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2 years ago

Rectangle ABCD was dilated to create rectangle A'B'C'D' using point R as the center of dilation.

Mathematics

2 answers:

Slav-nsk [51]2 years ago

8 0

Answer:

Step-by-step explanation:

kati45 [8]2 years ago

3 0

Answer:

The value of RD' is 5 units.

Step-by-step explanation:

It is given that rectangle ABCD was dilated to create rectangle A'B'C'D' using point R as the center of dilation.

The scale factor is the proportion of side length of image and side length of preimage.

$k=\frac{\text{lenght of image}}{\text{lenght of preimage}}$

$k=\frac{B'C'}{BC}$

$k=\frac{4}{12}$

$k=\frac{1}{3}$

Scale factor is also defined as

$k=\frac{RD'}{RD}$

$\frac{1}{3}=\frac{RD'}{15}$

Multiply both sides by 15.

$RD'=5$

Therefore the value of RD' is 5 units.

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We can create a parabola equation of the trajectory using the vertex form:

y = a (x – h)^2 + k

The center is at h and k, where h and k are the points at the maximum height so:

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Therefore:

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At the initial point, x = 0, y = 0, so we can solve for a:

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So the whole equation is:

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16.8 ft

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2 years ago

The general form of the equation of a circle is x2 + y2 + 42x + 38y − 47 = 0. The equation of this circle in standard form is .

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Answer:

(-21,-19)

$\sqrt{849}$

Standard form

Step-by-step explanation:

We are given the equation of circle

$x^2+y^2+42x+38y-47=0$

General equation of circle:

$x^2+y^2+2gx+2fy+c=0$

Centre: (-g,-f)

Radius: $\sqrt{g^2+f^2-c}$

Compare the equation to find f, g and c from the equation

$g\rightarrow 21$

$f\rightarrow 19$

$c\rightarrow -47$

Centre: (-21,-19)

Radius (r) $=\sqrt{21^2+19^2+47}=\sqrt{849}$

Standard form of circle:

$(x+21)^2+(y+19)^2=849$

The centre of circle at the point (-21,-19) and its radius is $\sqrt{849}$ .

The general form of the equation of a circle that has the same radius as the above circle is standard form.

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Step-by-step explanation:

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What is the lateral area of a right rectangular prism that has rectangular bases measuring 3" by 5" and a height of 6"?

Mademuasel [1]

Answer:

The answer is the option A

$96\ in^{2}$

Step-by-step explanation:

we know that

The lateral area of a right rectangular prism is equal to

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Answer:

a) $p$ represent the real population proportion of people who showed partial or complete resistance to the antibiotic

b) $\hat p=\frac{973}{1714}=0.568$ represent the estimated proportion of people who showed partial or complete resistance to the antibiotic

c) We are confident (95%) that the true proportion of individuals in Florida diagnosed with a strep infection was tested for resistance to the antibiotic penicillin present partial or complete resistance to the antibiotic is between 54.5% to 59.1%.

Step-by-step explanation:

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".

Part a

Description in words of the parameter p

$p$ represent the real population proportion of people who showed partial or complete resistance to the antibiotic

$\hat p$ represent the estimated proportion of people who showed partial or complete resistance to the antibiotic

n=1714 is the sample size required

$z_{\alpha/2}$ represent the critical value for the margin of error

The population proportion have the following distribution

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

Part b

Numerical estimate for p

In order to estimate a proportion we use this formula:

$\hat p =\frac{X}{n}$ where X represent the number of people with a characteristic and n the total sample size selected.

$\hat p=\frac{973}{1714}=0.568$ represent the estimated proportion of people who showed partial or complete resistance to the antibiotic

Part c

The confidence interval for a proportion is given by this formula

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

For the 95% confidence interval the value of $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.96$

And replacing into the confidence interval formula we got:

$0.568 - 1.96 \sqrt{\frac{0.568(1-0.568)}{1714}}=0.545$

$0.568 + 1.96 \sqrt{\frac{0.56(1-0.56)}{1714}}=0.591$

And the 95% confidence interval would be given (0.545;0.591).

We are confident that about 54.5% to 59.1% of individuals in Florida diagnosed with a strep infection was tested for resistance to the antibiotic penicillin present partial or complete resistance to the antibiotic.

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