Question: A biotechnology firm is planning its investment strategy for future products and research labs. A poll found that 14% of a random sample of 1043 adults approved of attempts to clone a human. Use this information to complete arts a through e.





a) Find the margin of error for this poll if we want 95% confidence in our estimate of the percent of adults who approve of the cloning humans.




ME = ____ (Round to three decimal places as needed.)





b) Explain what that margin of error means. (Select One.)




i) The pollsters are 95% confident that the margin of error contains the true proportion of adults who approve of attempts to clone a human.
ii) The margin of error is the value that should be subtracted from the 95% confidence level to obtain the pollsters� true confidence level.
iii) The margin of error is width of the confidence interval that contains the true proportion of adults who approve of attempts to clone a human.
iv) The pollsters are 95% confident that the true proportion of adults who approve of attempts to clone a human is within the margin of error of the estimated 14%.





c) If we only need to be 99% confident, will the margin of error be larger or smaller?




i) A 99% confidence interval requires a smaller margin of error. A wider interval leads to decreased confidence.
ii) A 99% confidence interval requires a larger margin of error. In order to increase confidence, the interval must be narrower.
iii) A 99% confidence interval requires a smaller margin of error. A narrower interval leads to decreased confidence.
iv) A 99% confidence interval requires a larger margin of error. In order to increase confidence, the interval must be wider.





d) Find that margin of error.




ME = ___ (Round to three decimal places as needed.)



e) In general, if all other aspects of the situation remain the same, would smaller samples produce smaller or larger margins of error?

Step-by-step explanation:

4y + 6 = 16

you can find y (meters)

then replace y value in every side of this shape

then plus all line you will receive the perimeter

Given Information:

Sample size = n = 25

Mean age of client = 46 years

Standard deviation of age of client = 5 years

Confidence level = 95%

Required Information:

Width of the confidence interval = ?

Answer:

[tex]$ \text {width of CI } = \pm 2.064 $\\\\[/tex]

Step-by-step explanation:

The width for the true mean client age is given by

[tex]$ \text {width of CI } =\pm t_{\alpha/2}(\frac{s}{\sqrt{n} } ) $[/tex]

Where n is the sample size, s is the standard deviation of age of client, and [tex]t_{\alpha/2}[/tex] is the t-score corresponding to 95% confidence level.

The t-score corresponding to 95% confidence level is

Significance level = 1 - 0.95 = 0.05/2 = 0.025

Degree of freedom = n - 1 = 25 - 1 = 24

From the t-table at α = 0.025 and DF = 24

t-score = 2.064

[tex]$ \text {width of CI } = \pm (2.064)(\frac{5}{\sqrt{25} } ) $\\\\[/tex]

[tex]$ \text {width of CI } =\pm (2.064)(\frac{5}{5 } ) $\\\\[/tex]

[tex]$ \text {width of CI } = \pm (2.064)(1) $\\\\[/tex]

[tex]$ \text {width of CI } = \pm 2.064 $\\\\[/tex]

Therefore, width of the 95% confidence Interval for the true mean client age is approximately ±2.064.

Bonus:

The corresponding 95% confidence interval is given by

[tex]$ \text {Confidence Interval } = \bar{x} \pm t_{\alpha/2}(\frac{s}{\sqrt{n} } ) $[/tex]

Where x_bar is the mean client age

[tex]$ \text {Confidence Interval } = 46 \pm 2.064 $[/tex]

[tex]$ \text {Confidence Interval } = (43.936, 48.064) $[/tex]

[tex]$ \text {Confidence Interval } = (44, 48) $[/tex]

Which means that we are 95% sure that the true mean client age is within the range of (44, 48) years.

Answer:

x = 19

Step-by-step explanation:

In the attached file

Answer:

[tex]\ S=\sqrt{\dfrac{3V}{H}}}[/tex]

Step-by-step explanation:

The opposite operation of squaring is taking the square root.

[tex]\ S=\sqrt{\dfrac{3V}{H}}}[/tex]

We know that the denominator of a fractional power is the index of the corresponding root:

[tex]\displaystyle x^\frac{1}{n}=\sqrt[n]{x}[/tex]

For n=2, we don't usually write the index in the root symbol:

[tex]x^{\frac{1}{2}}=\sqrt{x}[/tex]

In the case of this problem, ...

