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## Which statement is true? A sample statistic can never be equal to the population parameter. Point estimates are defined for both samples and populations. To calculate a sample proportion, we need to know the population size. To calculate a point estimate, we need to know the sample size

Option C is true. To calculate a sample proportion, we need to know the population size.

Step-by-step explanation:

To calculate a sample proportion, we need to know the population size. – This is the true statement.

A sample statistic can never be equal to the population parameter. This is false. A statistic is a feature of sample and a parameter is a feature of  population. Every sample of the selected size has an equal chance of being used.

Point estimates are defined for both samples and populations. This is false. A point estimate is used to estimate the population parameter.

To calculate a point estimate, we need to know the sample size. This is false. Population is needed.

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## The brain mass of a fetus can be estimated using the total mass of the fetus by the function b equals 0.22 m superscript 0.87b=0.22m0.87?, where m is the mass of the fetus? (in grams) and b is the brain mass? (in grams). suppose the brain mass of a 2323?-g fetus is changing at a rate of 0.240.24 g per day. use this to estimate the rate of change of the total mass of the? fetus, startfraction dm over dt endfraction dm dt.

We are given
b = 0.22 m^0.87
db/dt = 0.24 g/day at b = 23 g

where
b is the brain mass of the fetus
m is the total mass of the fetus
db/dt is the rate of change of the brain mass of the fetus

We are asked to get the rate of change of the total mass of the fetus

First, we take the first derivative of the given equation with respect to time
db/dt = 0.22 (0.87) m^(0.87-1) dm/dt
Next, simplify and substitute the given values. So,
0.24 g/day = 0.22(0.87)(23)^(0.87 -1 ) dm/dt
Solving for dm/dt
dm/dt = 1.88 g/day

The rate of change of mass of the fetus is 1.88 g/day.

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## LAW ENFORCEMENT: A police accident investigator can use the formula S=25L‾‾‾√S=25L to estimate the speed s of a car in miles per hour based on the length l in feet of the skid marks it left. How fast was a car traveling that left skid marks 109 feet long?

Option C – BD=76 cm

Step-by-step explanation:

Given : You are designing a diamond-shaped kite. you know that AD = 44.8 cm, DC = 72 cm, and AC = 84.8 cm.

To find : How long BD should it be?

Solution :

First we draw a rough diagram.

The given sides were AD = 44.8 cm, DC = 72 cm and AC = 84.8 cm.

According to properties of kite

Two disjoint pairs of consecutive sides are congruent.

DC=BC=72 cm

The diagonals are perpendicular.

So, AC ⊥ BD

Let O be the point where diagonal intersect let let the partition be x and y.

AC= AO+OC

AC=   …….[1]

Perpendicular bisect the diagonal BD into equal parts let it be z.

BD=BO+OD

BD=z+z

Applying Pythagorean theorem in ΔAOD

where H=AD=44.8 ,P= AO=x , B=OD=z

………[2]

Applying Pythagorean theorem in ΔCOD

where H=DC=72 ,P= OC=y , B=OD=z

…………[3]

Subtract [2] and [3]

……….[4]

Add equation [1] and [4], to get values of x and y

Substitute x in [1]

Substitute value of x in equation [2], to get z

We know, BD=z+z

BD= 38.06+38.06

BD= 76.12

Nearest to whole number BD=76 cm

Therefore, Option c – BD=76 cm is correct.

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## A country’s population in 1992 was 72 million. In 1998 it was 76 million. Estimate the population in 2012 using the exponential growth formula. Round your answer to the nearest million.P=Ae^kt

You need to determine the number of ways in which 30 competitors from 50 can qualify. First, you have to realize that the order is irrelevant, that is: it is the same competitor_1, competitor _2, competitor _3 than competitor_3, competitor_2, competitor_1, or any combination of those three competitors.

So, the number of ways is which 30 competitors from 50 can qualify is given by the formula of combinations, which is:

C (m,n) = m! / (n! * (m -n)! )

=> C (50,30) = 50! / (30! (50 – 30)! ) = (50!) / [30! (50 – 30)!] = 50! / [30! 20!] =

= 47,129,212,243,960 different ways the qualifiying round of 30 competitors can be selected from the 50 competitors.

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## Table to estimate how many pounds of dog food his dog eat in one year which of the following would be the best strategy

Table to estimate how many pounds of dog food his dog eat in one year which of the following would be the best strategy

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## What would be your estimate of the age of the universe if you measured a value for hubble’s constant of h0 = 30 km/s/mly ? you can assume that the expansion rate has remained unchanged during the history of the universe. express your answer using two significant figures. yr?

a) The time the police officer required to reach the motorist was 15 s.

b) The speed of the officer at the moment she overtakes the motorist is 30 m/s

c) The total distance traveled by the officer was 225 m.

