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2 years ago

A square of side x is cut out of a larger square of side y. What is the area of the remaining

Mathematics

1 answer:

KonstantinChe [14]2 years ago

3 0

Answer:

The area of the remaining figure is $y^2-x^2$

Step-by-step explanation:

<u>Area of the Square Shape</u>

Given a square of side length x, the area is calculated by the formula:

$A_x=x^2$

It's given a square of side x is cut out of a larger square of side y. Please refer to the image below.

The area of the square of side length y is:

$A_y=y^2$

The shaded area of the remaining figure is the difference between both areas:

$A=A_y-A_x$

$A=y^2-x^2$

The area of the remaining figure is $\mathbf{y^2-x^2}$

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2/3*x+3/4=8 what is x

matrenka [14]

Answer: x=10 7/8

Step-by-step explanation:

Subtract 3/4 from both sides. Multiply both sides by 3. Divide both sides by 2 (basically just isolate x on one side of the equal sign).

7 0

2 years ago

4.One attorney claims that more than 25% of all the lawyers in Boston advertise for their business. A sample of 200 lawyers in B

AleksAgata [21]

Answer:

$z=\frac{0.315 -0.25}{\sqrt{\frac{0.25(1-0.25)}{200}}}=2.123$

$p_v =P(Z>2.123)=0.0169$

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 of lawyers had used some form of advertising for their business is significantly higher than 0.25 or 25% .

Step-by-step explanation:

1) Data given and notation

n=200 represent the random sample taken

X=63 represent the lawyers had used some form of advertising for their business

$\hat p=\frac{63}{200}=0.315$ estimated proportion of lawyers had used some form of advertising for their business

$p_o=0.25$ 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 more than 25% of all the lawyers in Boston advertise for their business:

Null hypothesis: $p\leq 0.25$

Alternative hypothesis: $p > 0.25$

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:

$z=\frac{0.315 -0.25}{\sqrt{\frac{0.25(1-0.25)}{200}}}=2.123$

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:

$p_v =P(Z>2.123)=0.0169$

8 0

3 years ago

A ferritin test is a popular test to measure a person’s current iron stores. in women, ferritin is normally distributed with a m

MArishka [77]

Given:
μ = 89 ng/ml, population mean
σ = 23 ng/ml, population standard deviation

Random variable, x = 100
To test P(x < 100), calculate the z-score.
z = (x-μ)/σ = (100 - 89)/23 = 0.4783

From standard tables, obtain
P(x < 100) = 0.6838 = 68.4%

Answer: 68.4%

7 0

2 years ago

Solve the system by graphing y=-4x-2 -2x+y=-2 Plot both lines and point of intersection by moving the dots to the correct locati

UkoKoshka [18]

Answer:

The point of intersection is (0,-2).

Step-by-step explanation:

Equation 1: $y=-4x-2$