[tex](S^2)^{\frac{1}{2}}=\left(\dfrac{3V}{H}\right)^{\frac{1}{2}}\\\\S=\sqrt{\dfrac{3V}{H}}[/tex]

Answer:

1. The least squares regression is y = -0.1015·x + 6.51

2. The independent variable is b) age

Please see attached table

Step-by-step explanation:

The least squares regression formula is given as follows;

[tex]\dfrac{\sum_{i = 1}^{n}(x_{i} - \bar{x})\times \left (y_{i} - \bar{y} \right ) }{\sum_{i = 1}^{n}(x_{i} - \bar{x})^{2}}[/tex]

We have;

[tex]\bar x[/tex] = 24

[tex]\bar y[/tex] = 4

[tex]\Sigma (x_i - \bar x) (y_i - \bar y)[/tex] = -79

[tex]\Sigma (x_i - \bar x)^2[/tex] = 778

[tex]\therefore \hat \beta =\dfrac{\sum_{i = 1}^{n}(x_{i} - \bar{x})\times \left (y_{i} - \bar{y} \right ) }{\sum_{i = 1}^{n}(x_{i} - \bar{x})^{2}} = \frac{-79}{778} = -0.1015[/tex]

The least squares regression is y = -0.1015·x + α

∴ α = y  -0.1015·x = 6 - (-0.1015 × 5) = 6.51

The least squares regression is thus;

y = -0.1015·x + 6.51

2. The independent variable is the age b)

3. Steps to create an ANOVA table with α = 0.05

The overall mean = (43  + 30  + 22  + 20  + 5  + 1  + 6  + 4  + 3  + 6 )/10 = 14

There are 2 different treatment = [tex]df_{treat} = 2 - 1 = 1[/tex]

There are 10 different treatment measurement = [tex]df_{tot} = 10 - 1 = 9[/tex]

[tex]df_{res} = 9 - 1 = 8[/tex]

[tex]df_{treat} + df_{res} = df_{tot}[/tex]

The estimated effects are;

[tex]\hat A_1 = 24 - 14 = 10[/tex]

[tex]\hat A_2 = 4 - 14 = -10[/tex]

[tex]SS_{treat} = 10^2 \times 5 + (-10)^2 \times 5 =1000[/tex]

[tex]\sum_{i}\SS_{row}_i = \sum_{i}\sum_{j} (y_{ij} - \bar y)= [(1 - 4)^2 + (6 - 4)^2 + (4 - 4)^2 + (3 - 4)^2 + (6 - 4)^2] = 18[/tex]

[tex]\sum_{i} S S_{row}_i = \sum_{i}\sum_{j} (y_{ij} - \bar y) ^2= [(43 - 24)^2 + (30 - 24)^2 + (22 - 24)^2 + (20 - 24)^2 + (5 - 24)^2] = 778[/tex]

[tex]S S_{res} = \sum_{i} S S_{row}_i = 778 + 18 = 796[/tex]

[tex]SS_{tot}[/tex] = (43  - 14)² + (30  - 14)² + (22  - 14)² + (20  - 14)² + (5  - 14)² + (1 - 14)1² + (6  - 4 )² + (3  - 14)² + (6  - 14)² = 1796

[tex]MS_{treat} = \dfrac{SS_{treat} }{df_{treat} } = \dfrac{1000}{1} = 1000[/tex]

[tex]MS_{res} = \dfrac{SS_{res} }{df_{res} } = \dfrac{796}{8} = 99.5[/tex]

F- value is given by the relation;

[tex]F = \dfrac{MS_{treat} }{MS_{res} } = \frac{1000}{99.5} = 10.05[/tex]

We then look for the critical values at degrees of freedom 1 and 8 at α = 0.05 on the F-distribution tables 5.3177

Hence; [tex]F = 10.05 > F_{1,8}^{Krit}(5\%) = 5.3177[/tex], we reject the null hypothesis.

Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other.

Answer:

Each hiker will get 2 1/3 cups

Step-by-step explanation:

8 bags multiplied by 3.5

28 cups overall

The 28 cups is shared between 12 hikers

28/12=2 1/3 cups

Answer:

2,210,000 different schedules

Step-by-step explanation:

Cory needs to have an equal number of piano sonatas from J. S. Bach, Haydn, and Wagner.

