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3 years ago

15

An object falls 3 meters during the first second, another 15 meters during the second second, and then 75 meters more during the

third second. If this pattern continues, how far does the object fall during the first 4 seconds?

1 answer:

Lana71 [14]3 years ago

8 0

3 times 5 equals 15
15 times 5 equals 75
75 times 5 equals 375
hope this helped (:

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Two different samples will be taken from the same population of test scores where the population mean and standard deviation are

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Answer:

The sample consisting of 64 data values would give a greater precision.

Step-by-step explanation:

The width of a (1 - <em>α</em>)% confidence interval for population mean μ is:

$\text{Width}=2\cdot z_{\alpha/2}\cdot \frac{\sigma}{\sqrt{n}}$

So, from the formula of the width of the interval it is clear that the width is inversely proportion to the sample size (<em>n</em>).

That is, as the sample size increases the interval width would decrease and as the sample size decreases the interval width would increase.

Here it is provided that two different samples will be taken from the same population of test scores and a 95% confidence interval will be constructed for each sample to estimate the population mean.

The two sample sizes are:

<em>n</em>₁ = 25

<em>n</em>₂ = 64

The 95% confidence interval constructed using the sample of 64 values will have a smaller width than the the one constructed using the sample of 25 values.

Width for n = 25:

$\text{Width}=2\cdot z_{\alpha/2}\cdot \frac{\sigma}{\sqrt{25}}=\frac{1}{5}\cdot [2\cdot z_{\alpha/2}\cdot \sigma]$

Width for n = 64:

$\text{Width}=2\cdot z_{\alpha/2}\cdot \frac{\sigma}{\sqrt{64}}=\frac{1}{8}\cdot [2\cdot z_{\alpha/2}\cdot \sigma]$

Thus, the sample consisting of 64 data values would give a greater precision

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3 years ago

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What is the percent increased from 22.5 to 27.5

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Answer:6.27

Step-by-step explanation: 22.8 increased by 27.5%

27.5% × 22.8 = 6.27

27.5 ÷ 100 × 22.8 = 6.27

27.5 × 22.8 ÷ 100 = 6.27

627 ÷ 100 = 6.27

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What is the area of a rectangle with vertices with (2,3), (7,3), (7,10), and (2,10)

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35 square units

Step-by-step explanation:

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Pregnant women metabolize some drugs at a slower rate than the rest of the population. The half-life of caffeine is about 4 hour

UkoKoshka [18]

Answer:

Husband:

The husband will have 16.35 mg of caffeine in his body at 7 pm.

Woman:

The pregnant woman will have 51.33 mg of caffeine in her body at 7 pm.

Step-by-step explanation:

The amount of caffeine in the body can be modeled by the following equation:

$C(t) = C(0)e^{rt}$

In which C(t) is the amount of caffeine t hours after 8 am, C(0) is how much coffee they took and r is the rate the the amount of caffeine decreases in their bodies.

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So $C(0) = 110$

Husband

Half life of 4 hours. So

$C(4) = 0.5C(0) = 0.5*110 = 55$

$C(t) = C(0)e^{rt}$

$55 = 110e^{4r}$

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Applying ln to both sides

$\ln{e^{4r}} = \ln{0.5}$

$4r = \ln{0.5}$

$r = \frac{\ln{0.5}}{4}$

$r = -0.1733$

So for the husband

$C(t) = 110e^{-0.1733t}$

At 7 pm

7 pm is 11 hours after 8 am, so this is C(11)

$C(t) = 110e^{-0.1733t}$

$C(11) = 110e^{-0.1733*11} = 16.35$

The husband will have 16.35 mg of caffeine in his body at 7 pm.

Pregnant woman

Half life of 10 hours. So

$C(10) = 0.5C(0) = 0.5*110 = 55$

$C(t) = C(0)e^{rt}$

$55 = 110e^{10}$

$e^{10r} = 0.5$

Applying ln to both sides

$\ln{e^{10r}} = \ln{0.5}$

$10r = \ln{0.5}$

$r = \frac{\ln{0.5}}{10}$

$r = -0.0693$

At 7 pm

7 pm is 11 hours after 8 am, so this is C(11)

$C(t) = 110e^{-0.0693t}$

$C(11) = 110e^{-0.0693*11} = 51.33$

The pregnant woman will have 51.33 mg of caffeine in her body at 7 pm.

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4 years ago

Help me pls ASAP I’ll mark u brainlist !!

Fed [463]

Answer:

x is 56°

y is 13°

Step-by-step explanation:

Well we can find the missing angle of the triangle that doesn't contain x° or y° which is 180-92-15=73°

The angle opposite the 92° angle is 180-92=88.

Using this information, we can find x°:

180-36-88=x°

x°=56°

Now using x and 73° we found earlier, we can find y.

180-73-56=The missing angle in the triangle that has y°

The missing angle in the triangle that has y°=51°

Now we can find y:

180-116-51=13

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3 years ago