Explanation:

The equations for the position and velocity of an object moving in a straight line are as follows:

x = x0 + v0 · t + 1/2 · a · t²

v = v0 + a · t

Where:

x = position at time t

x0 = initial position

v0 = initial velocity

t = time

a = acceleration

v = velocity at time t

a)When the officer reaches the motorist, the position of the motorist is the same as the position of the officer:

x motorist = x officer

Using the equation for the position:

x motirist = x0 + v · t (since a = 0).

x officer = x0 + v0 · t + 1/2 · a · t²

Let´s place our frame of reference at the point where the officer starts following the motorist so that x0 = 0 for both:

x motorist = x officer

x0 + v · t = x0 + v0 · t + 1/2 · a · t²      (the officer starts form rest, then, v0 = 0)

v · t = 1/2 · a · t²

Solving for t:

2 v/a = t

t = 2 · 15.0 m/s/ 2.00 m/s² = 15 s

The time the police officer required to reach the motorist was 15 s.

b) Now, we can calculate the speed of the officer using the time calculated in a) and the  equation for velocity:

v = v0 + a · t

v = 0 m/s + 2.00 m/s² · 15 s

v = 30 m/s

The speed of the officer at the moment she overtakes the motorist is 30 m/s

c) Using the equation for the position, we can find the traveled distance in 15 s:

x = x0 + v0 · t + 1/2 · a · t²

x = 1/2 · 2.00 m/s² · (15s)² = 225 m

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## In a genetics experiment on? peas, one sample of offspring contained 402402 green peas and 3838 yellow peas. based on those? results, estimate the probability of getting an offspring pea that is green. is the result reasonably close to the value of 3 divided by 43/4 that was? expected?

The point that lie on the line is:

B.  (1,1)

## Step-by-step explanation:

We are given that a line passes through the point (0,-1) and has a slope of 2.

We know that the equation of a line passing through (a,b) and having slope m is given by:

Here we have:  (a,b)=(0,-1) and m=2

This means that the equation of line is:

Now we will check which option is true.

A)

(2,1)

when x=2

we have:

Hence, option: A is incorrect.

B)

(1,1)

when x=1

we have:

Hence, option: B is correct.

C)

(0,1)

when x=0

we have:

Hence, option: C is incorrect.

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## Lucy wants to divide 18.6 by 1.2 in order to estimate the quotient which is the best expression to use ? A:10÷1 B:10÷2 C:20÷1 D:20÷2

Option C is the best expression.

Step-by-step explanation:

We are asked to find 18.6 by 1.2.

Option A

10÷1 = 10

Difference = 15.5 – 10 = 5.5

Option B

10÷2 = 5

Difference = 15.5 – 5 = 10.5

Option C

20÷1 = 20

Difference = 20 – 15.5 = 4.5

Option D

20÷2 = 10

Difference = 15.5 – 10 = 5.5

So, the difference is minimum for option C

Option C is the best expression.

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## A jet flies at a rate of 1.3 x 10^ 6 feet per hour. Written in scientific notation, which is the best estimate of how many feet the jet will travel in 2.8 x 10^ 3 hours?

A jet flies at a rate of 1.3 x 10^ 6 feet per hour. Written in scientific notation, which is the best estimate of how many feet the jet will travel in 2.8 x 10^ 3 hours?

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## 7. Researchers captured and tagged 45 deer before releasing them back into their habitat. Several months later the researchers returned and captured 30 deer, 8 of which had tags. Use this information to estimate the total deer population for this area.

You need to determine the number of ways in which 30 competitors from 50 can qualify. First, you have to realize that the order is irrelevant, that is: it is the same competitor_1, competitor _2, competitor _3 than competitor_3, competitor_2, competitor_1, or any combination of those three competitors.

So, the number of ways is which 30 competitors from 50 can qualify is given by the formula of combinations, which is:

C (m,n) = m! / (n! * (m -n)! )

=> C (50,30) = 50! / (30! (50 – 30)! ) = (50!) / [30! (50 – 30)!] = 50! / [30! 20!] =

= 47,129,212,243,960 different ways the qualifiying round of 30 competitors can be selected from the 50 competitors.

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## It is desired to estimate the mean gpa of each undergraduate class at a large university. assume that the variance of the gpas is 1.44. how large a sample is necessary to estimate the mean gpa within 0.25 at the 99% confidence level

Mahtematical and statistical reasoning makes it evident that there is a mistake in the writing of the question and the digits were duplicated. So the right question is:

“You need to have a password with 5 letters followed by 3 odd digits between 0 and 9, inclusive. If the characters and digits cannot be used more than once, how many choices do you have for your passwor?”

