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2 years ago

Multiply Conjugates Using the Product of Conjugates Pattern

Mathematics

1 answer:

SpyIntel [72]2 years ago

5 0

Answer:

The product is the difference of squares is $\left(11-b\right)\left(11+b\right)=121-{{b}^2}$

Step-by-step explanation:

Explanation

The given expression is (11-b)(11+b).

We have to multiply the given expression.

Square the first term 11. Square the last term b.

$\begin{aligned}&(11-b)(11+b)=(11)^{2}-(b)^{2} \\&(11-b)(11+b)=121-b^{2}\end{aligned}$

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If someone could please help me I’m confused thanks:)

Sedbober [7]

<h3>Answer: x = 45</h3>

Work Shown:

x+x+90 = 180 .... all three angles of a triangle add to 180

2x+90 = 180

2x = 180-90

2x = 90

x = 90/2

x = 45

This is a 45-45-90 right triangle. We also consider it an isosceles right triangle because the base angles (45) are equal.

3 0

3 years ago

A random sample of 10 parking meters in a resort community showed the following incomes for a day. Assume the incomes are normal

GenaCL600 [577]

Answer:

A 95% confidence interval for the true mean is [$3.39, $6.01].

Step-by-step explanation:

We are given that a random sample of 10 parking meters in a resort community showed the following incomes for a day;

Incomes (X): $3.60, $4.50, $2.80, $6.30, $2.60, $5.20, $6.75, $4.25, $8.00, $3.00.

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

P.Q. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean income = $\frac{\sum X}{n}$ = $4.70

s = sample standard deviation = $\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }$ = $1.83

n = sample of parking meters = 10

$\mu$ = population mean

Here for constructing a 95% confidence interval we have used a One-sample t-test statistics because we don't know about population standard deviation.

So, 95% confidence interval for the population mean, $\mu$ is ;

P(-2.262 < $t_9$ < 2.262) = 0.95 {As the critical value of t at 9 degrees of

freedom are -2.262 & 2.262 with P = 2.5%}

P(-2.262 < $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ < 2.262) = 0.95

P( $-2.262 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X-\mu$ < $2.262 \times {\frac{s}{\sqrt{n} } }$ ) = 0.95

P( $\bar X-2.262 \times {\frac{s}{\sqrt{n} } }$ < $\mu$ < $\bar X+2.262 \times {\frac{s}{\sqrt{n} } }$ ) = 0.95

95% confidence interval for $\mu$ = [ $\bar X-2.262 \times {\frac{s}{\sqrt{n} } }$ , $\bar X+2.262 \times {\frac{s}{\sqrt{n} } }$ ]

= [ $4.70-2.262 \times {\frac{1.83}{\sqrt{10} } }$ , $4.70+ 2.262 \times {\frac{1.83}{\sqrt{10} } }$ ]

= [$3.39, $6.01]

Therefore, a 95% confidence interval for the true mean is [$3.39, $6.01].

The interpretation of the above result is that we are 95% confident that the true mean will lie between incomes of $3.39 and $6.01.

Also, the margin of error = $2.262 \times {\frac{s}{\sqrt{n} } }$

= $2.262 \times {\frac{1.83}{\sqrt{10} } }$ = 1.31

4 0

3 years ago

One out of every 25 workers at Dean Shipyard filed for Workers' Compensation this year. What percent of the workers filed for Wo

Len [333]

4% of workers filed for Workers' Compensation because 1/25 is equal to 4%.

6 0

3 years ago

Read 2 more answers

A recent survey was conducted to compare the cost of solar energy to the cost of gas or electric energy. Results of the survey r

Mariana [72]

Answer:

c) at most 11.1%

Step-by-step explanation:

We have the data that is 97 ± 12, with 97 being the mean and 12 the standard deviation.

Now, the percentage of people who reached them for less than 73 dollars, if it were a normal distribution:

z = (73 - 97) / 12 = - 2

so it would be, a probability of 0.0228 or 0.228%.

But we don't know what distribution it has, but we can get an idea.

A and D discarded, as they are very high values, and 73 is well below the average.

B) is still a very high value.

Therefore the answer is C, at most 11.1%

4 0

3 years ago

A bag contains five red marbles, four blue marbles, and four yellow marbles. You randomly pick a marble. What is the probability

Vikentia [17]

n(s)= 5+4+4=13

n(e)= red + blue

=5+4

so, p(e) = n(e)/n(s)

p(e)= 9/13

=0.69

it's your answer

it will help.

7 0

3 years ago