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20. GEOMETRY The measures of two sides of a triangle are given. If p isthe perimeter, and p=10x+5y, find the measure of the thir

algol [13]

The perimeter of any shape is a measure of the length of the peripheral of that shape.

For a triangle, it is an addition of the length of the 3 sides.

P = a + b + c where a, b, c are the lengths of the individual sides.

p = 10x + 5y = (3x + 4y) + (5x - y) + c

Collecting like terms on the RHS, we have

p = 10x + 5y = 8x + 3y + c

Subtracting 8x + 3y from both sides to give c leaves us with

10x + 5y - (8x + 3y) = c

c = 10x - 8x + 5y - 3y

c = 2x + 2y

7 0

1 year ago

There were 2430 Major League Baseball games played in 2009, and the home team won the game in 53% of the games. If we consider t

Ivahew [28]

Answer:

$z=\frac{0.53 -0.5}{\sqrt{\frac{0.5(1-0.5)}{2430}}}=2.958$

$p_v =P(Z>2.958)=0.0015$

So the p value obtained was a very low value and using the significance level given $\alpha=0.05$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion is significantly higher than 0.5 .

Step-by-step explanation:

1) Data given and notation

n=2430 represent the random sample taken

$\hat p=0.53$ estimated proportion when the home team won the game

$p_o=0.5$ is the value that we want to test

$\alpha=0.05$ represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

2) Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the proportion is higher than 0.5 or 50%:

Null hypothesis: $p\leq 0.5$

Alternative hypothesis: $p > 0.5$

When we conduct a proportion test we need to use the z statistic, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

3) Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.53 -0.5}{\sqrt{\frac{0.5(1-0.5)}{2430}}}=2.958$

4) Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level provided $\alpha=0.05$ . The next step would be calculate the p value for this test.

Since is a right tailed test the p value would be:

$p_v =P(Z>2.958)=0.0015$

So the p value obtained was a very low value and using the significance level given $\alpha=0.05$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion is significantly higher than 0.5 .

8 0

3 years ago

Categorize the graph as linear increasing, linear decreasing, exponential growth, or exponential decay.

dusya [7]

A. Linear Decreasing

3 0

3 years ago

Read 2 more answers

A rectangular flower garden in Samantha's backyard has 220 feet around its edge. The width of the garden is 50 feet. What is the

Ede4ka [16]

Answer: 60 ft

Step-by-step explanation:

Given

The perimeter of the garden is $220\ ft$

The width of the garden is $50\ ft$

Suppose the length of the garden is $x$

Perimeter is the sum of the lengths of the sides

$\Rightarrow 220=2(x+50)\\\Rightarrow 110=x+50\\\Rightarrow x=60\ ft$

So, the length of the garden is $60\ ft$

4 0

3 years ago

A teacher needs 256 lengths of string cut to 40cm each. If balls of string are 30M long, how many balls are needed?

Otrada [13]

First you need to work out how much string is needed -
256 pieces needed x 40cm each:
256 x 40 = 10240cm

Then, convert to metres (100cm = 1m)
10240 / 100 = 102.4m

Then, you work out how many balls are needed:
30 can fit into 102.4 3 times with .41m to spare. So, you need three balls of string, PLUS another one to cover the 41cm

So to conclude: 4 balls of string are needed.

4 0

3 years ago