The solution is:

5 letters from 26 with no repetition => 26*25*24*23*22 different choices.

odd digits are 1, 3, 5, 7 and 9 => 5 different digits to choose

3 digits from 5 with no repetition => 5*4*3 = 60

Then, the total number of choices is: 26*25*24*23*22*60 = 473,616,000

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## A tour boat operator wants to know the average age of all the people in her tour group. She randomly selects 8 people in the group and asks them for their ages. Their responses are 19, 27, 25, 21, 44, 22, 45, and 34. What is the best estimate of the average age of all the people in the tour group? Round to the nearest whole number.

You need to determine the number of ways in which 30 competitors from 50 can qualify. First, you have to realize that the order is irrelevant, that is: it is the same competitor_1, competitor _2, competitor _3 than competitor_3, competitor_2, competitor_1, or any combination of those three competitors.

So, the number of ways is which 30 competitors from 50 can qualify is given by the formula of combinations, which is:

C (m,n) = m! / (n! * (m -n)! )

=> C (50,30) = 50! / (30! (50 – 30)! ) = (50!) / [30! (50 – 30)!] = 50! / [30! 20!] =

= 47,129,212,243,960 different ways the qualifiying round of 30 competitors can be selected from the 50 competitors.

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## In a casino, the chance of winning a certain game is 14.5%. If you play the game 20 times, what’s your best estimate for the number of times you would win? Round off your answer to the nearest whole number.

You need to determine the number of ways in which 30 competitors from 50 can qualify. First, you have to realize that the order is irrelevant, that is: it is the same competitor_1, competitor _2, competitor _3 than competitor_3, competitor_2, competitor_1, or any combination of those three competitors.

So, the number of ways is which 30 competitors from 50 can qualify is given by the formula of combinations, which is:

C (m,n) = m! / (n! * (m -n)! )

=> C (50,30) = 50! / (30! (50 – 30)! ) = (50!) / [30! (50 – 30)!] = 50! / [30! 20!] =

= 47,129,212,243,960 different ways the qualifiying round of 30 competitors can be selected from the 50 competitors.

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## Which is the most reasonable estimate for 30% of 72?

Which is the most reasonable estimate for 30% of 72?

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## Joe runs 8.75 times around a track in 1,125.803 seconds. If one lap around the track is 420.3 meters, which is the best estimate of the runner's average speed in meters per second (m/s)?

Joe runs 8.75 times around a track in 1,125.803 seconds. If one lap around the track is 420.3 meters, which is the best estimate of the runner’s average speed in meters per second (m/s)?

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## Estimate the length of the radius if the area of the circle is 54 ft2.

x > 2

Step-by-step explanation:

Here, x represents the length of the poster,

Since, width of the poster is 2 inches shorter than its length,

Width of the poster = ( x – 2 ) inches,

Thus, the area of the poster = length × width,

A = x (x-2)

We know that,

Area of a poster must be greater than zero,

⇒ A > 0,

⇒ x(x-2) > 0

⇒ x > 0 and x-2 > 0

If x – 2 > 0 ⇒ x > 2,

That is, the length of the poster must be greater than 2 inches.

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## The director of a customer service center wants to estimate the mean number of customer calls the center handles each day, so he randomly samples 26 different days and records the number of calls. the sample yields a mean of 258.4 calls with a standard deviation of 32.7 calls per day. the 95% confidence interval for the mean number of calls per day has an upper bound of ________. (round your answer to 1 decimal place.)

First we calculate for the total number of possibilities
(permutation) to select 4 disks from the container:

Total number of possibilities = 10 * 9 * 8 * 7

Total number of possibilities = 5040

Now let us find the 4 disks that will result in a range of 7.

Range = highest number – lowest number

The pair of highest and lowest number that will result in
range of 7 is: (1 & 8), (2 & 9), (3 & 10)

As a basis of calculation, let us use the pair 1 & 8.

There are four possible ways to select 1 and three for 8.

Arrangements of maximum and minimum pair = 4 * 3

Arrangements of maximum and minimum pair=12

Now we need to calculate for the remaining 2 disk. There
are 6 numbers between 1 & 8. The total possibilities for selecting 2 disk
from the remaining 6 is:

Possibilities of selecting 2 disk from remaining 6 = 6 *
5

Possibilities of selecting 2 disk from remaining 6 = 30

Therefore, the total possibility to get a range of 7 from
a pair of 1 & 8 is:

Total possibility for a pair = 12 * 30

Total possibility for a pair = 360

Since there are a total of three pairs (1 & 8), (2
& 9), (3 & 10):

Total possibilities of the 3 pairs = 360 * 3

Total possibilities of the 3 pairs = 1080

Therefore:

Probability = Total possibilities of the 3 pairs / Total
number of possibilities

Probability
= 1080 / 5040 = 3 / 14                      (FINAL

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## A scientist counts 25 bacteria present in a culture and finds that the number of bacteria triples each hour. The function y = 25 ∙ 3x models the number of bacteria after x hours. Estimate when there will be about 1170 bacteria in the culture

A scientist counts 25 bacteria present in a culture and finds that the number of bacteria triples each hour. The function y = 25 ∙ 3x models the number of bacteria after x hours. Estimate when there will be about 1170 bacteria in the culture

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## Three people are running for class president. From a poll that was taken, the probability that Candidate A will win is estimated to be 0.3. The probability that Candidate B will win is estimated to be 0.55. Given a reasonable estimate of the probability that Candidate C will win.

