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2 years ago

You are given

Mathematics

1 answer:

Oksi-84 [34.3K]2 years ago

5 0

Answer:

a) Range: The range is easily calculated by subtracting the lowest value from the highest value in the data set.

R = Maximum -minimum = 9-3 = 6, So, R=6

b) Mean is the sum of all values in data set divided by number of elements in the data set

Mean = sum of all elements/total elements = 49/8 = 6.125

Mean = 6.125

c) Variance and Standard Deviation:

Variance is a measure of by how much the values in the data set are likely to differ from the mean of the values.

$s^2 ={\frac{1}{n-1} \sum_{i=1}^n (x_i-\bar{x})^2$$

$s^{2}$ = 3.6094

Standard Deviation is square root of variance which is 1.90

s=1.90

d) Ration of range and standard deviation is

Range/s = 3.16, SO the range is 3.16 times the standard deviation.

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Jason's mom drove at 100km/hr for a 160km trip.how much longer would the trip have taken if she had driven at 90km/hr

kondor19780726 [428]

We use the formule: t=S/v. So:
+ t1= 160/100 = 8/5 hrs = 5760''
+ t2= 160/90 = 16/9 hrs = 6400''

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3 years ago

Suppose the measure of an angle is 67 degrees what is the measure of its complementary angle

avanturin [10]

Complementary angles are angles whose sum is 90 degrees.

90 - 67 = 23

23 degrees is the measure of its complementary angle.

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3 years ago

Assume that body masses of Goldfinch birds follow a normal distribution with standard deviation equal to 0.04 oz. An ornithologi

il63 [147K]

Answer:

The formula to generate 70% confidence interval is: $[\overline{x} - 0.013, \overline{x} + 0.013]$ , in which $\overline{x}$ is the sample mean.

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1 - 0.7}{2} = 0.15$

Now, we have to find z in the Z-table as such z has a p-value of $1 - \alpha$ .

That is z with a pvalue of $1 - 0.15 = 0.85$ , so Z = 1.037.

Now, find the margin of error M as such

$M = z\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

Assume that body masses of Goldfinch birds follow a normal distribution with standard deviation equal to 0.04 oz.

This means that $\sigma = 0.04$ .

Sample of 10 birds:

This means that $n = 10$ .

The margin of error is of:

$M = z\frac{\sigma}{\sqrt{n}}$

$M = 1.037\frac{0.04}{\sqrt{10}}$

$M = 0.013$

The lower end of the interval is the sample mean of $\overline{x}$ subtracted by M.

The upper end of the interval is the sample mean of $\overline{x}$ added to M.

Then, the formula to generate 70% confidence interval is: $[\overline{x} - 0.013, \overline{x} + 0.013]$ , in which $\overline{x}$ is the sample mean.

8 0

3 years ago

A The length of a rectangle is 4 m more

Lady bird [3.3K]

Given :

The length of a rectangle is 4m more than the width.
The area of the rectangle is 45m²

⠀

To Find :

The length and width of the rectangle.

⠀

Solution :

We know that,

$\qquad { \pmb{ \bf{Length \times Width = Area_{(rectangle)}}}}\:$

So,

Let's assume the length of the rectangle as x and the width will be (x – 4).

⠀

Now, Substituting the given values in the formula :

$\qquad \sf \: { \dashrightarrow x \times (x - 4) = 45 }$

$\qquad \sf \: { \dashrightarrow {x}^{2} - 4x = 45 }$

$\qquad \sf \: { \dashrightarrow {x}^{2} - 4x - 45 = 0 }$

$\qquad \sf \: { \dashrightarrow {x}^{2} - 9x+ 5 x - 45 = 0 }$

$\qquad \sf \: { \dashrightarrow x(x - 9) + 5(x - 9) = 0 }$

$\qquad \sf \: { \dashrightarrow (x - 9) (x + 5) = 0 }$

$\qquad \sf \: { \dashrightarrow x = 9, \: \: x = - 5}$

⠀

Since, The length can't be negative, so the length will be 9 which is positive.

⠀

$\qquad { \pmb{ \bf{ Length _{(rectangle)} = 9\:m}}}\:$

$\qquad { \pmb{ \bf{ Width _{(rectangle)} = 9 - 4=5\: m}}}\:$

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2 years ago

Aiden is trying to save money and has $1800 to set aside in some type of savings account. He checked his bank one day, and found

kipiarov [429]

I = Prt

Interest on CD = 0.0425 x $1,800 = $76.5
Interest on savings = 0.0275 x $1,800 = $49.5

Difference of interest on CD and Interest on savings = $76.5 - $49.5 = $27

Therefre, he will earn $27 more if he invest in a CD rather than in a savings.

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3 years ago