Since he is setting up a schedule of 9 piano sonatas to be played, he needs:

We then calculate how many different schedules are possible using combination.

Number of possible Schedules

[tex]=$ ^5C_3$ \times ^{52}C_3$ \times ^5C_3\\=10 \times 22100 \times 10\\$=2210000 ways[/tex]

There are 2,210,000 different possible schedules.

Answer:

X=80

Y=9

Z=7

Step-by-step explanation:

Answer:

You will earn $483.55 in interest.

Step-by-step explanation:

The compound interest formula is given by:

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.

$3,000 T - note with a 3% annual rate

This means that [tex]P = 3000, r = 0.03[/tex]

Paid quarterly

Quarterly is 4 times per year, so [tex]n = 4[/tex]

Maturity in 5 years.

This means that [tex]t = 5[/tex]

How much interest will you earn?

Interest is the final amount subtracted by the principal.

Final amount:

A(5).

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

[tex]A(5) = 3000(1 + \frac{0.03}{4})^{4*5}[/tex]

[tex]A(5) = 3483.55[/tex]

Interest:

$3,483.55 - $3,000 = $483.55

You will earn $483.55 in interest.

Based on the information given, the correct option is A. The relationship is reported incorrectly.

It should be noted that in a research, the normal value or r can range between -1 to 1. This shows the linear relationship between the variables.

In this case, since r is reported to be 4.8, the relationship is reported incorrectly.

Learn more about regression on:

https://brainly.com/question/25987747

You would interpret this finding of r to be reported as 4.8 as (a) the relationship is reported incorrectly.

The variable r in regression represents correlation.

And in regression, correlation can only take values between -1 and 1 (inclusive)

Given that:

r = 4.8

4.8 is outside the range -1 to 1.

This means that, the value is either calculated incorrectly or reported incorrectly.

Hence, the true statement is (a)

Read more about regression and correlation at:

https://brainly.com/question/14585820

Answer:

-1 -2i

Step-by-step explanation:

(-7+6) + (6i-8i) = -1 -2i

Answer:

(-1 - 2i)

Step-by-step explanation:

You simply add them.

-7 + 6 = -1

6i + (-8i) = 6i - 8i = -2i

Answer: 9%

Step-by-step explanation:

In probabilities; when two or more conditions must be met, the "and" operator is used. The probability of grey and tails is 1/12

From the attached spinner, we have:

[tex]Grey = 1[/tex]

[tex]n =6[/tex] --- partitions

So, the probability of landing on grey is:

[tex]P(Grey) = \frac{Grey}{n}[/tex]

This gives:

[tex]P(Grey) = \frac{1}{6}[/tex]

In a coin, we have:

[tex]Tail = 1[/tex]

[tex]n =2[/tex] --- faces

So, the probability of tail is:

[tex]P(Tail) = \frac{Tail}{n}[/tex]

[tex]P(Tail) = \frac{1}{2}[/tex]

The probability of grey and tail is:

[tex]Pr = P(Grey) \times P(Tail)[/tex]

[tex]Pr = \frac{1}{6} \times \frac{1}{2}[/tex]

[tex]Pr = \frac{1}{12}[/tex]

Hence, the probability of getting grey and tail is 1/12

Read more on probability at:

https://brainly.com/question/13957582

Answer:

54

Step-by-step explanation:

Since diameter AB divides MN into two equal parts hence

MO = NO

NOW,

5x+34 = -2(1-7x)

5x+34 = -2+14x

34+2 = 14x-5x

36 = 9x

Dividing both sides by 9

x = 4

Now,

NO = -2(1-7(4))

NO = -2+56

NO = -2+56

NO = 54

Answer:

0 and  -1

Step-by-step explanation:

Hello,

[tex]x^3+2x^2+x = x(x^2+2x+1)=x(x+1)^2[/tex]

so the roots are

0 and -1 (to get x+1=0 )

do not hesitate if you need further explanation

hope this helps

Answer:

It's actually X = 0, X = - 1, with multiplicity 2, Option D, on Edge2020

Step-by-step explanation:

I just did it on edge :)

Answer:

[tex](C)\left(-\dfrac{1 }{2},-\dfrac{\sqrt{3} }{2} \right)$ and \left(\dfrac{1 }{2},\dfrac{\sqrt{3} }{2} \right)[/tex]

Step-by-step explanation:

The reference angle is the angle that the given angle makes with the x-axis.

