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Semmy [17]
2 years ago
8

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''

=> t2-t1= 6400 - 5760 = 640'' = 10'40''


3 0
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.
3 0
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}}}\:

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

8 0
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.
8 0
3 years ago
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