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2 years ago

A 2015 Gallup poll of 1,627 adults found that only 22% felt fully engaged with their mortgage provider.

Mathematics

1 answer:

Zigmanuir [339]2 years ago

4 0

Answer: $(20.0\%,24.0\%)$

Step-by-step explanation:

Given, A 2015 Gallup poll of 1,627 adults found that only 22% felt fully engaged with their mortgage provider.

Here , 1,627 adults are determining the sample.

Thus, sample size : n = 1627

Also, the sample proportion of adults felt fully engaged with their mortgage provider are $\hat{p}=22\%=0.22$

for 95% confidence level , critical z-value =1.96

Then , the 95% confidence interval would be :-

$\hat{p}\pm z\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

Substituting values , we get

$0.22\pm 1.96(\sqrt{\dfrac{0.22(1-0.22)}{1627}})\\\\=0.22\pm 1.96\sqrt{\dfrac{0.22\times0.78}{1627}}\\\\\approx0.22\pm0.0201\\\\=(0.22-0.0201,\ 0.22+0.0201)\\\\=(0.1999,\ 0.2401)\approx(20.0\%,24.0\%)$

Hence, the required 95% confidence interval using only 1 decimal : $(20.0\%,24.0\%)$ .

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Imogen sees a design for a garden in a magazine. She changes the scale because she wants a smaller garden. The figure below show

faust18 [17]

Answer:

Length A of the magazine garden is 28 feet is true.

Length B of the Magazine garden is 17.5 feet is true.

Length C of the Magazine garden is 35 feet is true.

Step-by-step explanation:

Please refer the attached figure.

Given:-

Magazine Scale is 1 inch = 3.5 feet.

Imogen's scale is 2 inches = 6 feet,

Therefore Imogen's scale is 1 inch = 3 feet.

In Triangle ABC,

side a = 8 inches, side b= 5 inches, side c= 10 inches.

To find:- The correct 3 options(actual size of sides of triangle ABC).

Solution:-

In triangle ABC,

Let,

AB=side a =8 inches

BC=side b =5 inches

AC=side c= 10 inches

Now, as per the given scale's of Magazine and Imogen's we can find the actual sizes.

Length A as per Magazine scale (1 inch = 3.5 feet) is,

$\therefore Length\ A=8\times 3.5$ -------------(as per scale)

$\therefore Length A=28\ feet$

and Length A as per Imogen's scale(1 inch =3 feet) is,

AB = side a

$\therefore Length\ A=8\times 3$ -------------(as per scale)

$\therefore Length A=24\ feet$

Therefore Length A of the magazine garden is 28 feet is true.

Now, Length B as per Magazine scale (1 inch = 3.5 feet) is,

BC = side b

$\therefore Length\ B=5\times 3.5$

$\therefore Length B=17.5\ feet$

Length B as per Imogen's scale (1 inch = 3 feet) is,

BC = side b

$\therefore Length\ B=5\times 3$

$\therefore Length B=15\ feet$

Therefore Length B of the Magazine garden is 17.5 feet is true.

Now, Length C as per Magazine scale (1 inch = 3.5 feet) is,

AC = side c

$\therefore Length\ C=10\times 3.5$

$\therefore Length C=35\ feet$

Length B as per Imogen's scale (1 inch = 3 feet) is,

AC = side c

$\therefore Length\ C=10\times 3$

$\therefore Length B=30\ feet$

Therefore Length C of the Magazine garden is 35 feet is true.

8 0

2 years ago

Read 2 more answers

Which graph shows a negative rate of change for the interval 0 to 2 on the x-axis?

vova2212 [387]

Answer:

<h2>Third graph.</h2>

Step-by-step explanation:

A negative rate of change refers to an decrease at certain interval.

In this case, we have to look a decrease between 0 and 2 along the horizontal axis.

So, if we observe the third graph, we'll se that inside the given interval, the graph is decreasing, that indicates the negative rate of change that's being ask.

Therefore, the correct graph is the third one.

8 0

2 years ago

A parachute is descending at a rate of 28 feet per minute. Find the total change in the altitude of the parachute after 4 minute

BigorU [14]

Answer:

The total change in the altitude of the parachute after 4 minutes is 92 ft

Step-by-step explanation:

Here, we want to calculate the total change in the altitude of the parachute.

The rate of change per minute = 28 ft/m

Now in 4 minutes, the total altitude change will be;

28 ft/min * 4 min = 92 ft

In 4 minutes, there would have been a change of 92 ft in the altitude of the parachute

8 0

2 years ago

A factory makes propeller drive shafts for ships. A quality assurance engineer at the factory needs to estimate the true mean le

borishaifa [10]

Answer:

$1000-1.96\frac{2}{\sqrt{4}}=998.04$

$1000+1.96\frac{2}{\sqrt{4}}=1001.96$

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that $z_{\alpha/2}=1.96$