For an ordered pair to share the same reference angle, the x and y coordinates must be the same or a factor of each other.

From the given options:

[tex](A)\left(-\dfrac{\sqrt{3} }{2} ,-\dfrac{1 }{2}\right)$ and \left(-\dfrac{1 }{2},-\dfrac{\sqrt{3} }{2} \right)\\\\(B)\left(\dfrac{1 }{2},-\dfrac{\sqrt{3} }{2} \right)$ and \left(-\dfrac{\sqrt{3} }{2}, \dfrac{1 }{2}\right)\\\\(C)\left(-\dfrac{1 }{2},-\dfrac{\sqrt{3} }{2} \right)$ and \left(\dfrac{1 }{2},\dfrac{\sqrt{3} }{2} \right)\\\\(D)\left(\dfrac{\sqrt{3} }{2},\dfrac{1 }{2} \right)$ and \left(\dfrac{1 }{2},\dfrac{\sqrt{3} }{2} \right)[/tex]

We observe that only the pair in option C has the same x and y coordinate with the second set of points being a negative factor of the first term. Therefore, they have the same reference angle.

Answer:

C

Step-by-step explanation:

Answer:

India's population will reach 2 billion during the year of 2050.

Step-by-step explanation:

India's population in t years after 2008 is modeled by the following equation:

[tex]P(t) = P(0)(1+r)^{t}[/tex]

In which P(0) is the population in 2008 and r is the growth rate, as a decimal.

Population in 2008 of about 1.14 billion people. The population is growing by about 1.34% each year.

This means that [tex]P(0) = 1.14, r = 0.0134[/tex]. So

[tex]P(t) = P(0)(1+r)^{t}[/tex]

[tex]P(t) = 1.14(1+0.0134)^{t}[/tex]

[tex]P(t) = 1.14(1.0134)^{t}[/tex]

If the population continues following this trend, during what year will the population reach 2 billion?

t years after 2008.

t is found when P(t) = 2. So

[tex]P(t) = 1.14(1.0134)^{t}[/tex]

[tex]2 = 1.14(1.0134)^{t}[/tex]

[tex](1.0134)^{t} = \frac{2}{1.14}[/tex]

[tex]\log{(1.0134)^{t}} = \log{\frac{2}{1.14}}[/tex]

[tex]t\log{1.0134} = \log{\frac{2}{1.14}}[/tex]

[tex]t = \frac{\log{\frac{2}{1.14}}}{\log{1.0134}}[/tex]

[tex]t = 42.23[/tex]

2008 + 42 = 2050

India's population will reach 2 billion during the year of 2050.

Answer:12 gallons

Step-by-step explanation: It is enough to fill 40

The number of gallons in 40 quarts will be 10 gallons. Then the one that contains 12 gallons of oil.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

Unit modification is the process of converting the measurement of a given amount between various units, often by multiplicative constants that alter the value of the calculated quantity without altering its impacts.

A motor oil retailer needs to fill 40 one-quart bottles.

We know that in 1 gallon, there are 4 quarts. Then the number of gallons in 40 quarts will be given as,

⇒ 40 / 4

⇒ 10 gallons

The number of gallons in 40 quarts will be 10 gallons. Then the one that contains 12 gallons of oil.

More about the Algebra link is given below.

https://brainly.com/question/953809

#SPJ2

Answer:

2.75

Step-by-step explanation:

The amplitude is half of the difference between the highest and lowest y-coordinates.

amplitude = 0.5|6.75 - 1.25| = 0.5(5.5) = 2.75

Answer:

The Pareto Optimal height is  [tex]i = 100 \ inch[/tex]

Step-by-step explanation:

The Pareto Optimal height is a height  of the seawall at which an increase in wall height will exceed the amount the resident are willing to pay and a decrease will affect the protection of the city

The number of residents is [tex]n = 100[/tex]

The amount each are willing to pay is  [tex]z=[/tex]$10 per inch

 The cost of building a wall that is i inches high is given by [tex]c(i) = 6i^2.[/tex]

