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2 years ago

The bacteria in a Petri dish culture are self-duplicating at a rapid pace.

Mathematics

1 answer:

tester [92]2 years ago

8 0

Answer:

66.44 Minutes

Step-by-step explanation:

The number of Bacteria, B(t) at any time t(in minutes) is given by the function:

$B(t)=100\cdot 2^{t/10}$

We want to determine the time(in minutes) for the culture to achieve 10,000 bacteria.

Therefore:

$10000=100\cdot 2^{t/10}$

Divide both sides by 100

$100=2^{t/10}\\$Change to logarithm form\\Log_{2}100=t/10\\\dfrac{Log 100}{Log 2}= \dfrac{t}{10}\\t=10*\dfrac{Log 100}{Log 2}\\t=66.44 $ minutes (correct to the nearest hundredth)$

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In the figure, AB║CD and ∠EIA is congruent to ∠GJB Complete the following statements to prove that ∠IKL is congruent to ∠DLH.

REY [17]

Here it is given that AB || CD

< EIA = <GJB

Now

∠EIA ≅ ∠IKC and ∠GJB is ≅ ∠ JLD (Corresponding angles)

∠EIA ≅ ∠GJB then ∠IKC ≅ ∠ JLD (Substitution Property of Congruency)

∠IKL + ∠IKC 180° and ∠DLH + ∠JLD =180° (Linear Pair Theorem)

m∠IKL + m∠IKC = 180° ....(1)

But ∠IKC ≅ ∠JLD

m∠IKC = m∠JLD (SUBTRACTION PROPERTY OF CONGRUENCY)

So we have

m∠IKL + m∠JLD = 180°

∠IKL and ∠JLD are supplementary angles.

But ∠DLH and ∠JLD are supplementary angles.

∠IKL ≅ ∠DLH (CONGRUENT SUPPLEMENTS THEOREM)

5 0

2 years ago

Read 2 more answers

A Gallup Poll in July 2015 found that 26% of the 675 coffee drinkers in the sample said they were addicted to coffee. Gallup ann

emmasim [6.3K]

Answer:

The 95% confidence interval for the percent of all coffee drinkers who would say they are addicted to coffee is between 21% and 31%.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

A confidence interval has two bounds, the lower and the upper

Lower bound:

$\pi - M$

Upper bound:

$\pi + M$

In this problem, we have that:

$\pi = 0.26, M = 0.05$

Lower bound:

$\pi - M = 0.26 - 0.05 = 0.21$

Upper bound:

$\pi + M = 0.26 + 0.05 = 0.31$

The 95% confidence interval for the percent of all coffee drinkers who would say they are addicted to coffee is between 21% and 31%.

4 0

2 years ago

Nadiya determines that there are no fractions equivalent to 2/10 with a denominator greater than 10, but less than 20, that have

frosja888 [35]

Answer:

Yes, Nadiya is correct. By multiplying the numerator and denominator by 2, the first fraction equivalent to 2/10 is 4/20.

Step-by-step explanation:

To find a fraction equivalent to 2/10, we need to multiply (or divide) the numerator and denominator by the same nonzero whole number.

As we need an equivalent fraction with a denominator greater than 10, we will need to multiply and not divide.

The first nonzero whole number we have is 1. If we multiply the numerator and denominator by 1, we get 2/10. Obviously, 2/10 is equivalent to 2/10 but the denominator is not greater than 10, so it doesn't help us.

The next whole number is 2. When we multiply the numerator and denominator by 2, we get 4/20. The denominator is not less than 20.

If we keep going, we will get 6/30, 8/40 and so on.

Therefore, Nadiya is correct.

The correct answer is the first one.

8 0

2 years ago

Read 2 more answers

The formula s = StartRoot StartFraction S A Over 6 EndFraction EndRoot gives the length of the side, s, of a cube with a surface

never [62]

Answer:

$2\sqrt{2}\ ft\ longer$

Step-by-step explanation:

Suppose a cube with side length s, the area of one side is

$A_s=s^2$

Since the cube has 6 sides, the total area is

$A=6A_s=6s^2$

But if we have the area, we can solve the above formula for s to get

$A=6s^2$

$\displaystyle s=\sqrt{\frac{A}{6}}$

We have two different cubes with areas 1,200 square inches and 768 square inches. Let's compute their side lengths

$\displaystyle s_1=\sqrt{\frac{1,200}{6}}=\sqrt{200}$

$\displaystyle s_1=10\sqrt{2}\ ft$

$\displaystyle s_2=\sqrt{\frac{768}{6}}=\sqrt{128}$

$\displaystyle s_2=8\sqrt{2} ft$

The difference between them is

$10\sqrt{2}\ ft-8\sqrt{2}\ ft=2\sqrt{2}\ ft\approx 2.83\ ft$

The side of the cube with area 1,200 square inches is $2\sqrt{2}\ ft$ longer then the side of the cube with area 768 square inches

7 0

2 years ago

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Motorola used the normal distribution to determine the probability of defects and the number of defects expected in a production

Whitepunk [10]

Answer:

32% probability of a defect.

The expected number of defects for a 1000-unit production run is 320.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 10

Standard deviation = 0.15.

Probability of a defect

Weights less than 9.85 oz or greater than 10.15 oz will be classified as defects.

9.85 = 10 - 0.15

10.15 = 10 + 0.15

By the Empirical Rule, 68% of weights are between 9.85 and 10.15, that is, within the limits. 32% are not within the limits.

So there is a 32% probability of a defect.

Expected number of defects for a 1000-unit production run.

E(X) = 0.32*1000 = 320

The expected number of defects for a 1000-unit production run is 320.

5 0

2 years ago