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Sergeeva-Olga [200]
3 years ago
13

K/6 = 15/18 Solve the proportion

Mathematics
2 answers:
Ilya [14]3 years ago
8 0

Answer:

k = 5

Step-by-step explanation:

<u>Step 1:  Cross multiply</u>

k/6 = 15/18

k(18) = 6(15)

<em>18k = 90</em>

<u>Step 2:  Divide both sides by 18</u>

18k / 18 = 90 / 18

<em>k = 5</em>

Answer:  k = 5

<u>Another way to do it is to multiply both sides by 6</u>

k/6 * 6 = 15/18 * 6

k = 90 / 18

<em>k = 5</em>

muminat3 years ago
7 0

Answer: 5

Step-by-step explanation: To solve for <em>k</em> in the given proportion, we use the means-extremes property. The product of the extremes, (k)(18), equals the product of the means, (6)(15).

So we have (k)(18) or 18k = (6)(15) or 90.

Now we have the equation 18k = 90.

Dividing both sides by 18, <em>k = 5</em>.

It's a good idea to check the answer in these types of problems so if we plug a 5 back in for <em>k</em> in the original proportion, we have \frac{(5)}{6}= \frac{15}{18} which is a true statement since 15/18 reduces to 5/6.

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Step-by-step explanation:

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Toa has 4 dimes a 12 nickels.Gail has 2 dimes and 3 nickels. What would be the ratio of dimes to nickels if they put these toget
Free_Kalibri [48]

Answer:

2 : 5

Step-by-step explanation:

Ratio expresses the relationship between two or more numbers. It shows the frequency of the number of times that one value is contained within other value(s).

We are to determine the ratio of dimes to nickels

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2 years ago
The head of maintenance at XYZ Rent-A-Car believes that the mean number of miles between services is 3639 3639 miles, with a var
Andrei [34K]

Answer:

96.6% probability that the mean of a sample would differ from the population mean by less than 126 miles

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

A reminder is that the standard deviation is the square root of the variance.

Normal probability distribution

When the distribution is normal, we use 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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question:

\mu = 3639, \sigma = \sqrt{145161} = 381, n = 41, s = \frac{381}{\sqrt{41}} = 59.5

Probability that the mean of the sample would differ from the population mean by less than 126 miles

This is the pvalue of Z when X = 3639 + 126 = 3765 subtracted by the pvalue of Z when X = 3639 - 126 = 3513. So

X = 3765

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

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{3765 - 3639}{59.5}

Z = 2.12

Z = 2.12 has a pvalue of 0.983

X = 3513

Z = \frac{X - \mu}{s}

Z = \frac{3513 - 3639}{59.5}

Z = -2.12

Z = -2.12 has a pvalue of 0.017

0.983 - 0.017 = 0.966

96.6% probability that the mean of a sample would differ from the population mean by less than 126 miles

3 0
3 years ago
Use the discriminant to find the number and type of solution for x^2+6x=-9​
likoan [24]

Answer:

D = 0; one real root

Step-by-step explanation:

Discriminant Formula:

\displaystyle \large{D =  {b}^{2}  - 4ac}

First, arrange the expression or equation in ax^2+bx+c = 0.

\displaystyle \large{ {x}^{2}  + 6x =  - 9}

Add both sides by 9.

\displaystyle \large{ {x}^{2}  + 6x + 9 =  - 9 + 9} \\  \displaystyle \large{ {x}^{2}  + 6x + 9 =  0}

Compare the coefficients so we can substitute in the formula.

\displaystyle \large{a {x}^{2}  + bx + c =  {x}^{2}  + 6x + 9 }

  • a = 1
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Substitute a = 1, b = 6 and c = 9 in the formula.

\displaystyle \large{D =  {6}^{2}  - 4(1)(9)} \\  \displaystyle \large{D =  36 - 36} \\  \displaystyle \large{D =  0}

Since D = 0, the type of solution is one real root.

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2 years ago
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