The distance it takes a truck to stop can be

modeled by the function

Determine the value off, rounde

hundredth.

2

DONE

2.150 ?

d(u)=-

64.4f

d = stopping distance in feet

y = initial velocity in miles per hour

f= a constant related to friction

When the truck's initial velocity on dry pavement is

40 mph, its stopping distance is 138 ft.

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:

(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: 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

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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: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.

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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:

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:

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:

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:

5% chance so 2 times

Step-by-step explanation:

Got chu:)

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:

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.

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:

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:

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.

Answer:

95

Step-by-step explanation:

just did it on ed

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:

X=80

Y=9

Z=7

Step-by-step explanation:

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:

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:

f(-1) = 2

f(0) = 3

Step-by-step explanation:

f(a) = 3a - a²

Answer:

The 3rd and the 4th statement are not the true statements.

Step-by-step explanation:

In the 3rd statement, if you put a=-1 into the equation f(a), it would be

=3x(-1) - (-1)2

=-3 - 1

=-4.

In the 4th statement, if you put a=0 into the equation f(a), it would be

=3x(0) - (0)2

=0 - 0

=0.

For the other statements, they show the correct results.

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:

555

Step-by-step explanation:

(357+452+589+602+775)/5

Step-by-step explanation:

I HAVE DONE AT HERE YOU HAVE ASK WHE\E *O PUT 120°

Corrected Question

One cylinder has a volume that is 8cm less than 7/8 of the volume of a second cylinder. If the first cylinder’s volume is 216cm³, what is the correct equation and value of x, the volume of the second cylinder?

Answer:

The equation is: [tex]216=\frac{7}{8}x-8[/tex]

Volume of the second cylinder= [tex]256cm^3[/tex]

Step-by-step explanation:

Volume of the first cylinder=[tex]216cm^3[/tex]

Let the volume of the second cylinder=x

7/8 of the volume of a second cylinder=[tex]\frac{7}{8}x[/tex]

8 less than 7/8 of the volume of a second cylinder=[tex]\frac{7}{8}x-8[/tex]

Therefore, the equation is:

[tex]216=\frac{7}{8}x-8[/tex]

Next, we solve for x

[tex]216=\frac{7}{8}x-8\\216+8=\frac{7}{8}x\\224=\frac{7}{8}x\\$Cross multiply\\7x=224*8\\Divide both sides by 7\\x=256cm^3[/tex]

The volume of the second cylinder is [tex]256cm^3[/tex]

Answer:

The answer is D

Step-by-step explanation:

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:

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.

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)

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https://brainly.com/question/14585820

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:

-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