A certain forest covers an area of 2600 km2. Suppose that each year this area decreases by 7.75%. What will the area be like after 15 years?

Answer:

a)Null hypothesis:- H₀: μ> 500

  Alternative hypothesis:-H₁ : μ< 500

b) (5211.05 , 5411.7)

95% lower confidence bound on the mean.

c) The test of hypothesis t = 5.826 >1.761 From 't' distribution table at 14 degrees of freedom at 95% level of significance.

Step-by-step explanation:

Step :-1

Given  a random sample of 15 devices is selected in the laboratory.

size of the small sample 'n' = 15

An average life of 5311.4 hours and a sample standard deviation of 220.7 hours.

Average of sample mean (x⁻) =  5311.4 hours

sample standard deviation (S) = 220.7 hours.

Step :- 2

a) Null hypothesis:- H₀: μ> 500

Alternative hypothesis:-H₁ : μ< 500

Level of significance :- α = 0.95 or 0.05

b) The test statistic

[tex]t = \frac{x^{-} - mean}{\frac{S}{\sqrt{n-1} } }[/tex]

[tex]t = \frac{5311.4 - 500}{\frac{220.7}{\sqrt{15-1} } }[/tex]

t = 5.826

The degrees of freedom γ= n-1 = 15-1 =14

tabulated value t =1.761 From 't' distribution table at 14 degrees of freedom at 95% level of significance.

calculated value t = 5.826 >1.761 From 't' distribution table at 14 degrees of freedom at 95% level of significance.

Null hypothesis is rejected at  95% confidence on the mean.

C) The 95% of confidence limits

[tex](x^{-} - t_{0.05} \frac{S}{\sqrt{n} } ,x^{-} + t_{0.05}\frac{S}{\sqrt{n} } )[/tex]

substitute values and simplification , we get

[tex](5311.4 - 1.761 \frac{220.7}{\sqrt{15} } ,5311.4 +1.761\frac{220.7}{\sqrt{15} } )[/tex]

(5211.05 , 5411.7)

95% lower confidence bound on the mean.

Answer:

Since Ashley swam more laps per minute, she's a faster swimmer than Austin.

Step-by-step explanation:

Austin:

She swam 1.4 laps per minute

Ashley:

9 laps in 6 minutes

So, per minute

9/6 = 1.5 laps per minute

Since Ashley swam more laps per minute, she's a faster swimmer than Austin.

Answer:

t

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

√(x-5)²=±√3

x-5=±√3

x=5±√3

To solve the quadratic equation (x - 5)² = 3, take the square root of both sides to give x - 5 = ± √3, then add 5 to each side to give x = 5 ± √3. The two possible solutions are x = 5 + √3 and x = 5 - √3.

The question is asking to solve the equation (x - 5)² = 3. This is a quadratic equation in the form (x-a)² = b. To solve it, you should start by taking the square root on both sides.

Step 1: √[(x - 5)²] = √[3]

This leads to: x - 5 = ± √3

Step 2: Followed by adding 5 to both sides

x = 5 ± √3

So there are two possible solutions: x = 5 + √3 and x = 5 - √3.

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Answer:

x = -12/6 = -2

x = -18/6 = -3

Step-by-step explanation:

The zeros in an equation is the same thing as the x's.

3x²+15x+18 = 0  (Where a = 3, b = 15, c = 18)

One thing you could do to find the answer is use the quadratic formula:

x = (-b ± √(b²-4ac))/2a =

(-15 ± √15² - (4*3*18))/2*3 =

(-15 ± √225 - 216)/6 =

(-15 ± √9)/6 =

(-15 ± 3) / 6.

To find the first x we need to do (-15 + 3) / 6 and to find the second x we need to do (-15-3) / 6.

x = -12/6 = -2

x = -18/6 = -3

To find the zeros of the quadratic equation 3x^2 + 15x + 18 = 0, use the quadratic formula to obtain the values of x.