The total amount the residents are willing to pay is

          [tex]n = 100 * 10[/tex] =  $1000

The maximum cost  is mathematically represented as

                [tex]\frac{dc(i)}{di} = 10i[/tex]

which implies that

          1000 =  10i

Hence the Pareto Optimal height is

=>         [tex]i = \frac{1000}{10}[/tex]

             [tex]i = 100 \ inch[/tex]

Answer:

0.37

Step-by-step explanation:

As shown in table,

The probability of the fruit is orange is P(A) = 0.3

The probability of the fruit is organic is P(B)

The probability of the fruit is orange and organic is P(A⋂B) = 0.11

=> The probability that a randomly selected orange is organic is calculated by applying the conditional probability formula:

P(B|A) =P(A⋂B)/P(A) = 0.11/0.3 = 0.37

=> Option D is correct

Hope this helps!

Answer:

11.51% probability that it will take less than 450 days to train all the contestants.

Step-by-step explanation:

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

Normal probability distribution

When the distribution is normal, we use 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.

For the sum of n variables, the mean is [tex]\mu*n[/tex] and the standard deviation is [tex]s = \sigma\sqrt{n}[/tex]

In this question:

[tex]n = 100, \mu = 100*5 = 500, s = 4\sqrt{100} = 40[/tex]

Approximate the probability that it will take less than 450 days to train all the contestants.

This is the pvalue of Z when X = 450.

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

By the Central Limit Theorem

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

[tex]Z = \frac{450 - 500}{40}[/tex]

[tex]Z = -1.2[/tex]

[tex]Z = -1.2[/tex] has a pvalue of 0.1151

11.51% probability that it will take less than 450 days to train all the contestants.

Answer:

(a)[tex]E \cap F ={(2, 6),(4, 6),(6, 2),(6, 4),(6, 6)}[/tex]

(b) [tex]E^c \cap G =\{ \}[/tex]

Step-by-step explanation:

The sample space of two dice rolled is given below:

[tex]\{(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)\\(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)\\(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)\\(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)\\(5, 1), (5, 2), (5, 3), (5, 4), (5, 5),(5,6)\\(6, 1), (6, 2), (6, 3), (6, 4), (6,5), (6,6)\}[/tex]

For Event E (The sum is even), the outcomes are:

[tex](1, 1), (1, 3), (1, 5),(2, 2), (2, 4), (2, 6)\\(3, 1), (3, 3), (3, 5), (4, 2), (4, 4), (4, 6)\\(5, 1),(5, 3), (5, 5), (6, 2), (6, 4), (6,6)[/tex]

For Event F (Rolling at least one six), the outcomes are:

[tex](1, 6), (2, 6), (3, 6), (4, 6),(5,6),(6, 1), (6, 2), (6, 3), (6, 4), (6,5), (6,6)[/tex]

For Event G (The sum is eight), the outcomes are:

[tex](2, 6), (3, 5),(4, 4), (5, 3),(6, 2)[/tex]

(a)[tex]E \cap F[/tex]

Therefore:

[tex]E \cap F ={(2, 6),(4, 6),(6, 2),(6, 4),(6, 6)}[/tex]

(b)[tex]E^c \cap G[/tex]

E is the event that the sum is even

Therefore: [tex]E^c$ is the event that the sum is odd.[/tex]

Since G is the event that the sum is eight( which is even), the intersection of the complement of E and G will be empty.

Therefore:

[tex]E^c \cap G =\{ \}[/tex]

Answer:

35

Step-by-step explanation:

35 is not divisible by 3 as all the other numbers are

Answer: The number to show he is incorrect is 35 because 35 divided by 3 is 11.6666666667 which is not a whole number.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given that :

the side of the square = 90ft

The speed of the runner = 31 ft/sec

By the time the runner is halfway to the first base;  the distance covered by the runner in time(t)  is (31 t) ft and the distance half the base = 90/2 = 45 ft

Thus; 31 t = 45

t = 45/31

From the second base ; the distance is given as:

P² = (90)² + (90 - 31t )²  

P = [tex]\sqrt{(90)^2 + (90 - 31t )^2}[/tex]

By differentiation with time;

[tex]\dfrac{dP}{dt} =\dfrac{1}{ 2 \sqrt{90^2 +(90-31t)^2} } *(0+ 2 (90-31t)(0-31))[/tex]

