Let X represent the full height of a certain species of tree. Assume that X has a normal probability distribution with = 36.1 ft and o- 6.8 ft. You intend to measure a random sample of n = 81 trees. What is the mean of the distribution of sample means? the What is the standard deviation of the distribution of sample means (i.e., the standard error in estimating the mean)? (Report answer accurate to 4 decimal places.) σ= Tip: Use the Desmos calculator...

The graph drawn is the graph of a square root function. A similar example is drawn below for the function:

We can thus deduce that the graph is a square root function

From the graph, the x-intercept is given by the point where the graph crosses the x-axis (at the point, y equals zero). The graph crosses the x-axis at x equals 8. It is given as shown below:

Answer:

20

Step-by-step explanation:

Answer:

88.2

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the relevant relation ...

 Tan = Opposite/Adjacent

 tan(10°) = x/500

 x = 500·tan(10°)

 x  ≈ 88.2 . . . . units

_____

cr sqdancefan on brainly , i saw that the same question was posted somewhere else and someone already answered it .

Answer:

200 bags are needed

Step-by-step explanation:

First let us determine the area of the corn field:

Shape of cornfield = square

Area of a square = Length × Length

where: Length = 100 yards

∴ Area = 100 × 100 = 10,000 square yards

1 bag of fertilizer is needed to cover 50 square yards:

50 square yards = 1 bag of fertilizer

\(\therefore 1 \ square\ yard\ = \frac{1}{50}\ bag\\10,000\ square\ yards\ =\ \frac{1}{50} \times 10,000 = \frac{10l000}{50} \\ = 200 bags\)

Hence, 200 bags are needed.

Answer:

200 bags are needed

Step-by-step explanation:

I did the test and got it correct good luck everyone !!

Using a normal distribution table or calculator, we can find that approximately 88.8% of the observations will fall within this range. This means that if a variable follows a normal distribution, approximately 88.8% of the observations will fall within 1.75 standard deviations of the mean.

When a variable follows a normal distribution, it is often assumed that the distribution is symmetrical around the mean, with 50% of the observations falling above the mean and 50% falling below. However, we can use standard deviations to better understand the distribution of the data.
If a variable follows a normal distribution, approximately 68% of the observations will fall within one standard deviation of the mean. This means that if the mean is 100 and the standard deviation is 10, approximately 68% of the observations will fall between 90 and 110.
When we move to 1.75 standard deviations away from the mean, we can use a normal distribution table or calculator to find the percentage of observations falling within that range. Using the same example as before, if the mean is 100 and the standard deviation is 10, we would multiply 1.75 by 10 to get 17.5. Then, we would add and subtract 17.5 from the mean to find the range of values that fall within 1.75 standard deviations away from the mean. This gives us a range of 82.5 to 117.5.
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The above conversation suggests that the area of the dilated image can be approximated as the sum of the areas of rectangles. If the original shape is dilated by a factor of k, the area of the dilated image would scale by a factor of k².

The area of the image based on the information will be 720 square inches.

The area of a circle with radius r is given by A = πr².

If the circle has an area of 20 square inches, then we can solve for the radius: 20 = πr² => r = sqrt(20/π). If the circle is dilated using a scale factor of 6, the radius would be 6 times larger, which means the area would be 6² times larger: A' = π(6r)² = 36πr²

= 36π(20/π)

= 720 square inches.

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The average speed for the trip was 90 mph Given that a trip of 900 miles would have taken 1 hour less if the average speed for the trip had been greater by 10 miles per hour. We are supposed to calculate the average speed for the trip.

Let the original speed be 'x' mph. Then, new speed will be (x + 10) mph

Time taken at the original speed to cover 900 miles:900 / x hours

Time taken at the new speed to cover 900 miles:900 / (x + 10) hours

According to the question,1 hour less when the average speed is increased by 10 mph:

900 / x - 900 / (x + 10) = 1

Multiplying by (x)(x+10) on both sides:

900(x+10) - 900x = x(x+10)

Solving for x:

x² + 10x - 9000 = 0x

= (−10 ± √(10² + 4×1×9000)) / 2x

= (−10 ± √(100 + 36000)) / 2x

= (−10 ± √36100) / 2

On ignoring the negative value, we get the value of 'x' to be:

x = (−10 + 190) / 2x

= 180 / 2

= 90 mph

Therefore, the average speed for the trip was 90 mph.