To find the zeros of the quadratic equation 3x^2 + 15x + 18 = 0, we can use the quadratic formula.

The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x are given by:

x = (-b ± sqrt(b^2 - 4ac)) / (2a)

Plugging in the values from our equation, we get:

x = (-15 ± sqrt(15^2 - 4*3*18)) / (2*3)

After evaluating the expression, we find that the zeros of the equation are x = -3 and x = -2.

The probable question may be:

find the zero of 3x^2+15x+18=0 using any method.

Answer:

E

Step-by-step explanation:

It's E because you have to add 13 and 14 and as you can see there's 14 boys so it's E.

The probability that the person chosen is a boy is 14/27.

Number of girls = 13

Number of boys = 14

Total students = 27

Probability is a measure of the likelihood of occurrence of an event.

P(event) = Favorable outcomes / total outcomes

Favourable outcomes = 14 because there are 14 boys

Total outcomes =27

So, the probability that the person chosen is a boy will be given by:

P(boy)=14/27

So, the probability that the person chosen is a boy is 14/27.

Hence, the probability that the person chosen is a boy is 14/27.

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Answer:

$15.88

Step-by-step explanation:

[tex]\frac{(21.28 - 16.72)}{(69-31)}[/tex]

$4.56 / 38 min

$0.12 / 1 min

76 - 69 = 7 minutes

7 x .12 = .84

16.72 - .84 = 15.88

Answer:

minimum and value of 4

Step-by-step explanation:

[tex]\frac{dx}{dy} = 2x-8[/tex]

When [tex]\frac{dx}{dy}=0[/tex]  we will be able to get the critical points.

[tex]2x-8 =0[/tex][tex]x=4[/tex]

The graph is a quadratic graph with a 'U' shape, thus it has a minimum critical point.

Answer:

The dimensions are 32 ft by 16 ft

Step-by-step explanation:

Area  of the coffee and recreation room=512 square foot

LB=512

L=512/B

Perimeter of the Room = Perimeter of north wall+Perimeter of east wall+ Perimeter of west wall =L+2B (West and East are opposite)

Cost of the Perimeter=16L+4(2B)

[tex]C(B)=16(\frac{512}{B})+8B\\C(B)=\frac{8192+8B^2}{B}[/tex]

To minimize cost, first, we take the derivative of C(B)

Using quotient rule

[tex]C^{'}(B)=\frac{8B^2-8192}{B^2}[/tex]

Setting the derivative equal to zero

[tex]8B^2-8192=0\\8B^2=8192\\B^2=1024\\B=32 ft[/tex]

[tex]L=\frac{512}{B}=\frac{512}{32}=16ft[/tex]

The dimension of the cheapest recreation area will be 32 ft by 16 ft

The answer is 17 free throws because I said so and that’s the correct answer

Answer:

my answer was gunna be his but that person answered first so ill just sound like i copied that person

Step-by-step explanation:

Answer:

Q= 27/10

Step-by-step explanation:

Answer: [tex]q=\frac{27}{10}[/tex]

Step-by-step explanation:

[tex]\frac{10}{9}=\frac{3}{q}[/tex]

Multiply by q.

[tex]q*\frac{10}{9}=\frac{3}{q}*q[/tex]

[tex]\frac{10}{9}q=3[/tex]

Now multiply by the reciprocal of [tex]\frac{10}{9}[/tex] which is the inverted fraction. [tex]\frac{9}{10}[/tex]

[tex]\frac{9}{10}*\frac{10}{9}q=3*\frac{9}{10}[/tex]

[tex]q=\frac{27}{10}[/tex]

Answer:

Probability that their mean weight will be between 413 grams and 464 grams is 0.8521.

Step-by-step explanation:

We are given that a particular fruit's weights are normally distributed, with a mean of 426 grams and a standard deviation of 37 grams.

Also, you pick 9 fruit at random.

