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3 years ago

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Rectangle ABCD is similar to rectangle QRST. The width of ABCD is 5 inches and the length is 8 inches. If the length of QRST is

12 inches, what is the width of QRST?

1 answer:

omeli [17]3 years ago

8 0

Answer: 7.5

Form your proportion. Let x be the width of QRST.

Length of ABCD Length of QRST
----------------------- = -------------------------
Width of ABCD Width of QRST

8/5 = 12/x

Solve for x by cross-multiplying.
(8)(x) = (12)(5)
8x = 60
x = 7.5

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3. 'a' and 'b' are the intercepts made

Julli [10]

Given:

'a' and 'b' are the intercepts made by a straight-line with the co- ordinate axes.

3a = b and the line pass through the point (1, 3).

To find:

The equation of the line.

Solution:

The intercept form of a line is

$\dfrac{x}{a}+\dfrac{y}{b}=1$ ...(i)

where, a is x-intercept and b is y-intercept.

We have, 3a=b.

$\dfrac{x}{a}+\dfrac{y}{3a}=1$ ...(ii)

The line pass through the point (1, 3). So, putting x=1 and y=3, we get

$\dfrac{1}{a}+\dfrac{3}{3a}=1$

$\dfrac{1}{a}+\dfrac{1}{a}=1$

$\dfrac{2}{a}=1$

Multiply both sides by a.

$2=a$

The value of a is 2. So, x-intercept is 2.

Putting a=2 in $b=3a$ , we get

$b=3(2)$

$b=6$

The value of b is 6. So, y-intercept is 6.

Putting a=2 and b=6 in (i), we get

$\dfrac{x}{2}+\dfrac{y}{6}=1$

Therefore, the equation of the required line in intercept form is $\dfrac{x}{2}+\dfrac{y}{6}=1$ .

5 0

2 years ago

Please help me out here ASAP. Thanks!

GuDViN [60]

y - y₁ = m(x - x₁)
y - (-1) = 4[x - (-3)]
y + 1 = 4(x + 3)
y + 1 = 4(x) + 4(3)
y + 1 = 4x + 12
- 1 - 1
y = 4x + 11

The answer is B.

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3 years ago

Does this graph have 10 or 9 squares, 10 or 9 years, I think I might be going insane

Yuliya22 [10]

Answer:

10 years

Step-by-step explanation:

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2 years ago

In a recent year, a poll asked 2362 random adult citizens of a large country how they rated economic conditions. In the poll,

Harman [31]

Answer:

a) The 99% confidence interval is given by (0.198;0.242).

b) Based on the p value obtained and using the significance level assumed $\alpha=0.01$ we have $p_v>\alpha$ so we can conclude that we fail to reject the null hypothesis, and we can said that at 1% of significance the proportion of people who are rated with Excellent/Good economy conditions not differs from 0.24. The interval also confirms the conclusion since 0.24 it's inside of the interval calculated.

c) $\alpha=0.01$

Step-by-step explanation:

<em>Data given and notation </em>

n=2362 represent the random sample taken

X represent the people who says that they would watch one of the television shows.

$\hat p=\frac{X}{n}=0.22$ estimated proportion of people rated as Excellent/Good economic conditions.

$p_o=0.24$ is the value that we want to test

$\alpha$ represent the significance level

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest) <em> </em>

<em>Concepts and formulas to use </em>

We need to conduct a hypothesis in order to test the claim that 24% of people are rated with good economic conditions:

Null hypothesis: $p=0.24$

Alternative hypothesis: $p \neq 0.24$

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 $p_o$ .

Part a: Test the hypothesis

<em>Check for the assumptions that he sample must satisfy in order to apply the test </em>

a)The random sample needs to be representative: On this case the problem no mention about it but we can assume it.

b) The sample needs to be large enough

np = 2362x0.22=519.64>10 and n(1-p)=2364*(1-0.22)=1843.92>10

Condition satisfied.

<em>Calculate the statistic</em>

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

$z=\frac{0.22 -0.24}{\sqrt{\frac{0.24(1-0.24)}{2362}}}=-2.28$

The confidence interval would be given by:

$\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$

The critical value using $\alpha=0.01$ and $\alpha/2 =0.005$ would be $z_{\alpha/2}=2.58$ . Replacing the values given we have:

$0.22 - (2.58)\sqrt{\frac{0.22(1-0.22)}{2362}}=0.198$

$0.22 + (2.58)\sqrt{\frac{0.22(1-0.22)}{2362}}=0.242$

So the 99% confidence interval is given by (0.198;0.242).

Part b

<em>Statistical decision </em>

P value method or p value approach . "This method consists on 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 is $\alpha=0.01$ . The next step would be calculate the p value for this test.

Since is a bilateral test the p value would be:

$p_v =2*P(z$

So based on the p value obtained and using the significance level assumed $\alpha=0.01$ we have $p_v>\alpha$ so we can conclude that we fail to reject the null hypothesis, and we can said that at 1% of significance the proportion of people who are rated with Excellent/Good economy conditions not differs from 0.24. The interval also confirms the conclusion since 0.24 it's inside of the interval calculated.

Part c

The confidence level assumed was 99%, so then the signficance is given by $\alpha=1-confidence=1-0.99=0.01$

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2 years ago

Which expression would the model be most helpful in solving?

vovangra [49]

This question is awfully vague without any images of the equation to back it up, sorry

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3 years ago