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3 years ago

May anyone help please

Mathematics

1 answer:

lapo4ka [179]3 years ago

4 0

Depending on how flexibly you interpret "about 20 times larger" to mean, the answers are B and D.

Check the ratios of the larger number to the smaller number:

A: (2.01 x 10^7)/(4.25 x 10^6) = 2.01/4.25 x 10^1 = 20.1/4.25 = 4.729

B: (8.21 x 10^-3)/(4.13 x 10^-4) = 8.21/4.13 x 10^1 = 82.1/4.13 = 19.879

C: (4.91 x 10^6)/(5.09 x 10^3) = 4.91/5.09 x 10^3 = 4910/5.09 = 964.637

D: (5.97 x 10^4)/(3.12 x 10^3) = 5.97/3.12 x 10^1 = 59.7/3.12 = 19.135

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Which phrase best describes the translation from the graph y=(x-5)^2+7 to the graph of y=(x+1)^2-2

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Start from the parent function $f(x)=x^2$

In the first case, you are computing

$f(x-5)+7$

In the second case, you are computing

$f(x+1)-2 /tex] There are two translation going on: when you transform [tex] f(x) \to f(x+k)$ , you translate the function horizontally, $k$ units left if $k>0$ and $k$ units right if $k$ .

On the other hand, when you transform $f(x) \to f(x)+k$ , you translate the function vertically, $k$ units up if $k>0$ and $k$ units down if $k$ .

So, the first function is the "original" parabola $f(x)=x^2$ , translated $5$ units right and $7$ units up. Likewise, the second function is the "original" parabola $f(x)=x^2$ , translated $1$ units left and $2$ units down.

So, the transformation from $(x-5)^2+7$ to $(x+1)^2-2$ is: go $6$ units to the left and $2$ units down

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Many high school students take the AP tests in different subject areas. In 2007, of the 144,796 students who took the biology ex

Nataly [62]

Answer:

$(0.582-0.485) - 1.64 \sqrt{\frac{0.582(1-0.582)}{144796} +\frac{0.485(1-0.485)}{211693}}=0.0942$

$(0.582-0.485) + 1.64 \sqrt{\frac{0.582(1-0.582)}{144796} +\frac{0.485(1-0.485)}{211693}}=0.09978$

And the 90% confidence interval would be given (0.0942;0.09978).

We are confident at 90% that the difference between the two proportions is between $0.0942 \leq p_A -p_B \leq 0.09978$

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$p_A$ represent the real population proportion female for Biology

$\hat p_A =\frac{84199}{144796}=0.582$ represent the estimated proportion female for biology

$n_A=144796$ is the sample size for A

$p_B$ represent the real population proportion female for calculus AB

$\hat p_B =\frac{102598}{211693}=0.485$ represent the estimated proportion female for Calculus AB

$n_B=211693$ is the sample size required for B

$z$ represent the critical value for the margin of error

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

The confidence interval for the difference of two proportions would be given by this formula

$(\hat p_A -\hat p_B) \pm z_{\alpha/2} \sqrt{\frac{\hat p_A(1-\hat p_A)}{n_A} +\frac{\hat p_B (1-\hat p_B)}{n_B}}$

For the 90% confidence interval the value of $\alpha=1-0.90=0.1$ and $\alpha/2=0.05$ , with that value we can find the quantile required for the interval in the normal standard distribution.