Let [tex]\bar X[/tex] = sample mean weight

The z-score probability distribution for sample mean is given by;

              Z = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = population mean weight = 426 grams

            [tex]\sigma[/tex] = population standard deviation = 37 grams

            n = sample of fruits = 9

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) 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.

So, probability that the mean weight of 9 fruits picked at random will be between 413 grams and 464 grams is given by = P(413 grams < [tex]\bar X[/tex] < 464 grams) = P([tex]\bar X[/tex] < 464 grams) - P([tex]\bar X[/tex] [tex]\leq[/tex] 413 grams)

 P([tex]\bar X[/tex] < 464 grams) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\frac{464-426}{\frac{37}{\sqrt{9} } }[/tex] ) = P(Z < 3.08) = 0.99896

 P([tex]\bar X[/tex] [tex]\leq[/tex] 413 grams) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] [tex]\leq[/tex] [tex]\frac{413-426}{\frac{37}{\sqrt{9} } }[/tex] ) = P(Z [tex]\leq[/tex] -1.05) = 1 - P(Z < 1.05)

                                                               = 1 - 0.85314 = 0.14686

{Now, in the z table the P(Z [tex]\leq[/tex] x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 3.08 and x = 1.05 in the z table which has an area of 0.99896 and 0.85314 respectively.}

Therefore, P(413 grams < [tex]\bar X[/tex] < 464 grams) = 0.99896 - 0.14686 = 0.8521

Hence, the probability that their mean weight will be between 413 grams and 464 grams is 0.8521.

Answer: 265

Step-by-step explanation:

Add up all the numbers and divide this value by the total number of terms,in this case 6 terms.

(153+ 176+ 249+ 150+ 620+ 242)/6 =265

Answer:  a) 0.9980, b) 0.0013, c) 0.0020, d) 0.00000026, e) 0.0318

Step-by-step explanation:

Problem 8-4 A computer time-sharing system receives teleport inquiries at an average rate of .1 per millisecond. Find the probabilities that the number of inquiries in a particular 50-millisecond stretch will be:

Since we have given that

[tex]\lambda=0.1\ per\ millisecond=5\ per\ 50\ millisecond=5[/tex]

Using the poisson process, we get that

(a) less than or equal to 12

probability=  [tex]P(X\leq 12)=\sum _{k=0}^{12}\dfrac{e^{-5}(-5)^k}{k!}=0.9980[/tex]

(b) equal to 13

probability= [tex]P(X=13)=\dfrac{e^{-5}(-5)^{13}}{13!}=0.0013[/tex]

(c) greater than 12

probability= [tex]P(X>12)=\sum _{k=13}^{50}\dfrac{e^{-5}.(-5)^k}{k!}=0.0020[/tex]

(d) equal to 20

probability= [tex]P(X=20)=\dfrac{e^{-5}(-5)^{20}}{20!}=0.00000026[/tex]

(e) between 10 and 15, inclusively

probability=[tex]P(10\leq X\leq 15)=\sum _{k=10}^{15}\dfrac{e^{-5}(-5)^k}{k!}=0.0318[/tex]

Hence, a) 0.9980, b) 0.0013, c) 0.0020, d) 0.00000026, e) 0.0318

Using the Poisson distribution, the probability of x inquires in a particular 50-millisecond stretch will be:

[tex]P(X = x) = \frac{e^{-5}5^{x}}{(x)!}[/tex]

In this problem, we are given the mean during an interval, which means that the Poisson distribution is used.

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

The parameters are:

x is the number of successes

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval.

We are given an average rate of 0.1 inquires per millisecond.

50-millisecond interval, thus [tex]\mu = 50(0.1) = 5[/tex]

Then, the probability of x inquires in a particular 50-millisecond stretch will be:

[tex]P(X = x) = \frac{e^{-5}5^{x}}{(x)!}[/tex]

A similar problem is given at https://brainly.com/question/24098004

Answer:

c. Opt-out: Allow consumers to quest to be removed from have been contacted.