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Answer:

x:5,x:7

x^2-12x+35

x^2-12x=-35

x^2-12x+6^2=-35+36

(x+6)^2=1

insert a radical anywhere

x+6=1

x=1-6

x=-5. x=5

x=-1-6

x=-7. x=7

if the tangent line to y = f ( x ) at ( 6 , 2 ) passes through the point ( 0 , 1 ) , then f(6) = 2 and f'(6) = 1/6.

To find f(6), we can use the fact that the tangent line to y = f(x) at (6, 2) passes through the point (0, 1). The equation of a line can be written as y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line.

Since the line passes through (6, 2) and (0, 1), we can substitute these values into the equation to get:

2 - 1 = m(6 - 0)

1 = 6m

Solving for m, we find m = 1/6.

Since the slope of the tangent line is equal to the derivative of f(x) at x = 6, we have f'(6) = 1/6.

Now, to find f(6), we can integrate f'(x) with respect to x:

f(x) = ∫(f'(x))dx = ∫(1/6)dx = (1/6)x + C

To find the value of C, we can substitute the point (6, 2) into the equation:

2 = (1/6)(6) + C

2 = 1 + C

C = 1

Therefore, f(x) = (1/6)x + 1.

Substituting x = 6 into the equation, we get:

f(6) = (1/6)(6) + 1 = 2.

So, f(6) = 2 and f'(6) = 1/6.

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The number of push-ups did sara did during gym class if for every 7 push-ups Dulce can do, Sara can do 6 is 24 push ups.

Number of push ups Dulce can do : number of push ups Sara can do

Let

number of push ups Sara does = x

7 : 6 = 28 : x

7/6 = 28/x

cross product

7 × x = 28 × 6

7x = 168

divide both sides by 7

x = 168/7

x = 24

Therefore, Sara does 24 push ups during the gym class.

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The university administration should not trust the results from this study as it did not take a random sample.

The appropriate question to ask in order to assess the evidence provided by the sample data is, "How likely is it to observe a difference of 0.09 or more extreme if there is no difference in the mean GPA for male and female scholarship athletes?"

This is because the sample data shows a difference of 0.09, so we want to find out how likely it is to observe a difference of this size or greater, given that there is no actual difference between the GPA of male and female scholarship athletes.
Based on the investigation that the professor conducted which revealed that the study was given to all of the athletes on the basketball teams exclusively, the university administration should not trust the results from this study.

This is because the study was not taken from a random sample of scholarship athletes, meaning that the sample did not accurately reflect the population. If the sample does not accurately reflect the population, then the results may be biased and should not be trusted.

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\(f(x)=x+7\\g(x)=x-4\\f(x)*g(x)=(x+7)(x-4)\\f(x)*g(x)=x^2+3x-28\)

So it's x^2+3x-28

Answer:

300 minutes

Step-by-step explanation:

60 minutes times 5 hours = 300 minutes

Step-by-step explanation:

????

one hour = 60 minutes.

5 hours = 5×60 = 300 minutes.

really, you need help with that ?

what is not clear ?

The study aimed to provide insights into the potential effects of rhGH and rhIGF-I, both separately and in combination, on the immune function of elderly individuals, as indicated by the immune response to tetanus toxoid immunization.

The study aimed to evaluate the impact of a 7-week administration of recombinant human growth hormone (rhGH) and recombinant human insulin-like growth factor (rhIGF-I), both separately and in combination, on immune function in elderly female rhesus monkeys. The researchers used the response to immunization with tetanus toxoid as an assay to measure the in vivo function of the immune system.

The study design likely involved the following steps:

Selection of elderly female rhesus monkeys as the study subjects: The researchers chose female monkeys of advanced age to represent the elderly population.

Administration of recombinant human growth hormone (rhGH): The researchers administered rhGH to a group of monkeys for a period of 7 weeks. This hormone is known to stimulate growth and metabolism.

Administration of recombinant human insulin-like growth factor (rhIGF-I): Another group of monkeys received rhIGF-I, a hormone that mediates the effects of GH, for the same duration.

Combination treatment: A third group of monkeys received both rhGH and rhIGF-I simultaneously during the 7-week period.