[tex]\dfrac{dP}{dt} =\dfrac{1}{ 2 \sqrt{90^2 +(90-31t)^2} } * 2 (-31)(90-31t)[/tex]

At t = 45/31

[tex]\dfrac{dP}{dt} =\dfrac{1}{ 2 \sqrt{90^2 +45^2} } * 2 (-31)(45)[/tex]

[tex]\dfrac{dP}{dt} =\dfrac{-35*45}{100.623}[/tex]

= - 13.86 ft/sec

Hence, we can conclude that  as soon as the runner  is halfway to the first base, the distance to the second base is therefore decreasing by 13.86 ft/sec

b) The distance from third base can be expressed by the relation:

q² = (31t)² + (90)²

[tex]q = \sqrt{(31t)^2+(90)^2}[/tex]

By differentiation with respect to time:

[tex]\dfrac{dq}{dt} = \dfrac{1}{2\sqrt{90^2 + (31)t^2} } *(0+31^2 + 2t)[/tex]

At t = 45/31

[tex]\dfrac{dq}{dt} = \dfrac{1}{2\sqrt{90^2 + 45^2} } *(0+31^2 + \frac{45}{31})[/tex]

[tex]= \dfrac{31*45}{100.623}[/tex]

[tex]= 13.86 \ ft/sec[/tex]

Thus, the rate at which the runner's distance is from the third base is increasing at the same moment of 13.86 ft/sec. So therefore; he is moving away from the third base at the same speed to the first base)

a) The distance from second base is decreasing when the batter is halfway to first base at a rate of 13.9 feet per second.

b) The distance from third base is increasing when the batter is halfway to first base at a rate of 13.9 feet per second.

a) As the batter runs towards the first base, both the distance from second base and the length of the line segment PQ decrease in time. The distance from the second base is determined by Pythagorean theorem:

[tex]QS^{2} = QP^{2}+PS^{2}[/tex] (1)

By differential calculus we derive an expression for the rate of change of the distance from second base ([tex]\dot QS[/tex]), in feet per second:

[tex]2\cdot QS \cdot \dot{QS} = 2\cdot QP\cdot \dot{QP} + 2\cdot PS\cdot \dot {PS}[/tex]

[tex]\dot{QS} = \frac{QP\cdot \dot QP + PS\cdot \dot{PS}}{QS}[/tex]

[tex]\dot {QS} = \frac{QP\cdot \dot {QP}+PS\cdot \dot {PS}}{\sqrt{QP^{2}+PS^{2}}}[/tex] (2)

If we know that [tex]QP = 0.5L[/tex], [tex]PS = L[/tex], [tex]L = 90\,ft[/tex], [tex]\dot {QP} = -31\,\frac{ft}{s}[/tex] and [tex]\dot {PS} = 0\,\frac{ft}{s}[/tex], then the rate of change of the distance from second base is:

[tex]\dot {QS} = \frac{(45\,ft)\cdot \left(-31\,\frac{ft}{s} \right)}{\sqrt{(45\,ft)^{2}+(90\,ft)^{2}}}[/tex]

[tex]\dot {QS} \approx -13.864\,\frac{ft}{s}[/tex]

The distance from second base is decreasing when the batter is halfway to first base at a rate of 13.9 feet per second.

b) As the batter runs towards the first base, both the distance from third base increases and the distance from home increase in time. The distance from the third base is determined by Pythagorean theorem:

[tex]QT^{2} = HT^{2}+QH^{2}[/tex] (3)

By differential calculus we derive an expression for the rate of change of the distance from third base ([tex]\dot QT[/tex]), in feet per second:

[tex]2\cdot QT\cdot \dot{QT} = 2\cdot HT\cdot \dot {HT} + 2\cdot QH\cdot \dot {QH}[/tex]

[tex]\dot {QT} = \frac{HT\cdot \dot {HT}+QH\cdot \dot {QH}}{QT}[/tex]

[tex]\dot {QT} = \frac{HT\cdot \dot {HT}+QH\cdot \dot {QH}}{\sqrt{HT^{2}+QH^{2}}}[/tex]

If we know that [tex]HT = 90\,ft[/tex], [tex]QH = 45\,ft[/tex], [tex]L = 90\,ft[/tex], [tex]\dot{HT} = 0\,\frac{ft}{s}[/tex] and [tex]\dot {QH} = 31\,\frac{ft}{s}[/tex], then the rate of change of the distance from third base is:

[tex]\dot{QT} = \frac{(45\,ft)\cdot \left(31\,\frac{ft}{s} \right)}{\sqrt{(90\,ft)^{2}+(45\,ft)^{2}}}[/tex]

[tex]\dot{QT} \approx 13.864\,\frac{ft}{s}[/tex]

The distance from third base is increasing when the batter is halfway to first base at a rate of 13.9 feet per second.

