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Rufina
8 days ago
7

Alyssa is jogging near Central Park. She runs along 65th Street for about 0.19 miles, turns right and runs along Central Park We

st for about 0.28 miles. She then turns right again and runs along Broadway until she reaches her starting point. How long is her total run to the nearest hundredth of a mile?

Mathematics
2 answers:
zzz [9K]8 days ago
8 0
Approximately 0.81 miles.
AnnZ [9K]8 days ago
6 0
Roughly 0.81 miles.
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Which is equivalent to RootIndex 3 StartRoot 8 EndRoot Superscript x?
Zina [9171]

To determine an equivalent for RootIndex 3 StartRoot 8 EndRoot Superscript x, we can proceed with =2^x

Detailed Explanation:

We aim to express RootIndex 3 StartRoot 8 EndRoot Superscript x in a different form.

In mathematical terms:

(\sqrt[3]{8})^x

To solve:

Notably, 8 can be broken down into 2 multiplied by itself three times = 2^3

and \sqrt[3]{x}=x^{\frac{1}{3}}

Using these principles:

=((2^3)^{\frac{1}{3}})^x

=(2^{\frac{3}{3}})^x\\

=2^x

Thus, as we find a solution to RootIndex 3 StartRoot 8 EndRoot Superscript x, it results in =2^x

Terms: Radical Expression

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8 0
22 days ago
An experiment was conducted to record the jumping distances of paper frogs made from construction paper. Based on the sample, th
tester [8842]

Answer:

9.9676 - 2.326*0.5904 =8.594

9.9676 + 2.326*0.5904 =11.341

Step-by-step explanation:

Notation

\bar X is the sample mean

\mu indicates the population mean (the variable of interest)

s signifies the sample standard deviation

n denotes the sample size

Solution to the problem

The mean's confidence interval is derived from the following formula:

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}   (1)

In this instance, the 9% confidence interval corresponds to:

8.8104 \leq \mu \leq 11.1248

We can determine the mean using the following:

\bar X = \frac{8.8104 +11.1248}{2}= 9.9676

Additionally, the margin of error can be calculated as:

ME= \frac{11.1248- 8.8104}{2}= 1.1572

The margin of error for this situation is expressed as:

ME = t_{\alpha/2}\frac{s}{\sqrt{n}} = t_{\alpha/2} SE

Next, we find the standard error:

SE = \frac{ME}{t_{\alpha/2}}

The critical value for a 95% confidence interval using a normal standard distribution is roughly 1.96, and substituting gives us:

SE = \frac{1.1572}{1.96}= 0.5904

For the 98% confidence interval, the significance corresponds to \alpha=1-0.98= 0.02 and \alpha/2 = 0.01 with a critical value of 2.326, yielding a confidence interval of:

9.9676 - 2.326*0.5904 =8.594

9.9676 + 2.326*0.5904 =11.341

8 0
16 days ago
A mail clerk found that the total weight of 155 packages was 815 pounds. if each of the packages weighed either 3 pounds or 8 po
tester [8842]
To solve this problem, you'll need to create two equations:
x + y = 155 (total packages)
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Next, multiply the first equation by 3: 3x + 3y = 465.
Then, subtract the first equation from the second to find that 5y = 350, which means y = 70. Thus, there are 70 packages that weigh 8 pounds. 
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1 month ago
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The sum of two consecutive integers is one less than three times the smaller integer. Find the two integers
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6 days ago
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