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3 years ago

Solve the following system by the comparison method.

Mathematics

1 answer:

agasfer [191]3 years ago

5 0

Answer:

2p + q = 1

9p + 3q + 3 = 0

q = 1 - 2p

replace q = 1 - 2p into 9p + 3q + 3 = 0

9p + 3(1 - 2p) + 3 = 0

9p + 3 - 6p + 3 = 0

3p + 6 =0

3p = -6

p = -2

q = 1 - 2p

q = 1 -2(-2)

q = 1 + 4

q = 5

(-2 , 5)

there for the answer would be

{(-2, 5)}

Hopefully this was helpful <3 :3

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The thickness of each type of coin is shown in the table. How much thicker is stack of dollars worth of nickels than a dollars w

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Let our basis be worth 1 dollar. A nickel's worth is $0.05. In order to come up with $1, the number of nickels should be:

Number of nickels = $1 * 1 nickel/$0.05 = 20 nickels
Thickness of 20 nickels = 20 nickels * 1.95 mm = 39 mm

Let's do the same for the quarters. Each quarter is worth $0.25.

Number of quarters = $1 * 1 quarter/$0.25 = 4 quarters
Thickness of 4 quarters = 4 quarters * 1.75 mm = 7 mm

Find the ratio of the two:
39 mm/7 mm = 5.57

Therefore, a stack of nickels is 5.57 times thicker than a stack of quarters worth one dollar.

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4 years ago

The measures of the angles of a convex polygon form an arithmetic sequence. The least measurement in the sequence is 128º. The g

Over [174]

$\bf \qquad \qquad \textit{sum of a finite arithmetic sequence}\\\\
S_n=\cfrac{n}{2}(a_1+a_n)\quad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\ a_n=n^{th}~value\\
----------\\
\stackrel{least}{a_1}=128\\\\
\stackrel{greatest}{a_n}=172
\end{cases}$

$\bf S_n=\cfrac{n}{2}(128~+~172)\implies S_n=\cfrac{n}{2}(300)\implies S_n=150n
\\\\\\
\textit{but we also know that sum of all interior angles is }180(n-2)
\\\\\\
\stackrel{\textit{sum of the angles}}{S_n}=\stackrel{\textit{sum of the angles}}{180(n-2)}=150n
\\\\\\
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3 years ago

Read 2 more answers

What makes a mathematical statement an equation.

kirza4 [7]

Answer:

Step-by-step explanation:

In mathematics, an equation is a statement that asserts the equality of two expressions, which are connected by the equals sign "=".

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3 years ago

During a professional Field hockey game,every spectator placed his or her ticket sub into one of several containers,after the ga

maria [59]

Answer:

The sixteen people to March in the sportsmanship parade

Step-by-step explanation:

A sample refers to a smaller, manageable version of a larger group. It is a subset containing the characteristics of a larger population.

A sample should represent the population as a whole and not reflect any bias toward a specific attribute.

Since the coach chose 16 people to March in the sportsmanship parade, the sample in this situation, The sixteen people to March in the sportsmanship parade is the sample

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3 years ago

Men are believed to have a slightly longer average length of short hospital stays than women; 5.2 days versus 4.5 days respectiv

Georgia [21]

Answer:

Since our calculated value is lower than our critical value, $z_{calc}=2.02$ , we have enough evidence to FAIL to reject the null hypothesis at 1% of singificance. So there is not nough evidence to conclude that mean for men it's significantly higher than the mean for female.

Step-by-step explanation:

1) Data given and notation

$\bar X_{1}=5.2$ represent the mean for group men

$\bar X_{2}=4.5$ represent the mean for group women

Assuming these values for the remaining data:

$\sigma_{1}=1.2$ represent the population standard deviation for the sample men

$\sigma_{2}=1.5$ represent the population standard deviation for the sample women

$n_{1}=32$ sample size for the group men

$n_{2}=30$ sample size for the group women

z would represent the statistic (variable of interest)

$p_v$ represent the p value

2) Concepts and formulas to use

We need to conduct a hypothesis in order to check if the mean for men it's higher than the mean for women, the system of hypothesis would be:

H0: $\mu_{1} \leq \mu_{2}$

H1: $\mu_{1} > \mu_{2}$

If we analyze the size for the samples both are higher than 30, and we know the population deviation's, so for this case is better apply a z test to compare means, and the statistic is given by:

$z=\frac{\bar X_{1}-\bar X_{2}}{\sqrt{\frac{\sigma^2_{1}}{n_{1}}+\frac{\sigma^2_{2}}{n_{2}}}}$ (1)

z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

3) Calculate the statistic

We have all in order to replace in formula (1) like this:

$z=\frac{5.2-4.5}{\sqrt{\frac{1.2^2}{32}+\frac{1.5^2}{30}}}=2.02$

4) Find the critical value

In order to find the critical value we need to take in count that we are conducting a right tailed test, so we are looking on the normal standard distribution a value that accumulats 0.01 of the area on the right and 0.99 of the area on the left. We can us excel or a table to find it, for example the code in Excel is:

"=NORM.INV(1-0.01,0,1)", and we got $z_{critical}=2.33$

5) Statistical decision

Since our calculated value is lower than our critical value, $z_{calc}=2.02$ , we have enough evidence to FAIL to reject the null hypothesis at 1% of significance. So there is not nough evidence to conclude that mean for men it's significantly higher than the mean for female.

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4 years ago