takes a job with a starting salary of $100,000 for the first year. she earns a 3% increase each year. what does s5 represent

steposvetlana [31]

$S_{n} = \frac{ a_{1}(1- r^{n}) }{1-r}$ $a_{1} = 100000, r=1.03, n=5$
$S_{5} = \frac{100000(1- 1.03^{5}) }{1-1.03} = \frac{100000(-.159)}{-.03} =530,000$

So after 5 years she is making $530,000.

Hope that helps

8 0

3 years ago

Read 2 more answers

a machinist can produce 114 Parts in 6 minutes at this rate how many parts can the machinist is produce in 15 minutes

tigry1 [53]

114/6=x/15
6x=1710
x=285 parts

4 0

3 years ago

A consumer survey indicates that the average household spendsμ= $185on groceries each week. The distribution of spending amounts

Vitek1552 [10]

Answer:

$P(X>200)=P(\frac{X-\mu}{\sigma}>\frac{200-\mu}{\sigma})=P(Z>\frac{200-185}{25})=P(Z>0.6)$

And we can find this probability using the complement rule and with the normal standard table or excel:

$P(Z>0.6)=1-P(z$

Step-by-step explanation:

Previous concepts

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 Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the average household spent of a population, and for this case we know the distribution for X is given by:

$X \sim N(185,25)$