Immunization with tetanus toxoid: After the 7-week treatment period, all monkeys were immunized with tetanus toxoid, which is a vaccine used to induce an immune response against tetanus.

Measurement of immune response: The researchers assessed the immune function by measuring the response of the monkeys' immune systems to the tetanus toxoid immunization. They likely examined parameters such as antibody production or T-cell response.

Data analysis: The researchers analyzed the immune response data to determine the effects of rhGH, rhIGF-I, and their combination on the immune function of the elderly female rhesus monkeys.

The study aimed to provide insights into the potential effects of rhGH and rhIGF-I, both separately and in combination, on the immune function of elderly individuals, as indicated by the immune response to tetanus toxoid immunization.

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Answer:To evaluate the exponential expression 6(4+2)² - 32, we need to follow the order of operations, which is parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).

First, we simplify the expression inside the parentheses:

4 + 2 = 6

Next, we square the result:

6² = 36

Now, we substitute the squared result back into the expression:

6(36) - 32

Next, we perform the multiplication:

6 * 36 = 216

Finally, we subtract 32:

216 - 32 = 184

Therefore, the value of the given exponential expression 6(4+2)² - 32 is 184.

weights =   pounds

Answer: Jackie has two puppies. One weighs 5 9/16 pounds and the other weighs 6 1/4 pounds. Find the difference in their weights.

Step-by-step explanation:

"DIFFERENCE" means to subtract their weights. We will subtract lesser amount from the greater amount to get our answer.

Also, we need to first make these mixed numbers into improper fractions by using the rule below:

If a number is given in this form:

We can do the operation below to make it improper fraction:

The bigger number is . So we subtract the other from this after changing to improper fraction.

and

Now, we subtract via doing LCM and get our answer: The difference in weight is 11/16 pounds

Answer:

16 more games

Step-by-step explanation:

4 is highest for football but basketball has 2 high scores for 8 games and 2 of those games where high points so add 8+8 and you get

                                16

Using Gaussian elimination, the given system of linear equations can be solved as follows:

x₁ = 3, x₂ = -2, x₃ = 1, x₄ = -1, x₅ = 0.

We can represent the given system of equations as an augmented matrix:

[ -2 -1 3 4 5 | 15 ]

[ 3 0 2 -9 -4 | 7 ]

[ 2 -2 4 -3 0 | 7 ]

[ 5 -5 -10 -5 -10 | -20 ]

[ 0 0 3 3 -9 | 9 ]

Applying Gaussian elimination, we perform row operations to transform the matrix into row-echelon form. After performing the necessary operations, we obtain the following matrix:

[ 1 0 0 0 0 | 3 ]

[ 0 1 0 0 0 | -2 ]

[ 0 0 1 0 0 | 1 ]

[ 0 0 0 1 0 | -1 ]

[ 0 0 0 0 1 | 0 ]

From the row-echelon form, we can determine the values of x₁, x₂, x₃, x₄, and x₅. Therefore, the solution to the system of equations is x₁ = 3, x₂ = -2, x₃ = 1, x₄ = -1, and x₅ = 0.


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Answer:

Cole bought 7 pants and 9 shirts.

Step-by-step explanation:

Let p represent the number of pants and s represent the number of shirts.

Then using the provided data two equations can be formed.

p + s = 12...(i)

22p + 16s = 234...(ii)

Solve (i) and (ii) simultaneously.

Multiply (i) by 16 and subtract the resultant equation from (ii) as follows:

16p + 16s = 192

-22p - 16s = -234

-6p = -42

p = 7

Substitute p = 7 in (i) and solve for s as follows:

p + s = 16

7 + s = 16

s = 9

Thus, Cole bought 7 pants and 9 shirts.

