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shutvik [7]
2 years ago
5

Factor this expression fully

0%2B%208%28x%20-%201%29" id="TexFormula1" title=" {x}^{2}(x - 1) - 9x(x - 1) + 8(x - 1)" alt=" {x}^{2}(x - 1) - 9x(x - 1) + 8(x - 1)" align="absmiddle" class="latex-formula">
​
Mathematics
1 answer:
AnnZ [28]2 years ago
8 0

Answer:

1,0

Step-by-step explanation:

No need to expand look at the roots of the brackets.

(x-1)=0

x=1

x^2 and -9x have roots 0

Think of it as whatever sets the expression to 0.

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A news report states that the 99% confidence interval for the mean number of daily calories consumed by participants in a medica
expeople1 [14]

Answer:

The sample mean is of 1925 calories.

The margin of error is of 75 calories.

The sample standard deviation is of 109.7992 calories.

Step-by-step explanation:

Sample mean:

The sample mean is the mean value of the two bounds of the confidence interval. So

M = \frac{1850 + 2000}{2} = 1925

The sample mean is of 1925 calories.

The margin of error

Difference between the bounds and the sample mean. So

2000 - 1925 = 1925 - 1850 = 75 calories.

The margin of error is of 75 calories.

Sample standard deviation:

Here, I am going to expand on the t-distribution.

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 = 18 - 1 = 17

99% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 17 degrees of freedom(y-axis) and a confidence level of 1 - \frac{1 - 0.99}{2} = 0.995. So we have T = 2.898

The margin of error is:

M = T\frac{s}{\sqrt{n}}

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

Since M = 75, T = 2.898, n = 18

M = T\frac{s}{\sqrt{n}}

75 = 2.898\frac{s}{\sqrt{18}}

s = \frac{75\sqrt{18}}{2.898}

s = 109.7992

The sample standard deviation is of 109.7992 calories.

6 0
2 years ago
Can you explain to me the answers in a and b?
Hoochie [10]

a. The constant of proportionality is k = 2

b. If Micah saves $150, his parents will give him $300

<h2>Explanation:</h2>

<h3>PART A.</h3>

From mathematics, we know that y varies directly as x or y is directly proportional to x if and only if:

y=kx for some nonzero constant k.

Here we know some facts:

  • For every $5 that Micah saves, his parents give him $10.

In other words:

Let y be the money his parents give him.

Let x be the money that Micah saves.

We \ know \ that: \\ y=kx \\ \\ \\ Solving \ for \ k: \\ \\ k=\frac{y}{x} \\ \\ k=\frac{10}{5} \\ \\ \boxed{k=2}

So,<em> the constant of proportionality is k = 2</em>

<h3>PART B.</h3>

In this case, we know that Micah saves $150. So we need to find the amount of his parents will give him. So what we know here is the value of x, because x represents the amount of money Micah saves. Therefore, by knowing x and k, we can calculate the value of y, which is the amount of money his parents will give him. Hence:

For \ x=150 \ and \ k=2: \\ \\ y=2(150) \\ \\ \boxed{y=300}

Finally, <em>if Micah saves $150, his parents will give him 300$</em>

<h2>Learn more:</h2>

Cost of pizzas: brainly.com/question/12878495

#LearnWithBrainly

5 0
3 years ago
Handles-n-Things is a small enterprise company buying new carpet for their office room. The room is 15 ft. wide and 24 ft. long.
elena55 [62]
You find this by finding the number of yards in 15 feet (15÷3) and that number of yards in 24 feet (24÷3) and multiplying them together. 5X8=40sq yards.
8 0
3 years ago
Read 2 more answers
he amount of corn chips dispensed into a 12​-ounce bag by the dispensing machine has been identified as possessing a normal dist
const2013 [10]

Answer:

The probability will be 0.3085 or 0

Step-by-step explanation:

Given:

True mean=12.5

Sample mean =12.6

Standard deviation=0.2

Samples=100

To Find:

Probability that exceeds 12.6 ounces.

Solution:

Calculate the Z-score for given means and standard deviation.

So

Z-score= (true mean -sample mean)/standard deviation.

Z-score=(12.5 -12.6)/0.2

=-0.1/0.2

=-0.5

Now Using Z-table

P(X≥-0.5)=p(Z≥-0.5)=0.3085

Hence Probability that sample mean weight exceeds will be  0.3085

                 OR

By using Normal distribution with sampling ,it will be as follows

Z=(X-u)/[Standard deviation/Sqrt(No of samples)]

Z=(12.6-12.5)/(0.2/Sqrt(100)

Z=0.1/0.2/10

Z=5

So P(X≥12.6  )=P(Z≥5)=1

Pr(Z≥5)=1-1=0.

(Refer the attachment )

Hence Probability of getting ounces greater than 12.6 is '0'.

The sampling is of 0.02 size hence graphically it looks likely.

as shown in attachment.

3 0
2 years ago
Which of the following shows the length of the third side, in inches, of the triangle below?
Alex777 [14]

\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-b^2}=a \qquad \begin{cases} c=\stackrel{hypotenuse}{61}\\ a=adjacent\\ b=\stackrel{opposite}{11}\\ \end{cases} \\\\\\ \sqrt{61^1-11^2}=a\implies \implies \sqrt{3600}=a\implies 60=a

7 0
3 years ago
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