Keith is riding his bicycle. He rides at a speed of 13 kilometers per hour for 32.5 kilometers. For how many hours does he ride?​

Answer:

a) 0.1151 = 11.51% probability that an individual distance is greater than 210.00 cm.

b) 0.883 = 88.3% probability that the mean for 20 randomly selected distances is greater than 197.80 cm.

c) The distribution of the population is normal, which means that the sample size does not need to exceed 30.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The overhead reach distances of adult females are normally distributed with a mean of 200 cm and a standard deviation of 8.3 cm.

This means that [tex]\mu = 200, \sigma = 8.3[/tex]

a. Find the probability that an individual distance is greater than 210.00 cm.

This is 1 subtracted by the pvalue of Z when X = 210. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{210 - 200}{8.3}[/tex]

[tex]Z = 1.2[/tex]

[tex]Z = 1.2[/tex] has a pvalue of 0.8849

1 - 0.8849 = 0.1151

0.1151 = 11.51% probability that an individual distance is greater than 210.00 cm.

b. Find the probability that the mean for 20 randomly selected distances is greater than 197.80 cm

Now [tex]n = 20, s = \frac{8.3}{\sqrt{20}} = 1.8559[/tex]

This probability is 1 subtracted by the pvalue of Z when X = 197.8. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{197.8 - 200}{1.8559}[/tex]

[tex]Z = -1.19[/tex]

[tex]Z = -1.19[/tex] has a pvalue of 0.117

1 - 0.117 = 0.883

0.883 = 88.3% probability that the mean for 20 randomly selected distances is greater than 197.80 cm.

c. Why can the normal distribution be used in part​ (b), even though the sample size does not exceed​ 30?

The distribution of the population is normal, which means that the sample size does not need to exceed 30.

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There are 1440 minutes in 1 hour

Step-by-step explanation:

Since there are 60 minutes in 1 hour multiply 60 by 24, you get 1440.

Answer:

133

Step-by-step explanation:

180 - 47 = 133

Answer:

133°

Step-by-step explanation:

If we assume the the given to adjacent lines to be parallel then ,

Therefore :-

=> x = 180° - 47°

=> x = 133° .

Answer:

0.35 or 35%

Step-by-step explanation:

The probability that any seed will germinate is said to be 0.65 (or 65%) in the question. This means that the remaining percentage is the probability that the randomly selected seed will not germinate. This is because there is only two possible outcomes to that given scenario, which is it will germinate or not. Meaning that the remaining percentage/probability is that it will not germinate

1 - 0.65 = 0.35 or 35%

Answer:

[tex]9\sqrt{3}[/tex]

Step-by-step explanation:

The right triangle on the right is a special right triangle: a 30-60-90 triangle

30-60-90 corresponds with the angle measures on the triangle

the sides on a 30-60-90 relate to the angle opposite of it

30 ⇒x       60 ⇒ x[tex]\sqrt{3}[/tex]      90 ⇒ 2x

27 is opposite to the 60° angle

[tex]\frac{x\sqrt{3}} {\sqrt{3}} =x[/tex]   [tex]\frac{27}{\sqrt{3}}[/tex]  simplify [tex]\frac{27}{\sqrt{3} }[/tex] × [tex]\frac{\sqrt{3} }{\sqrt{3} }[/tex]     [tex]\frac{27\sqrt{3} }{3}[/tex] = [tex]9\sqrt{3}[/tex]

The required value of altitude y is 9 units which is determined by the geometric theorem.

A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.

As we know that the geometric theorem states that h = √(ab),

where h is the altitude of a right triangle, a and b are the segments formed when the altitude divides the hypotenuse of a right triangle.

We have to determine the value of altitude y

As per the given figure, a = 3, and b = 27

Substitute the values  in the formula, and we get

y = √(3 × 27)

y = √81

y = 9

Therefore, the measure of y = 9.

Learn more about the right triangle here:

brainly.com/question/6322314

#SPJ2

Answer:

To determine the explicit rule for the arithmetic sequence of 20.5, 16, 11.5, 7, 2.5, ..., the following logical reasoning must be performed:

20.5 - 16 = 4.5

16 - 11.5 = 4.5

11.5 - 7 = 4.5

7 - 2.5 = 4.5

Thus, the explicit rule of the arithmetic sequence is that the numbers are gradually subtracted by 4.5, with which the next number of said sequence would be -2.

to find the area of the rectangle it is is length x width  so we do 3x4=12. then area of triangle is base x height divide by 2, so 2x4=8. 8 divide by 2 is 4, then we need to add them all up, so 12 + 4 + 4 is 20. Your answer is 20 cm2.