For a normally distributed data, with mean, μ, and standard deviation, σ, the probability that a randomly selected data, X, is less than a given value, x, is given by

and the probability that a randomly selected data, X, is greater than a given value, x, is given by

Given that the length of a social media interaction is normally distributed with a mean of 3 minutes and a standard deviation of 0.4 minutes, the probability that an interaction lasts longer than 4 minutes is given by

We use the normal distribution table or calculator to evalute that P(X < 2.5) = 0.99379

Therefore, the probability that an interaction lasts longer than 4 minutes = 1 – 0.99379 = 0.00621
[the last option]

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## A bakery can make 175 pastries each day. The bakery has been sold out of 3 days in a row. Determine of an estimate or exact answer is needed. then determine how many pasties were sold during the 3 days

The correct option is D. -17.5 degrees

Step-by-step explanation:

The daytime temperature in Apple Valley is falling by 2.5 degrees each day

Therefore, Change in the temperature each day = -2.5 degrees

Now, we need to find the net change in the daily temperature after one calendar week

Now, number of days in one calendar week = 7

So, Net change in the daily temperature after one calendar week = Daily change × Number of days in one calendar week

⇒  Net change in the daily temperature after one calendar week = -2.5 × 7

⇒  Net change in the daily temperature after one calendar week = -17.5 degrees

Therefore, The correct option is D. -17.5 degrees

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## Round each number to the nearest hundredth. What is the best estimate for the sum of 34.719 51.626? A. 86.35 B. 86.34 C. 86.33 D. 85.35

Add them first. 34.719 + 51.626 = 86.345.
You can find where the hundredth place is. It’s always two places from the decimal. So in 86.345, the hundredth is 4.

The answer is A. 86.35. It’s because the number that is beside 4 is 5. If the number is 4 and below, you don’t round. If the number is 5 and above, you round it.

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Posted in Mathematics

Show that, except for 2 and 5, every prime number can be expressed as 10k+1, 10k+3 10k+7, 10k+9, where k is an interger

10(6)+1=61
10(15)+3=153
10(4)+7=
47
1
0(9)+9=99

this is true because when you multiply a number by 10 it will be an even number(2,4,6,8,etc…)…then when you add an odd number to that the number will turn odd(153,47,99,etc..)… and when you multiple integers they will always multiply to an even number

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## The rate of the number of bags mishandled by the airlines fell to 3.74 bags per 1000 passengers in 1011. at this rate, estimate how many bags would be mishandled for 1750 passengers ?

The rate of the number of bags mishandled by the airlines fell to 3.74 bags per 1000 passengers in 1011. at this rate, estimate how many bags would be mishandled for 1750 passengers ?

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## Carl. put \$1.10 in his piggy bank every day in the month of July. His total savings was \$55 at the end of June. hat is the best estimate for Carl's savings at the end of July

Carl. put \$1.10 in his piggy bank every day in the month of July. His total savings was \$55 at the end of June. hat is the best estimate for Carl’s savings at the end of July

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## Sophia has \$20. she buys a hair band for \$3.99, gum for \$1.29, and a brush for \$6.75. not including tax estimate how much change she should receive????? PLEASE HELP

28.47º of latitude, 7.35º of longitude

Step-by-step explanation:

The latitude and longitude are simple imaginary lines (horizontal for latitude and vertical for longitude) that divide the Earth from an angle point of view. When used as a combination of both, you can get an exact location in any part of the world. For the 2 references, there a 0º divisions that make one side positive angles and negative on the other side (in the case of latitude, positive angles are above the equator line and for longitude positive angles are from the right of the Greenwich Meridian).

With the above mentioned we can observe that Hong Kong and Jakarta are away 22.27º and 6.2º respectively from the equator. So, the total degrees in latitude wil simply be the sum of the 2 absolute values (222.7º+6.2º) giving as a result of 28.47º.

On the other hand, we have in longitude that both cities are several degrees away from the same reference, and because they are from the right side of the Greenwich Meridian, the net change will be the substraction of 114.5-106.8º, giving as a result a total of 7.35º.

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