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1 year ago

△RST is dilated with the rule DT,1/3 (x, y), where the center of dilation is T(3, –2).

Mathematics

2 answers:

dmitriy555 [2]1 year ago

6 0

△RST is dilated with the rule DT,1/3 (x, y), where the center of dilation is T(3, –2).

The distance between the x-coordinates of R and T is 3 .

The distance between the y-coordinates of R and T is 6.

R' is 1 unit left,2 units up from T, so the coordinates of R' are (2,0)

Gala2k [10]1 year ago

6 0

Answer:

△RST is dilated with the rule DT,1/3 (x, y), where the center of dilation is T(3, –2). The distance between the x-coordinates of R and T is 3. See below.

Step-by-step explanation:

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A random sample of 25 employees of a local company has been taken. A 95% confidence interval estimate for the mean systolic bloo

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Answer:

(B) If the sampling procedure were repeated many times, 95% of the resulting confidence intervals would contain the population mean systolic blood pressure.

Step-by-step explanation:

A confidence interval of 95% means that there is a 95% certainty that for a given sample, the population mean will be within the confidence interval estimated.

This is the same as saying that if he sampling procedure were repeated many times, 95% of the time the population mean would be contained in the resulting confidence interval.

Therefore, the answer is B)

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1 year ago

You are facing North. Turn 90 degrees left. Turn 180 degrees right. Turn around to reverse your direction. Turn 45 degrees left.

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2 years ago

Read 2 more answers

The length, l cm, of a simple pendulum is directly proportional to the square of its period (time taken to complete one oscillat

Greeley [361]

Answer:

1) $L \propto T^2$

Using the condition given:

$2.205 m = K (3)^2$

$K = 0.245 \approx \frac{g}{4\pi^2}$

So then if we want to create an equation we need to do this:

$L = K T^2$

With K a constant. For this case the period of a pendulumn is given by this general expression:

$T = 2\pi \sqrt{\frac{L}{g}}$

Where L is the length in m and g the gravity $g = 9.8 \frac{m}{s^2}$ .

2) $T = 2\pi \sqrt{\frac{L}{g}}$

If we square both sides of the equation we got:

$T^2 = 4 \pi^2 \frac{L}{g}$

And solving for L we got:

$L = \frac{g T^2}{4 \pi^2}$

Replacing we got:

$L =\frac{9.8 \frac{m}{s^2} (5s)^2}{4 \pi^2} = 6.206m$

3) $T = 2\pi \sqrt{\frac{0.98m}{9.8\frac{m}{s^2}}}= 1.987 s$

Step-by-step explanation:

Part 1

For this case we know the following info: The length, l cm, of a simple pendulum is directly proportional to the square of its period (time taken to complete one oscillation), T seconds.

$L \propto T^2$

Using the condition given:

$2.205 m = K (3)^2$

$K = 0.245 \approx \frac{g}{4\pi^2}$

So then if we want to create an equation we need to do this:

$L = K T^2$

With K a constant. For this case the period of a pendulumn is given by this general expression:

$T = 2\pi \sqrt{\frac{L}{g}}$

Where L is the length in m and g the gravity $g = 9.8 \frac{m}{s^2}$ .

Part 2

For this case using the function in part a we got:

$T = 2\pi \sqrt{\frac{L}{g}}$

If we square both sides of the equation we got:

$T^2 = 4 \pi^2 \frac{L}{g}$

And solving for L we got:

$L = \frac{g T^2}{4 \pi^2}$

Replacing we got:

$L =\frac{9.8 \frac{m}{s^2} (5s)^2}{4 \pi^2} = 6.206m$

Part 3

For this case using the function in part a we got:

$T = 2\pi \sqrt{\frac{L}{g}}$

Replacing we got:

$T = 2\pi \sqrt{\frac{0.98m}{9.8\frac{m}{s^2}}}= 1.987 s$

8 0

2 years ago

Which expression is equivalent to 144 Superscript three-halves? 216 1,728 RootIndex 3 StartRoot 12 EndRoot RootIndex 3 StartRoot

Afina-wow [57]

Question:

Which expression is equivalent to 144^(3/2)

Answer:

1728

Step-by-step explanation:

The options are not well presented. However, this is the solution to the question.

Given:

144^(3/2)

Required:

Find Equivalent.

We start my making use of the following law of logarithm.

A^(m/n) = (A^m)^1/n

So,

144^(3/2) = (144³)^½

Another law of indices is that

A^½ = √A

So,

144^(3/2) = (144³)^½ = √(144³)

144³ can be expanded as 144 * 144 * 144.

This gives

144^(3/2) = √(144 * 144 * 144)

The square root can then be splitted to

144^(3/2) = √144 * √144 * √144

144^(3/2) = 12 * 12 * 12

144^(3/2) = 1728.

Hence, the equivalent of 144^(3/2) is 1728

8 0

1 year ago

Read 2 more answers

The pillars in front of Mr. Jefferson's home are shaped like cylinders. The pillars have a height of 24 ft and a radius of 8 in.

GREYUIT [131]

Answer:

Option A. about 100.5ft²

Explanation:

Since the bases must not be painted, their areas are not included in the calculation.

The surface to paint, of each pillar, is equal to the lateral area of a cylinder with he dimensions given.

The formula for the laeral area of a cylinder is:

$Lateral\text{ }area=2\pi \times radius \times height$

Substitute including the conversion factor to convert inches to feet:

$Lateral\text{ }area=2\pi \times 8in\times 1ft/12in \times 24ft=100.5ft^2$

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2 years ago