(Ps please mark brainliest i need for next rank)

Answer:

50-6= 54

54÷4= 13.5

editing for clarity.

first you subtract the 6 from the 50 to find out what the "4 times a number" came to.

in this case, 50-6, which equals 54.

then, you divide the 54 by 4 to get 13.5.

so, the whole math problem would be

4 times 13.5 plus 6 equals 50.

Answer:

hwqvh bjvs bhs ebf

Step-by-step explanation:

Answer:

Step-by-step explanation:

The answer is 6.868 10

The number of times that diameter of cell G is larger than diameter of Cell H is; 46 × 10¯¹ times

We are given;

Now, to find how much more larger the diameter of cell G is than diameter of cell H, we will divide the diameter of cell G by the diameter of cell H to get;

(4.21 × 10^(-3))/(9.2 × 10^(-4)) = 4.6

Thus,diameter of cell G is 4.6 times larger than diameter of Cell H

Read more about ratios at; https://brainly.com/question/2784798

Answer:[tex]a^2-b^2=3[/tex]

Step-by-step explanation:

We need to find the value of the below expression i.e.

[tex]a^2-b^2[/tex] when a = 2 and b = 1.

So,

Put a = 2 and b = 1 in the above expression. So,

[tex]a^2-b^2=(2)^2-1^2\\\\=4-1\\\\=3[/tex]

Hence, the value of the expression is equal to 3.

Answer:

z=9

Step-by-step explanation:

we are given: 2/3z=6

we need to find what z is by itself

6 is 2/3rds of what the value of z is.

to find z, we need to multiply both sides by 3/2 (the reciprocal of 2/3z, to make the coefficient of 1)

3/2*2/3z=6*3/2

z=9

hope this helps :)

z = 9

Step-by-step explanation:

2/3 . z = 6

2z/3 = 6

Multiple all terms by the same value to eliminate fraction denominator,

3 x 2z/3 = 3 x 6

2z = 18 ( 3,3 got cancelled)

Divide both sides of the equation by the same term,

2z/2 = 18/2

On Simplify,

z = 9.

*(2,2 gets cancelled and 18/2 = 9)

Answer: 180ft

Step-by-step explanation:

Answer:

The Pythagorean theorem only works for right triangles. This is not a right triangle.

x = 23

All interior angles of a triangle = 180 degrees.

 A  +      B      +     C    + 180

(3x) + (2x+12) + (2x+7) = 180

7x + 19 = 180

7x = 161

x = 23

A = 3(23) = 69 degrees

B = 2(23) + 12 =58 degrees

C = 2(23) + 7 = 53 degrees

Answer:

x=23

Step-by-step explanation:

u see this is how the Pythagorean theorem works a^2 + b^2 = c^ i hope this helps have a great day bye please mark as brainliest :D

Answer:

4:9

Step-by-step explanation:

There's 4 of men and 9 to children and 5 of women

Answer:

x-6=6

Step-by-step explanation:

6+6=12

Answer:

c

Step-by-step explanation:

because 6+6=12 and the missing number would be 12 because 12-6=6

Answer:

Step-by-step explanation:

C

Answer:

the slope is 2/3 bcoz u do 2-0/3-0

Answer:

-64

Step-by-step explanation:

The computation of the 10th term of the progression is shown below:

The 3rd term is -9

A_n = a + (n - 1)d

-9 = a + (3 - 1)d

-9 = a + 2d

-9 - 2d = a

Now the 7th term is -29

A_n = a + (n - 1)d

-29 = a + (7 - 1)d

-29 = a + 6d

Put the a value to the above equation

-29 = -9 - 2d + 6d

-29 + 9 = 4d

-20 = 4d

d = -5

Now

-9 - 2d = a

-9 - 2(-5) = a

-9 - 10 = a

a = -19

Now finally the 10th term of the progression is

= a + (n - 1)d

= -19 + (10- 1)-5

= -19 -45

= -64

Answer:

the shorter leg is 10 meters, longer leg is 24 meters and the hypotenuse is 26 meters

Answer:

for every rise of 1 the run would be 25

Answer:

139

Step-by-step explanation:

x^2 + y^3 2+x = 3^2 + 5^3 + 2 + 3

= 9 + 125 + 5

= 139!

Answer:

I THINK the first and second choice, because it said the last two digits are between the numbers 0-9, them two are the only ones that end with them.

Step-by-step explanation:

You have a nice day to!!

Answer:

x=122°

Step-by-step explanation:

sum of all interior angles in a quadrilateral = 360°

then ,

119+105+78+m = 360

m = 58

....

m+ x = 180 ( linear pair)

58+x = 180

x = 122

Answer:

0.66? (0.67 if you rounded it)

Step-by-step explanation:

2*1/3

2/3 = 0.6666666666

Answer:

24+12=36you find the total length

Answer:

3 feet

Step-by-step explanation:

Answer:

6) K is less than negative seven.

7) m is less than or equal to two and three fifths.

Step-by-step explanation: