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3 years ago

10

Ali has a spinner with 12 equal-size sections. Each section is colored blue, red, or yellow. He performs 5 trials in which he sp

ins the spinner 20
times and records the color that the spinner lands on each time. The table below shows the results.
Spinner Results
Section Color
Number of Times per Trial
Trial 1 Trial 2 Trial 3 Trial 4
1113
7
Trial 5
Blue
10
11
Red
7
1
8
8
NI
Yellow
12
Which table most likely shows the results for a spinner with sections that have the same distribution of colors as Ali found in his trials?

1 answer:

Sergio [31]3 years ago

4 0

Answer: Trial 4

Step-by-step explanation:

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The graph below represents which of the following functions?

GenaCL600 [577]

Answer:

Graph C

Step-by-step explanation:

Good luck.

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3 years ago

Convert R=(12)/4+8sin the theta to rectangular form

kompoz [17]

$r=\dfrac{12}{4+8\sin\theta}=\dfrac3{1+2\sin\theta}$

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You can stop there, or try to find something that looks somewhat nicer.

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3 years ago

Kenny reads 4/9 page in 3/5 min. what is Kenny's unit rate? <br><br> Step by step.

il63 [147K]

Answer:

The unit rate is $\frac{27}{20}\text{ page/minute}$

Step-by-step explanation:

Given : Kenny reads $\frac{4}{9}$ page in $\frac{3}{5}$ min.

To find : What is Kenny's unit rate?

Solution :

Kenny reads $\frac{4}{9}$ page in $\frac{3}{5}$ minute

This can be written as,

$\frac{4}{9}\text{ page}=\frac{3}{5}\text{ minute}$

Divide both side by $\frac{9}{4}$

$\frac{4}{9}\times \frac{9}{4}\text{ page}=\frac{3}{5}\times \frac{9}{4}\text{ minute}$

$1\text{ page}=\frac{27}{20}\text{ minute}$

The unit rate is $\frac{27}{20}\text{ page/minute}$

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3 years ago

Connecticut families were asked how much they spent weekly on groceries. Using the following data, construct and interpret a 95%

Amanda [17]

Answer:

The 95% confidence interval for the population mean amount spent on groceries by Connecticut families is ($73.20, $280.21).

Step-by-step explanation:

The data for the amount of money spent weekly on groceries is as follows:

S = {210, 23, 350, 112, 27, 175, 275, 50, 95, 450}

<em>n</em> = 10

Compute the sample mean and sample standard deviation:

$\bar x =\frac{1}{n}\cdot\sum X=\frac{ 1767 }{ 10 }= 176.7$

$s= \sqrt{ \frac{ \sum{\left(x_i - \overline{x}\right)^2 }}{n-1} } = \sqrt{ \frac{ 188448.1 }{ 10 - 1} } \approx 144.702$

It is assumed that the data come from a normal distribution.

Since the population standard deviation is not known, use a <em>t</em> confidence interval.

The critical value of <em>t</em> for 95% confidence level and degrees of freedom = n - 1 = 10 - 1 = 9 is:

$t_{\alpha/2, (n-1)}=t_{0.05/2, (10-1)}=t_{0.025, 9}=2.262$

*Use a <em>t</em>-table.

Compute the 95% confidence interval for the population mean amount spent on groceries by Connecticut families as follows:

$CI=\bar x\pm t_{\alpha/2, (n-1)}\cdot\ \frac{s}{\sqrt{n}}$

$=176.7\pm 2.262\cdot\ \frac{144.702}{\sqrt{10}}\\\\=176.7\pm 103.5064\\\\=(73.1936, 280.2064)\\\\\approx (73.20, 280.21)$

Thus, the 95% confidence interval for the population mean amount spent on groceries by Connecticut families is ($73.20, $280.21).

7 0

3 years ago

A rectangular package sent by a postal service can have a maximum combined length and girth (perimeter of a cross sectio) of 108

Morgarella [4.7K]

Answer:

The maximum volume of the package is obtained with a cross section of side 18 inches and a length of 36 inches.

Step-by-step explanation:

This is a optimization with restrictions problem.

The restriction is that the perimeter of the square cross section plus the length is equal to 108 inches (as we will maximize the volume, we wil use the maximum of length and cross section perimeter).

This restriction can be expressed as:

$4x+L=108$

being x: the side of the square of the cross section and L: length of the package.

The volume, that we want to maximize, is:

$V=x^2L$

If we express L in function of x using the restriction equation, we get:

$4x+L=108\\\\L=108-4x$

We replace L in the volume formula and we get

$V=x^2L=x^2*(108-4x)=-4x^3+108x^2$

To maximize the volume we derive and equal to 0

$\dfrac{dV}{dx}=-4*3x^2+108*2x=0\\\\\\-12x^2+216x=0\\\\-12x+216=0\\\\12x=216\\\\x=216/12=18$

We can replace x to calculate L:

$L=108-4x=108-4*18=108-72=36$

The maximum volume of the package is obtained with a cross section of side 18 inches and a length of 36 inches.

4 0

3 years ago

Read 2 more answers