1 gallon to ounces show work

This distance-time graph represents a journey made by Jo.

julsineya [31]

Answer:

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Step-by-step explanation:

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6 0

3 years ago

How do I solve this with Substitution?

TiliK225 [7]

They give you an "x =" statement so you plug in the right side of the equals sign into the first equation wherever x appears. So...

y = 10 - 2(y - 4)
y = 10 - 2y + 8
y = 18 - 2y
y + 2y = 18
3y = 18
y = 6

Now we plug in this result for the y-value into the "x =" statement.

x = 6 - 4
x = 2

Your answer is (2, 6)

8 0

3 years ago

Find a1 if Sn = 89,800, r = 3.4, and n = 10. Round to the nearest hundredth if necessary.

xxMikexx [17]

Answer:

$a_1=1.04$

Step-by-step explanation:

We have a geometric sequence with:

$Sn = 89,800$ , $r = 3.4$ , and $n = 10$

Where

Sn is the sum of the sequence

r is the common ratio

$a_1$ is the first term in the sequence

n is the number of terms in the sequence

The formula to calculate the sum of a finite geometric sequence is:

$S_n=\frac{a_1(1-r^n)}{1-r}$

Then:

$89,800=\frac{a_1(1-(3.4)^{10})}{1-3.4}$

Now we solve for $a_1$

$89,800(1-3.4)=a_1(1-(3.4)^{10})$

$a_1=\frac{89,800(1-3.4)}{1-(3.4)^{10}}\\\\a_1=1.04$

4 0

4 years ago

Suppose babies born in a large hospital have a mean weight of 3242 grams, and a standard deviation of 446 grams. If 107 babies a

777dan777 [17]

Answer:

64.76% probability that the mean weight of the sample babies would differ from the population mean by less than 40 grams

Step-by-step explanation:

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

Normal probability distribution:

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.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$