Step-by-step explanation:

The Caffe Gutoso is considering a marketing strategy to promote its business. The owner want to send emails to its potential customers. Before sending the email the sender must insert email permission strategy as send an email from Caffe Gutoso and place and Opt-out option for those customers who are not willing to receive any email from the Caffe.

Answer:

Step-by-step explanation:

The given function is

[tex]f(t)=-10t^{2}+40t+8[/tex]

To find the maximum height reached by the ball, we need to find the vertex of the parabolla represented by the given quadratic equation.

Remember that a vertex has coordinates (h,k), where [tex]h=-\frac{b}{2a}[/tex] and [tex]k=f(h)[/tex].

According to the given function, we have

[tex]a=-10[/tex] and [tex]b=40[/tex]

[tex]h=-\frac{40}{2(-10)}=\frac{40}{20}=2[/tex]

[tex]k=f(2)=-10(2)^{2} +40(2)+8=-10(4)+80+8=-40+80+8=48[/tex]

So, the vertex has coordinates of (2,48), which means the maximum height reached by the baseball is 48 feet.

Answer:

26

Step-by-step explanation:

p = 19

p + 7 = 19 + 7

= 26

So, the value of p + 7 is 26

Hope it helps and is useful :)

Answer:

9

Step-by-step explanation:

[tex] \frac{(15 + 39)}{6} \\ \frac{54}{6 } \\ ans = 9 \\ [/tex]

Answer:B) Two inscribed angles that intercept the same arc are congruent.

Step-by-step explanation:

I just took the test

Answer:

In the equation of a straight line (when the equation is written as "y = mx + b"), the slope is the number "m" that is multiplied on the x, and "b" is the y-intercept (that is, the point where the line crosses the vertical y-axis). This useful form of the line equation is sensibly named the "slope-intercept form".

Step-by-step explanation:

This is just something to keep in mind

Answer:

-2

Step-by-step explanation:

Well, lt me hope the expression is complete amd correct.

Let's go on with the information you submitted.

y² + 7y + 4

When y= -6.

Let's substitute the value, y= -6 in the expression. We'll have to be careful with the signs.

y² + 7y + 4

-6² + 7(-6) + 4

36 - 42 + 4

40 - 42 =

-2

To solve for an in the equation 3ab = c, divide both sides by 3b, yielding a = c / (3b), with the condition that b is not zero.

To solve the equation 3ab = c for a, we need to isolate an on one side of the equation. Starting with the original equation:

3ab = c

We divide both sides of the equation by 3b to get:

a = c / (3b)

This is the solution for an in terms of b and c. It's important to note that b cannot be zero, as division by zero is undefined.

Complete Question:

The typical lifespan for various mammal species in captivity (L) in years has been related to average adult size (M) in kilograms according to the regression equation seen below.

[tex]ln L = 2.468 + 0.2 (lnM)[/tex]

A typical adult Meerkat weighs about 0.9 kilograms. What is the predicted lifespan of a Meerkat incaptivity, according to this equation? * 2 points 11.6 years 2.4 years 14.1 years 2.6 years 28.8 years

Answer:

Option A) L = 11.6 years

Step-by-step explanation:

From the given equation:

[tex]ln L = 2.468 + 0.2 (lnM)[/tex]..........(1)

Average adult size, M = 0.9 kg

Putting the value of M into the regression equation in (1)

[tex]ln L = 2.468 + 0.2 (ln0.9)\\ln L = 2.468 + (-0.02107)\\ln L = 2.447\\L = e^{2.447} \\L = 11.55 years[/tex]

The question is an illustration of regressions.

