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2 years ago

Obtain the common ratio of the geometric series 0.27+...=54%

Mathematics

1 answer:

Nana76 [90]2 years ago

3 0

Answer:

Common ratio r = 0.5

Step-by-step explanation:

Given the geometric series 0.27 + ...

This is infinite geometric series with $b_1=0.27,$ unknown common rate r and sum S of 54% that is 0.54 as decimal.

Use formula

$S=\dfrac{b_1}{1-r}$

Hence,

$0.54=\dfrac{0.27}{1-r}\\ \\1-r=\dfrac{0.27}{0.54}=\dfrac{27}{54}=\dfrac{1}{2}=0.5\\ \\r=1-0.5=0.5$

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Graph the line y = kx +1 if it is known that the point M belongs to it: M(1,3)

tigry1 [53]

Answer:

$M(x,y) = (1,3)$ belongs to the line $y = 2\cdot x +1$ . Please see attachment below to know the graph of the line.

Step-by-step explanation:

From Analytical Geometry we know that a line is represented by this formula:

$y=k\cdot x + b$

Where:

$x$ - Independent variable, dimensionless.

$y$ - Dependent variable, dimensionless.

$k$ - Slope, dimensionless.

$b$ - y-Intercept, dimensionless.

If we know that $b = 1$ , $x = 1$ and $y = 3$ , then we clear slope and solve the resulting expression:

$k = \frac{y-b}{x}$

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

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Then, we conclude that point $M(x,y) = (1,3)$ belongs to the line $y = 2\cdot x +1$ , whose graph is presented below.

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2 years ago

a salesperson has averaged $120 in commissions for each of the past ten days. For how many days must her commissions average $16

Arada [10]

OKOK

A salesperson averaged $120 per 10 days sooo 120/10 is 12 so about 12 per day

So,
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2 years ago

The weight of a small Starbucks coffee is a normally distributed random variable with a mean of 330 grams and a standard deviati

just olya [345]

Answer:

Weights of at least 340.1 are in the highest 20%.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 330, \sigma = 12$

a. Highest 20 percent

At least X

100-20 = 80

So X is the 80th percentile, which is X when Z has a pvalue of 0.8. So X when Z = 0.842.

$Z = \frac{X - \mu}{\sigma}$

$0.842 = \frac{X - 330}{12}$

$X - 330 = 12*0.842$

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Spring stretches by 21.0 cm when a 135 n object is attached. what is the weight of a fish that would stretch the spring by 62.1

Marta_Voda [28]

Caution: you need to use the same units of measurement throughout. If the spring stretches by 21 cm when a 135 newton object is attached, then you must ask for the mass (in newtons) of a fish that would stretch the spring by 62.1 cm.

We will need to assume that the spring is not stretched at all if and when no object is attached to the spring.

Write the ratio

21.0 cm 135 newtons
------------- = --------------------
62.1 cm x

Solve this for x. This x value represents the mass of a fish that would stretch the spring by 62.1 cm. You can cancel "cm" in the equation above:

21.0 135 newtons
------ = --------------------
62.1 x

Then 21.0x = (62.1)(135 newtons). Divide both sides of this equation by 21.0 to solve it for x.

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2 years ago

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Obtain the common ratio of the geometric series 0.27+...=54%​

Obtain the common ratio of the geometric series 0.27+...=54%