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Answer:

95

Step-by-step explanation:

just did it on ed

Answer:

Mauna Kea has from the base that is to say the deepest 10 km of height that is to say 10,000 m which is equivalent to being higher than Mount Everest.jj

Step-by-step explanation:

 The main reason why we could say that Mauna Kea is the highest mountain, even surpassing Mount Everest, is because of its altitude if we compare them we see the difference; for example Mauna Kea from its base that is to say from the deepest the ocean measures 10,000 m of altitude, on the other hand the Mount Everest has an altitude of 8848 meters (29,029 ft) above sea level, that is to say from its base it measures 8848 m altitude.

Answer:

Yes, there is enough evidence to support the claim that dog owners in the country spend more time walking their dogs than do dog owners in the city (P-value=0.0000263).

Step-by-step explanation:

This is a hypothesis test for the difference between populations means.

The claim is that dog owners in the country (sample 2) spend more time walking their dogs than do dog owners in the city (sample 1).

Then, the null and alternative hypothesis are:

[tex]H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2< 0[/tex]

The significance level is 0.05.

The sample 1, of size n1=20 has a mean of 10 and a standard deviation of 3.

The sample 2, of size n2=21 has a mean of 15 and a standard deviation of 4.

The difference between sample means is Md=-5.

[tex]M_d=M_1-M_2=10-15=-5[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{3^2}{20}+\dfrac{4^2}{21}}\\\\\\s_{M_d}=\sqrt{0.45+0.762}=\sqrt{1.212}=1.101[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{-5-0}{1.101}=\dfrac{-5}{1.101}=-4.54[/tex]

The degrees of freedom for this test are:

[tex]df=n_1+n_2-1=20+21-2=39[/tex]

This test is a left-tailed test, with 39 degrees of freedom and t=-4.54, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=P(t<-4.54)=0.0000263[/tex]

As the P-value (0.0000263) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that dog owners in the country spend more time walking their dogs than do dog owners in the city.

Using the t-distribution, it is found that since the test statistic is t = 4.54 > 2.32, it can be concluded that dog owners in the country spend more time walking their dogs than do dog owners in the city.

At the null hypothesis, we test if dog owners in the country and in the city spend the same amount of time walking their dogs, that is:

[tex]H_0: \mu_{Co} - \mu_{Ci} = 0[/tex]

At the alternative hypothesis, we test if dog owners in the country spend more time, that is:

[tex]H_1: \mu_{Co} - \mu_{Ci} > 0[/tex]

The standard errors are:

[tex]s_{Co} = \frac{4}{\sqrt{21}} = 0.8729[/tex]

[tex]s_{Ci} = \frac{3}{\sqrt{20}} = 0.6708[/tex]

The distribution of the differences has:

[tex]\overline{x} = \mu_{Co} - \mu_{Ci} = 15 - 10 = 5[/tex]

[tex]s = \sqrt{s_{Co}^2 + s_{Ci}^2} = \sqrt{0.8729^2 + 0.6708^2} = 1.1009[/tex]

We have the standard deviation for the samples, hence, the t-distribution is used. The test statistic is given by:

[tex]t = \frac{\overline{x} - \mu}{s}[/tex]

In which [tex]\mu[/tex] is the value tested at the null hypothesis, for this problem [tex]\mu = 0[/tex], hence:

[tex]t = \frac{\overline{x} - \mu}{s}[/tex]

[tex]t = \frac{5 - 0}{1.1009}[/tex]

[tex]t = 4.54[/tex]

Since the test statistic is t = 4.54 > 2.32, it can be concluded that dog owners in the country spend more time walking their dogs than do dog owners in the city.

A similar problem is given at https://brainly.com/question/17192140

Answer:

5% chance so 2 times

Step-by-step explanation:

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