The lifespan of a typical adult Meerkat that weighs about 0.9 kilograms is (a) 11.6 years

The regression equation is given as:

[tex]\ln(L) = 2.468 + 0.2\ln(M)[/tex]

From the question, we have:

M = 0.9

Substitute 0.9 for M in [tex]\ln(L) = 2.468 + 0.2\ln(M)[/tex]

[tex]\ln(L) = 2.468 + 0.2\ln(0.9)[/tex]

Take natural logarithm of 0.9

[tex]\ln(L) = 2.468 + 0.2\times -0.1054[/tex]

[tex]\ln(L) = 2.468 -0.02108[/tex]

[tex]\ln(L) = 2.44692[/tex]

Take exponents of both sides

[tex]L = e^{2.44692}[/tex]

[tex]L = 11.553[/tex]

Approximate

[tex]L = 11.6[/tex]

Hence, the lifespan is (a) 11.6 years

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Answer: 3 foot

Step-by-step explanation:

Answer:

Step-by-step explanation:

The amount Gia got for her car was ...

  1800/3000 × 100% = 60%

of the amount it is worth. This percentage is less than the 70% Gia wanted as a minimum. She did not get what she wanted.

Answer:

-A 90% confidence interval would be narrower than the 95% confidence interval if we don't need to be as sure about our estimate.

-This confidence interval is not valid since the distribution of spending in the sample data is right skewed.

-The margin of error is $4.4.

-This confidence interval is valid since the sampling distribution of sample mean would be approximately normal with sample size of 436.

-We are 95% confident that the average spending of all American adults over this holiday season is between $80.31 and $89.11.

Step-by-step explanation:

A 90% confidence interval would be narrower than the 95% confidence interval if we don't need to be as sure about our estimate.

TRUE. The 90% confidence is less strict in its probability of having the mean within the interval, so it is narrower than the 95% CI. It relies more in the information given by the sample.

In order to decrease the margin of error of a 95% confidence interval to a third of what is is now, we would need to use a sample 3 times larger.

FALSE. The margin of error is z*σ/(n^0.5). So to reduce it by two thirds, the sample size n needs to be 3^2=9 times larger.

This confidence interval is not valid since the distribution of spending in the sample data is right skewed.

FALSE. There is no information about the skewness in the sample.

The margin of error is $4.4.

TRUE. The margin of error is (89.11-80.31)/2=$4.4.

We are 95% confident that the average spending of these 435 American adults over this holiday season is between $80.31 and $89.11.

FALSE. The CI is related to the populations mean. We are 95% confident that the average spending of the population is between $80.31 and $89.11.

This confidence interval is valid since the sampling distribution of sample mean would be approximately normal with sample size of 436.

TRUE. This happens accordingly to the Central Limit Theorem.

95% of random samples have a sample mean between $80.31 and $89.11.

FALSE. The confidence interval refers to the population mean.

We are 95% confident that the average spending of all American adults over this holiday season is between $80.31 and $89.11.

TRUE. This is the conclusion that is looked for when constructing a confidence interval.

Answer:

-7

Step-by-step explanation:

Given  : sequence  56, 49, 42, 35, ...

To find : Find the common difference.

Solution : We have given that 56, 49, 42, 35, ...

By the common difference of an arithmetic sequence is:

d = a_{2} -a_{1}a2−a1

Where, a_{1}a1 is the first term and  a_{1}a1 is the second term.

Then common difference =  49 -56

                                          = -7 .

Answer:

It's either B or A

Step-by-step explanation:

If I had to choose one I would pick B because I did the math; and logically, that answer makes the most sense.

Answer:

The solution to the equation is

x = -4

Step-by-step explanation:

We want to find the solution to the equation

(1/4)x - 1/8 = 7/8 + (1/2)x

First, add -(1/2)x + 1/8 to both sides of the equation.

(1/4)x - 1/8 - (1/2)x + 1/8 = 7/8 + (1/2)x - (1/2)x + 1/8

[1/4 - 1/2]x = 7/8 + 1/8

x(1 - 2)/4 = (7 + 1)/8

-(1/4)x = 8/8

-(1/4)x = 1

Multiply both sides by -4

x = -4

Answer:

x=-4

Step-by-step explanation:

Answer:

C) The initial number of leaves on the plant was 3.

Step-by-step explanation:

The plant has initially 3 leaves and is multiplied by 2 every week. Therefore, the answer is C.