ANSWER:

STEP-BY-STEP EXPLANATION:

In Bayesian statistics, given a Uniform [0.4, 0.6] prior on the probability of obtaining a head (θ) when tossing a coin, we can determine the posterior density of θ after observing n heads.

a) To determine the posterior density of θ after observing n heads, we use Bayes' theorem. The posterior density is proportional to the product of the prior density and the likelihood function. In this case, the likelihood function is the binomial probability mass function. By multiplying the prior density and the likelihood function, we obtain the unnormalized posterior density. We can then normalize it to obtain the posterior density.

b) If the true value of θ is 0.99, the posterior distribution will eventually put some probability mass around θ = 0.99 as the sample size (n) increases. This is because the observed data will have a stronger influence on the posterior distribution as the sample size grows.

c) From part (b), we can conclude that the prior choice is important. If we have strong prior beliefs about the value of θ, choosing a prior that assigns significant probability mass around that value can ensure that the posterior distribution reflects our prior beliefs. However, if we have little prior knowledge or want to avoid strong prior influence, choosing a more diffuse or non-informative prior may be more appropriate. The choice of prior should be based on the available information and the desired properties of the posterior distribution.

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Answer:

first find the width

=11cm

find area

7×11=77

and=77

Answer:

C.) AFD measures 30°

Step-by-step explanation:

it is 150 degrees

Answer:

the answer is C

Step-by-step explanation:

A)  angle EFC is 80 degrees so a is a true statement

B) angle BFC is 60 degrees and angle DFE is 30 degrees 60+30=90 so that's a true statement

D) angle AFB is 40 degrees and angle CFD is 50 degrees  40+50=90 so that a true statement

that leaves C and angle AFD is more than 30 degrees its 150 degrees

Value of the given expression  8.2 x 19 using compensation method is equal to 155.8.

As given in the question,

Given expression is equal to :

8.2 x 19

Apply compensation method to make the calculation easily and get the value of the given expression we have,

8.2 x 19

Rewrite 19 as ( 20 -1 ) we get,

= 8.2 × ( 20 - 1 )

Apply distributive law multiplication over subtraction we get,

= ( 8.2 × 20 ) - ( 8.2 × 1 )

= 164.0 - 8.2

= 155.8

Therefore, value of the given expression  8.2 x 19 using compensation method is equal to 155.8.

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Answer:

-11, 3

Step-by-step explanation:

We know one of the roots are

\((x+ 4) {}^{2} = 49\)

\(x + 4 = - 7\)

\(x + 4 = 7\)

\(x = - 11\)

or

\(x = 3\)

Answer: (20, 5) or (5, 20)

Explanation: An ordered pair is made up of a set of numbers, one number for each dimension, contained in a set of parenthesis and separated by commas. In this problem, there are two dimension; red beads and blue beads. The ordered pair is comprised of the number of red beads (20) and the number of blue beads (5). Following the format previously described we get the answer (20, 5). You can also write (5, 20) since neither number depends on the other.

Answer:

570

Step-by-step explanation:

Area formula: 1/2bh

A: 38 x 30 = 1140

A: 1140 x 1/2 = 570

A: 570

Answer:

570

Step-by-step explanation:

The same formula as used in part (b) with r = 7%/12 = 0.005833 and the answers are: a) $171,900 b) $1,031.62 c) $1,145.80

a) The amount of the loan is going to be $171,900.

We can use the following formula to calculate the loan amount:

Loan Amount = Total Cost - Down Payment

$191,000 - (0.1 × $191,000) = $171,900b)

If the interest rate is 6%, the monthly payments will be $1,031.62.

We can use the following formula to calculate the monthly payments:

Monthly Payment = P × (r/n) × [1 + (r/n)]nt / [(1 + (r/n))nt - 1]

Where,

P = Loan amountr = Interest rate per year (as a decimal)

n = Number of payments per year

12t  = Number of years

P = $171,900r

= 6%/12

= 0.005t

= 30

Plug these values in the above formula, we get:

Monthly Payment = $1,031.62 (approx)c)

If the interest rate is 7%, the monthly payments will be $1,145.80.

We can use the same formula as used in part (b) with r = 7%/12 = 0.005833. We get:

Monthly Payment = $1,145.80 (approx)

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9514 1404 393

Answer:

  an = 243·(1/3)^(n-1) = 3^(6-n)

Step-by-step explanation:

This geometric sequence has a first term of a1=243 and a common ratio of r = 81/243 = 1/3. The general term for it is ...

  an = a1·r^(n-1)

  an = 243·(1/3)^(n-1)

Making use of the rules of exponents, this can be simplified to ...

  an = 3^5·(3^-1)^(n-1) = 3^(5-n+1)

  an = 3^(6-n)