Combine like terms to create an equivalent expression. 3.26d+9.75d−2.65

According to the fundamental theorem of algebra, how many zeros does the polynomial below have?

Oxana [17]

It has 3 zeros, because its a polynomial of degree 3.

6 0

3 years ago

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Solve For Each Variable.

bixtya [17]

The first equation given $6=1-2n+5$

We have to add 1 and 5 to the right side first. We will get,

$6= 6 - 2n$

To get rid of 6 from the right side we have to subtract 6 from both sides.

$6-6 = 6-6-2n$

$6-6 = -2n$

$0=-2n$

To find n we have to move -2 to the other side by dividing both side by -2.

$0/-2 = -2n/-2$

$0= n$

$n=0$

So we have got the required answer for the first question.

The solution is n = 0.

The second equation given,

$8x-2 = -9+7x$

First we have to move 7x to the left side by subtracting it from both sides.

$8x-7x-2 = -9+7x-7x$

$8x-7x-2 = -9$

$x-2 = -9$

Now we have to move -2 to the right side by adding 2 to both sides.

$x-2+2 = -9+2$

$x = -9+2$

$x = -7$

We have got the required answer for the second question.

The solution is x = -7.

The third equation given,

$-8 = -(x+4)$

We have to get rid of that negative sign from both sides. As we have negative sign to both sides we can cancel it out. We will get,

$8=x+4$

Now we have to move 4 to left side by subtracting it from both sides.

$8-4 = x+4-4$

$8-4 = x$

$4=x$

$x = 4$

So we have got the required answer .

The solution is x = 4.

3 0

3 years ago

Ieda and Thanh both offer piano lessons. Ieda charges an initial fee of $8.50 and an hourly rate of $11.00. Thanh charges an ini

Verizon [17]

Answer:

after 3 hours of instruction.

Step-by-step explanation:

First, start by setting up the equation.

Leda charges an initial fee, meaning this fee is only going to be one time. However, there is an hourly rate of 11. Since we do not know how many hours these piano lessons are going to last, we put a variable (I will use x), after this number.

The initial fee is 8.50. There needs to be a variable after 11 because that is the number we don't know.

The equation for Leda's lessons are 8.50+11.00x.

Now, we need to find out what the equation for Thanh's lessons are going to be, because we're going to be setting both equations equal to each other to find out when they cost the same. At the moment both equal each other, is when they are the same amount.

Thanh's equation also has an intial fee and an hourly rate. So, the equation will be

10.00+10.50x.

Now we solve.

8.50+11.00x = 10.00+10.50x

First, subtract from both sides. We will do the numbers without variables first.

8.50+11.00x = 10.00+10.50x

-8.50 -8.50

____________________

0 +11.00x = 1.50 +10.50x

Then, subtract the x's. (taking away the zero because it is equivalent to nothing)

11.00x = 1.50 +10.50x

- 10.50x -10.50x

__________________

0.50x = 1.50

Lastly, to find out the answer, we divide.

1.50/0.50= 3.

To check your answer, you can plug into the original equation.

8.50+11.00 times 3 = 10.00+10.50 times 3

Both sides equal 41.50, meaning they are equal to each other!

7 0

3 years ago

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$10.82 for 2 earmuffs markup rate is 72%. what is the markup and retail price for 2 earmuffs

Katarina [22]

Markup=10.82(72/100)≈$7.79 (to nearest cent)

retail=10.82(100+72)/100≈$18.61 (to nearest cent)

3 0

2 years ago

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A tobacco company claims that the amount of nicotene in its cigarettes is a random variable with mean 2.2 and standard deviation

Aleksandr-060686 [28]

Answer:

0% probability that the sample mean would have been as high or higher than 3.1 if the company’s claims were true.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central limit theorem

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$